connecting the formation of stars and planets. i
TRANSCRIPT
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Revista Mexicana de Astronomıa y Astrofısica 57 199ndash216 (2021)
copy 2021 Instituto de Astronomıa Universidad Nacional Autonoma de Mexico
httpsdoiorg1022201ia01851101p2021570115
CONNECTING THE FORMATION OF STARS AND PLANETS I ndashSPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE
L M Flor-Torres1 R Coziol1 K-P Schroder1 D Jack1 J H M M Schmitt2 and S Blanco-Cuaresma3
Received February 6 2020 accepted January 7 2021
ABSTRACT
In search for a connection between the formation of stars and the formationof planets a new semi-automatic spectral analysis method using iSpec was devel-oped for the TIGRE telescope installed in Guanajuato Mexico TIGRE is a 12mrobotic telescope equipped with an Echelle spectrograph (HEROS) with a resolu-tion R 20000 iSpec is a synthetic spectral fitting program for stars that allows todetermine in an homogeneous way their fundamental parameters effective temper-ature Teff surface gravity log g metallicities [MH] and [FeH] and rotationalvelocity V sin i In this first article we test our method by analysing the spectra of46 stars hosts of exoplanets obtained with the TIGRE
RESUMEN
En la busqueda de una conexion entre la formacion estelar y planetaria sedesarrollo un nuevo metodo semiautomatico de analisis espectral estelar usandoiSpec para el telescopio TIGRE instalado en Guanajuato Mexico El TIGRE esun telescopio robotico de 12m el cual esta equipado con el espectrografo EchelleHEROS que tiene una resolucion R 20 000 iSpec es un programa de ajusteespectral sintetico para estrellas que permite determinar de manera homogenea susparametros fundamentales temperatura efectiva Teff gravedad superficial log gmetalicidades [MH] y [FeH] y velocidad de rotacion V sin i En este artıculoprobamos nuestro metodo analizando una muestra de 46 estrellas que alberganexoplanetas observadas por el TIGRE
Key Words planetary systems mdash stars formation mdash stars fundamental parame-ters mdash stars rotation
1 INTRODUCTION
Since the discovery of the first planet orbiting an-other star in the 1990s the number of confirmed ex-oplanets had steadily increased reaching in Novem-ber of last year 41334 The urgent tasks with whichwe are faced now are determining the compositionsof these exoplanets and understanding how theyformed However although that should have beenstraightforward (Seager 2010) the detection of newtypes of planets had complicated the matter chang-ing in a crucial way our understanding of the forma-tion of planetary systems around stars like the Sun
1Departamento de Astronomıa Universidad de Guanajua-to Guanajuato Gto Mexico
2Hamburger Sternwarte Universitat Hamburg HamburgGermany
3Harvard-Smithsonian Center for Astrophysics Cam-bridge MA USA
4httpexoplaneteu
The first new type of planets to be discov-ered was the ldquohot Jupitersrdquo (HJs Mayor amp Queloz1995) which are gas giants like Jupiter and Sat-urn but with extremely small periods P lt 10 daysconsistent with semi-major axes smaller thanap = 005 AU The existence of HJs is problematicbecause according to the model of formation of thesolar system they can only form in the protoplane-tary disk (PPD) where it is cold enough for volatilecompounds such as water ammonia methane car-bon dioxide and monoxide to condense into solid icegrains (Plummer et al 2005) In the Solar Systemthis happens beyond the ice-line which is locatedclose to 3 AU (Martin amp Livio 2012) This impliesthat HJs must have formed farther out in the cold re-gions of the PPD then migrated close to their stars(Lin et al 1996) Subsequent discoveries have thenshown that far from being exceptional artifacts ofan observational bias HJs turned out to be very
199
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200 FLOR-TORRES ET AL
common around Sun-like stars suggesting that largescale migration is a standard feature of the planetformation process (Butler et al 2000 Udry amp San-tos 2007)
Two other new types of planets discovered are theldquoSuper-Earthsrdquo (Leconte et al 2009 Valencia et al2006 Martin amp Livio 2015 Chabrier et al 2009) andthe ldquomini-Neptunesrdquo (Gandolfi et al 2017) Thesetoo were found to be common and very close to theirstars which consequently also makes them ldquohotrdquoTheir discoveries are important for two reasons Thefirst reason is that it makes the alternative ldquoin siturdquomodel for the formation of HJs (eg Boss 1997)a special model since it cannot explain the largemass range and diversity of the ldquohotrdquo exoplanetsobserved (Super-Earths and mini-Neptunes in situmodels are discussed in Raymond et al 2008 Chi-ang amp Laughlin 2013) The second reason is thatit was recently established by Lee et al (2017) thattheir numbers around their host stars fall rapidly forperiods P lt 10 days (asymp 009 AU) which assumingKeplerian orbits clearly implies they all formed far-ther out (beyond 01 AU) and have migrated inwardbut with a good many disappearing into their starsThis once again puts large scale migration at thefront scene of the planet formation process
This brings us to the present fundamental ques-tion in planet formation theory (McBride amp Gilmour2004) what explains the fact that large scale migra-tion did not happen in the Solar System Or inother words assuming all planets form in a PPDaround a low mass star (Nomura et al 2016 van derMarel et al 2018 Perez et al 2019) what differ-ence would make migration more important in onecase and less important in another (see discussion inWalsh et al 2011)
Integrating the migration process into a consis-tent model of planet formation is an extremely activeand fast evolving field of research (a recent review ofthis important subject can be found in Raymond ampMorbidelli 2020) In the case of the HJs two mi-gration mechanisms are accepted now as most prob-able (Dawson amp Johnson 2018)(1) disk migrationwhere the planet forms beyond the ice-line and thenmigrates inward by loosing its orbit angular momen-tum to the PPD (see thorough reviews in Baruteauet al 2014 Armitage 2020) and (2) high-eccentricitymigration according to which the planet first gainsa high eccentricity through interactions with otherplanets which makes it to pass very close to itsstar where it looses its orbit angular momentum bytidal interactions (this is a more complicated pro-cess involving different mechanisms eg Rasio amp
Ford 1996 Weidenschilling amp Marzari 1996 Marzariamp Weidenschilling 2002 Chatterjee et al 2008 Na-gasawa et al 2008 Beauge amp Nesvorny 2012) How-ever what is not clear in these two models is whatimportance must be put on the characteristics of thePPD its mass size depth and composition
According to PPD formation theory there aretwo possible mass scenarios (Armitage 2020) theminimum mass model between 001 to 002 Mwhich suggests that the PPD initial mass is onlysufficient to explain the masses of the planets thatformed within it and the maximum mass modelwhich suggests the mass could have been muchhigher close to 05 M Consequently more mas-sive PPD (compared to the Solar System) might haveeither favored the formation of more massive plan-ets (consistent with PPD observations see Figure 2and discussion in Raymond amp Morbidelli 2020) or alarger number of planets The problem is that thismakes both migration mechanisms equally probable(also the masses observed seem too low also relatedto Figure 2 in Raymond amp Morbidelli 2020) An-other caveat is that the Solar System is a multipleplanet system where migration on large scale did nothappen
In terms of angular momentum the differencesbetween the minimum and maximum mass modelfor the PPD might also be important By definitionthe angular momentum of a planet is given by therelation (eg Berget amp Durrance 2010)
Jp = Mp
radicGMlowastap(1minus e2
p) (1)
where Mp and Mlowast are the masses of the planet andits host star ap is the semi-major axis of the planetand ep its eccentricity This suggests that within themaximum mass model more massive planets wouldalso be expected to have higher orbital angular mo-mentum (through their PPD) and consequently tohave lost a larger amount of their angular momen-tum during large scale migration (ap rarr 0) This im-plies that the efficiency of the migration mechanismmust increase with the mass of the planet (or itsPPD) In principle such requirement might be oneway to distinguish which migration process is morerealistic However the problem is bound to be morecomplicated First stars rotate much more slowlythan expected assuming conservation of angular mo-mentum during their formation (McKee amp Ostriker2007) Second defining the angular momentum of aplanetary system as Jsys = Jlowast+ΣJp where ΣJp is thesum of the angular momentum of all the planets andJlowast the angular momentum of the host star (cf Berget
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 201
amp Durrance 2010) the angular momentum of mas-sive planets (even after migration assuming ap 6= 0)will always dominate over the angular momentum ofits host stars That is JlowastΣJp lt 1 and this is de-spite the enormous loss of angular momentum of thestar during its formation This implies that a sort ofcoupling must exist between the angular momentumof the stars and their planets through their PPDsUnderstanding the nature of this coupling thereforeis an important step in understanding how the PPDand the planets forming in it are connected to theformation of their stars This on the other handrequires completing our information about the starsand the planets rotating around them
In the case of the planets the two most success-ful detection techniques the radial velocity (RV) andtransit (Tr) methods yield estimates of the mass ofa planet Mp and its radius Rp as well as the semi-major axis ap and the eccentricity of its orbit epThe first two parameters constrain their composi-tion and formation process in the PPD while thelast two give information about their migration Bycombining the four parameters we can also retrievethe angular momentum of the orbits of the planets(cf equation 1) In the case of the stars the most im-portant characteristics that can be derived from theirspectra are the effective temperature Teff the sur-face gravity log g the metallicities [MH] or [FeH]and the rotational velocity V sin i The first two canbe used in combination with their magnitudes anddistances (using GAIA parallaxes) to determine theirradii and masses which taken in combination withthe rotational velocity yield the angular momentum(or spin) of the star Jlowast
Jlowast = γlowastMlowastRlowastVrotlowast (2)
where Mlowast Rlowast and γlowast are the star mass radius andmoment of inertia (which depends on the mass of thestar cf Irwin 2015) and V rotlowast = V sin i sin i is theequatorial rotation velocity (where i is the inclina-tion angle of the rotation axis relative to our line ofsight)
To understand how the formation of planets isconnected with the formation of their host stars wemust consequently make an effort to determine inparallel with the discovery of the former the physicalcharacteristics of the latter Present data banks forexoplanets (eg Kepler and now TESS with 51 con-firmed discoveries and future surveys like PLATO)5
require follow-up observations and analysis for the
5httpstessmitedu about PLATO see httpsplatomissioncomabout
host stars which are usually done with large diame-ter telescopes equipped with high resolution spectro-graphs However for the brightest stars (TESS tar-gets for example being 30-100 times brighter thanKEPLER stars) the use of smaller diameter tele-scopes equipped with lower resolution spectrographsmight be more efficient in acquiring the informationMoreover although high resolution spectra is jus-tified when one uses the standard spectral analysismethod which is based on modeling the equivalentwidth (EW) of spectral lines this might not be nec-essary when one uses the synthetic spectral analysis(eg Valenti amp Debra 2005) which consists in fit-ting observed spectra to grids of synthetic spectrawith well determined physical characteristics thatcan be produced at different spectral resolutionsAnother problem in using large aperture telescopesfor host stars follow-up is that since these telescopesare in high demand (for faint objects) data are col-lected on short duration runs by different groupsusing different techniques and codes (although thesame analysis method) which introduces discrepan-cies between the results (Hinkel et al 2014 2016Blanco-Cuaresma 2014 Jofre et al 2017) This sug-gests that a follow-up using a dedicated telescopeand applying only one method of analysis could pro-duce more homegeneous data (one effort to homog-enize data is the Stars With ExoplanETs CATalogor SWEET-Cat for short Sousa et al 2008) Forthese reasons we developed a new method based onstellar spectral analysis for data obtained with theTIGRE telescope (Telescopio Internacional de Gua-najuato Robotico Espectroscopico) that is installedat our institution in Guanajuato
TIGRE is a 12 m fully robotic telescope lo-cated at the La Luz Observatory (in central Mex-ico) at an altitude of 2400 m a more detailed de-scription can be found in Schmitt et al (2014) Itsprincipal instrument is the fibre-fed echelle spectro-graph HEROS (Heidelberg Extended Range Opti-cal Spectrograph) which yields a spectral resolu-tion R asymp 20 000 covering a spectral range from3800 A to 8800 A The queue observing mode and au-tomatic reduction pipeline already implemented forthis telescope allow to optimize the observation andreduction process producing highly homogeneousdata rapidly and confidently To optimize the anal-ysis process we developed a semi-automatic methodthat allows us to derive efficiently the most impor-tant physical characteristics of the stars Teff log g[MH] [FeH] and V sin i This was done by apply-ing the synthetic spectral fitting technique as offeredby the code iSpec (Blanco-Cuaresma 2014) which
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202 FLOR-TORRES ET AL
was shown to yield results that are comparable toresults in the literature obtained through differentmethods and codes (Blanco-Cuaresma 2019)
The goal of this first article is to explain our spec-tral analysis method based on iSpec and to compareresults obtained by TIGRE with data taken from theliterature In an accompanying paper (Flor-Torres etal hereinafter Paper II) we will present a prelimi-nary study based on our own observational resultsabout the coupling of the angular momentum of theexoplanets and their host stars
2 SAMPLE OF HOST STARS WITHEXOPLANETS OBSERVED WITH TIGRE
Our initial target list for a pilot project was builtfrom the revised compendium of confirmed exoplan-ets in the Exoplanet Orbit Database (hereinafter Ex-oplanetsorg6) selecting all stars with spectral typesF G or K located on the main sequence (based ontheir luminosities and colors) and for which a con-firmed planet with well determined mass radius andsemi-major axis was reported Note that we did notapply a restriction to single systems since from thepoint of view of the angular momentum we verifiedthat only the major planet of a system counts (likeJupiter in our solar system) To optimize our obser-vation with TIGRE we restricted further our targetlist by retaining only host stars that have a magni-tude V le 105 obtaining a much shorter list of 65targets
Our observed sample consists of 46 stars hostsof 59 exoplanets which were observed by TIGREin queue mode In Table 1 the stars observed aregiven a running number (Column 1) which is usedto identify them in the different graphics The Vmagnitude of each star and its distance as calculatedfrom Gaia parallaxes are listed in Columns 3 and4 respectively Also shown are the exposure timesin Column 5 and the signal to noise ratio (SN)in Column 6 as measured in the red part of thespectrum The last column lists the main referencesfound in the literature with data about the host starsand their planetary systems
The HEROS spectrograph on TIGRE is cou-pled to two ANDOR CCDs cooled by thermocou-ple (Peltier cooling to -100 C) blue iKon-L cameraDZ936N-BBB and red iKon-L camera DZ936N-BVThis yields for each star two spectra one in the bluecovering a spectral range from 3800 A to 5750 A andone in the red covering a spectral range from 5850 Ato 8750 A All the data were automatically reduced
6httpexoplanetsorg
50 100 150 200 250
05
01
00
15
0
SN
Exp
tim
e (
min
)
magv
105
9
75
6
45
Fig 1 SN as a function of exposure time for our samplelimited to stars with magnitude limit V le 105 Notethat the exposure time was adjusted to reach SN ge 60in less than two hours
by the TIGREHEROS standard pipeline which ap-plies automatically all the necessary steps to extractEchelle spectra (Hempelmann et al 2016 Mittag etal 2016) bias subtraction flat fielding cosmic raycorrection order definition and extraction and wave-length calibration which was carried out by means ofTh-Ar lamp spectra taken at the beginning and endof each night Finally we applied a barycentric cor-rection and as a final reduction step corrected eachspectrum for telluric lines using the code Molecfitdeveloped by Smette et al (2015) After verificationof the results of the reduction process we decidedto concentrate our spectral analysis only on the redpart of the spectra where the SN is higher
In Figure 1 we show the SN obtained as a func-tion of the exposure time For each star the totalexposure time during observation was adjusted toreach SN ge 60 Note that this result only dependson the telescope diameter the fiber transmissionthe spectrograph resolution (we used R = 20 000but the resolution is adjustable in iSpec) and thephotometric conditions (explaining most of the vari-ance)The average exposure time was 74 s for anaverage SN asymp 87 which makes observation withTIGRE a very efficient process
To determine how faint a follow-up with TIGREcould be done efficiently we traced in Figure 2 anexponential growth curve based on our data deter-mining the SN expected in one hour for stars withdifferent magnitudes One can see that a star with105 mag in V would be expected to have a SNnear 30 (or 60 in 2 hours) The lowest we could go
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 203
TABLE 1
STARS OBSERVED WITH THE TIGRE
Id Star Magnitude Distance Exp time SN Ref
(V) (pc) (min) (as found in exoplanetsorg)
1 KELT-6 103 2424 971 54 Damasso et al (2015)
2 HD 219134 56 65 80 139 Motalebi et al (2015)
3 KEPLER-37 98 640 932 75 Batalha et al (2013)
4 HD 46375 78 296 1080 107 Marcy et al (2000)
5 HD 75289 64 291 378 99 Udry et al (2000)
6 HD 88133 80 738 1160 94 Fischer et al (2005)
7 HD 149143 79 734 1080 93 Fischer et al (2006) da Silva et al (2006)
8 HAT-P-30 104 2153 1009 59 Johnson et al (2011)
9 KELT-3 98 2113 925 68 Pepper et al (2013)
10 KEPLER-21 83 1089 294 83 Borucki et al (2011)
11 KELT-2A 87 1346 543 95 Beatty et al (2012)
12 HD86081 87 1042 614 100 Johnson et al (2006)
13 WASP-74 98 1498 965 73 Hellier et al (2015)
14 HD 149026 81 760 374 98 Sato et al (2005)
15 HD 209458 76 484 400 98 Henry et al (2000) Charbonneau et al (2000)
16 BD-10 3166 100 846 1008 72 Butler et al (2000)
17 HD 189733 76 198 331 102 Bouchy et al (2005)
18 HD 97658 77 216 350 123 Howard et al (2011)
19 HAT-P-7 105 3445 435 32 Pal et al (2008)
20 KELT-7 85 1372 472 93 Bieryla et al (2015)
21 HAT-P-14 100 2241 840 57 Torres et al (2010)
22 WASP-14 97 1628 746 66 Joshi et al (2009)
23 HAT-P-2 87 1282 700 69 Bakos et al (2007)
24 WASP-38 94 1368 758 82 Barros et al (2011)
25 HD 118203 81 925 415 92 da Silva et al (2006)
26 HD 2638 94 550 1046 82 Moutou et al (2005)
27 WASP-13 104 2290 1237 51 Skillen et al (2009)
28 WASP-34 103 1326 1368 62 Smalley et al (2011)
29 WASP-82 101 2778 981 51 West et al (2016)
30 HD17156 82 783 463 98 Fischer et al (2007)
31 XO-3 99 2143 708 60 Johns-Krull et al (2008)
32 HD 33283 80 901 534 101 Johnson et al (2006)
33 HD 217014 55 155 400 254 Mayor amp Queloz (1995)
34 HD 115383 52 175 40 105 Kuzuhara et al (2013)
35 HAT-P-6 105 2775 1250 49 Noyes et al (2008)
36 HD 75732 60 126 287 141 Marcy et al (2002)
37 HD 120136 45 157 93 174 Butler et al (2000)
38 WASP-76 95 1953 911 73 West et al (2016)
39 Hn-Peg 60 181 80 99 Luhman et al (2007)
40 WASP-8 99 902 1500 81 Queloz et al (2010)
41 WASP-69 99 500 900 76 Anderson et al (2014)
42 HAT-P-34 104 2511 1050 56 Bakos et al (2012)
43 HAT-P-1 99 1597 750 60 Bakos et al (2007)
44 WASP-94 A 101 2125 1050 58 Neveu-VanMalle et al (2014)
45 WASP-111 103 3005 900 58 Anderson et al (2014)
46 HAT-P-8 104 2128 1500 74 Latham et al (2009)
An in front of the name of the star identifies multiple planetary systems
would be SN asymp 10 which would be reached in onehour for a 125 mag star (or 2 hours for a 13 magstar) Since it is not clear how low the SN of astar could be to be efficiently analysed using thesynthetic-spectra method we judged safer to adopta limit SN of 60 which can be reached within twohours using TIGRE This justifies the magnitudelimit V le 105 adopted for this pilot project Ourobservations suggest that a 12 m telescope couldcontribute significantly to the follow-up of exoplanetsurveys like TESS searching for small rocky plan-
ets around bright stars (stars much brighter thanKEPLER stars) and in the near future PLATOwhich will search for Earth-like planets in the habit-able zones of one million nearby Solar type stars
3 SPECTRAL ANALYSIS USING ISPEC
Our spectral analysis was developed using the syn-thetic spectral fitting technique offered by the codeiSpec (version 20161118 Blanco-Cuaresma 20142019) In brief this technique consists in compar-
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204 FLOR-TORRES ET AL
4 5 6 7 8 9 10 11 120
200
400
600
800
1000
1200
1400
1600
Mag V
SN
(t e
xp =
1 h
ou
r)
Fig 2 Exponential growth curve giving the SN ex-pected after one hour exposure time for stars with differ-ent magnitudes
ing an observed spectrum with synthetic spectra in-terpolated from pre-computed grids calculated us-ing different radiative transfer codes and applyinga least-squares minimization algorithm to convergetowards the closest approximation possible In Fig-ure 3 we show one example of a synthetic spectralfit for the star HD 46375 The fit has a rms 00319which is relatively good considering HEROS inter-mediate resolution (Piskunov amp Valenti 2017) Dueto the low resolution of our spectra we can fit at thesame time in a homogeneous manner the intensityand spectral profiles of more than 100 lines (com-pared to a few 10s at high resolution eg Valenti ampDebra 2005) The best fit then allows to determinefive important atmospheric parameters ie the ef-fective temperature Teff the surface gravity log gtwo indexes of metallicities [MH] and [FeH] andthe rotational velocity V sin i
To optimize our analysis a crucial step of ourmethod consisted in applying iSpec to a TIGREspectrum from the Sun (as reflected by the Moon)Our main goal was to determine a subset of spectrallines and segments that best reproduced the physi-cal characteristics of our star Although this step istime consuming because each line and segment has tobe tested incrementally by running iSpec once theselines and segments are established the analysis ofstars becomes straightforward and efficient the fullprocess taking only a few minutes to converge on amodern desktop computer Starting with the wholeline-list available in the VALD database (Kupka etal 1999 2011) we kept only 122 lines in the redfor which we defined specific segments in Table 6 ofAppendix A As we already verified in Eisner et al(2020) these lines and segments can also be used iniSpec as a standard basis for observations obtained
5880 5885 5890 5895 5900 5905
00
02
04
06
08
10
12
Wavelength [nm]
Flu
x [photsm
2micro
ma
s2 ]
Fe I Fe I Na I Na IFe I Fe I Fe IFe IFe ITi I Ti I
Observed spectrum
iSpec synthethic spectrum
Fig 3 Example of the result for the synthetic spec-tral fitting method in iSpec The star is HD 46375 theobserved spectrum is shown in blue and the fitted spec-trum in red with a rms of 00319 The color figure canbe viewed online
with different telescopes and (once adjusted for theresolution) other spectrographs
Our initial analysis of the Sun also allowedus to decide which solar abundance atmosphericmodel and radiative transfer code were optimalWe adopted the solar abundance of Asplund et al(2009) the ATLAS atmospheric model of Kurucz(2005) and the radiative transfer code SPECTRUM ofGray amp Corbally (1994) Another parameter thatturned out to be important using iSpec is a correc-tion for limb darkening which we fixed to a valueof 06 (Hestroffer amp Magnan 1998 Blanco-Cuaresma2019)
After working out the analysis of the Sun wefound an unexpected difficulty in obtaining the ro-tation velocity V sin i for our stars The problemcomes from the fact that in low mass stars the tur-bulence velocity Vmic and Vmac have values com-parable to V sin i (Doyle et al 2014) and there isconsequently no fail-proof recipe how to ldquoconstrainrdquothese velocities using the synthetic method Oneway to approach this problem (following differentresearchers in the field) is to adopt ad hoc valuesbased on theory or observation (Gray 1984ab Fis-cher amp Valenti 2005 Bruntt et al 2010 Tsantaki etal 2014 Doyle et al 2014) For our analysis we de-cided to adopt empirical values For Vmac we usedthe relation (Doyle et al 2014)
Vmac = a+ b∆T + c∆T 2 minus 200(log g minus 444) (3)
where ∆T = (Teffminus5777) a = 321 b = 233times10minus3
and c = 200 times 10minus6 For Vmic we used the relation
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 205
6500 6000 5500 5000
02
46
8
Teff (K)
vm
ac (
km
sminus1
)
Gray (1984)Valenti amp Fischer (2005)Doyle et al (2014)Bruntt et al (2010)
log g
49
455
42
385
35
Fig 4 Values of Vmac adopted for our analysis withiSpec as a function of our results for Teff
(Tsantaki et al 2014)
Vmic = 6932times 10minus4Teff minus 0348 log g minus 1437 (4)
Note that neither authors give uncertainties on thesevalues However Doyle et al (2014) suggest genericuncertainties of the order of plusmn 027 kms and plusmn 015for Vmac and Vmic respectively which we adopted forour study
In Figure 4 we show the final values of Vmac ob-tained in our analysis Traced over the data wedraw the different relations proposed in the litera-ture to fix this parameter At high temperatures(Teff gt 5800 K) one can see that our values forVmac are well above the upper limit determined byValenti amp Fischer (2005) while at low temperaturesthe values are well above the lower limit determinedby Bruntt et al (2010) In general our results forVmac are consistent with the values expected basedon the relation proposed by Gray (1984b)
Our final result for the Sun is shown in Table 2These values were obtained after only ten iterationsusing the parameters of the Sun as initial guess andfixing Vmac and Vmic using equation 3 and equa-tion 4 For comparison we also included in Table 2the values adopted for the Gaia Benchmark starsAlthough our best fit reproduces well the physicalcharacteristics of the Sun the uncertainty estimatedby iSpec for V sin i is relatively high But this as wealready explained is expected considering the prob-lem related to Vmic and Vmac The different solutions(as shown in Figure 4) to this problem might explainfor example why the macro turbulence we used forthe Sun is lower than what was used by Gaia In
TABLE 2
RESULTS FOR THE SOLAR SPECTRUMUSING ISPEC
Char iSpec Sun
Teff 5571 plusmn 30 K 5571 K
log g 444 plusmn 004 dex 444 dex
[MH] 000 plusmn 003 0
[FeH] 000 plusmn 003 0
V sin i 160 plusmn 145 kms 160 kms
Vmic 102 kms 107 kms
Vmac 319 kms 421 kms
rms of fit 00289
Gaia benchmark Stars values(Blanco-Cuaresma 2019)
Doyle et al (2014) the authors already noted a simi-lar difference by comparing the values they obtainedby their relation with results reported by Fischer ampValenti (2005) where the Vmac were systematicallyhigher by as much as 054 km sminus1 However addingthis difference (as a systematic correction) to bringour result for Vmac closer to the value proposed inthe Gaia Benchmark did not lower the uncertaintieson V sin i obtained with iSpec Therefore consider-ing that our method easily reproduces the value ofV sin i for the Sun we judged more realistic to keepa high uncertainty on this parameter Besides thequestion is possibly more complex considering theuncertainty on the existence of a J minus M relationJlowast prop Mα for low mass stars (Herbst et al 2007)and taking into account that V sin i might also de-pend on the age of the star (that is decreasing withthe age Kraft 1967 Wilson 1963 Skumanich 1972)
For the analysis of the stars our semi-automaticmethod can be summarized in the following way Wefirst run iSpec using the parameters of the Sun asinitial input This implies calculating Vmac and Vmicusing equation 3 and equation 4 keeping these valuesfixed and leaving all the other parameters free Theresults of the first run give us new values of Teff andlog g based on which we calculate new initial valuesfor Vmac and Vmic before running iSpec a secondtime
To verify our solutions for each star we use thefinal value of Teff to calculate its mass and radius(first we get the mass then the corresponding ra-dius) using the mass-luminosity relation for starswith masses between 043 M and 2 M (Wang ampZhong 2018)
M
M=
(L
L
)14
=TeffT
(R
R
)12
(5)
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206 FLOR-TORRES ET AL
where L is the bolometric luminosity as determinedfrom its magnitude in V and its distance calculatedfrom Gaia in Table 1 Then we verify that the valueof log g given by iSpec is consistent with the massand radius obtained using the relation (equation 7in Valenti amp Debra 2005)
log(MM) = log(glowast) + 2 log(RR)minus 4437 (6)
In general we obtained consistent values forlog g within the generic errors suggested by Doyleet al (2014) However for eight stars we founddiscrepant masses the masses obtained using equa-tion 6 being higher than the masses using equation 5To solve this problem we found it important to bet-ter constrain the initial value of log g before runningiSpec a second time The reason for this constraint isphysically clear since as shown by equation 5 andequation 6 log g is coupled to Teff In Valenti ampDebra (2005) for example the authors took into ac-count this coupling by first fixing the initial valueof Teff related to the B minus V color of the star thenused a generic log g consistent with this temperatureIn our case we decided to use as initial parametersfor the second run the value of Teff obtained fromthe first run with iSpec (which uses the values ofthe Sun as first guesses) and to use as second guessthe value of log g given by equation 6 that makesthe two masses consistent This also implies recal-culating Vmac and Vmic for these new values whichas before are kept fixed running iSpec The uniqueconsequence of adding this constraint for the eightstars with discrepant masses was to lower the finalvalues of their log(g) all the other parameters beingequal For each star our method requires only tworuns of ten iterations each which amounts to about30 minutes CPU time on a fast desktop computerThis makes our analysis process quite efficient
4 RESULTS CHARACTERIZATION OF THEHOST STARS OF EXOPLANETS OBSERVED
WITH TIGRE
Our measurements for the physical parameters of thehost stars as determined with our semi-automaticmethod are presented in Table 3 Note that for themetallicities [MH] and [FeH] an extra correc-tion was needed following Valenti amp Debra (2005)to eliminate spurious abundance trends (see theirexplanations in sect 64) This correction is based onthe assumption that the ratio of one elemental abun-dance to another must not vary systematically withthe temperature The correction then is simple itconsists in tracing the metallicities as a function of
Teff fitting a second order relation then subtract-ing this spurious relation from the data All theuncertainties reported in Table 3 were calculated byiSpec while the errors of the radii and masses arethe quadratic sums of the uncertainties of the pa-rameters used to calculate these values (see sect 72in Valenti amp Debra 2005) As explained in Valentiamp Debra (2005) and in Piskunov amp Valenti (2017)the uncertainties estimated by the algorithms thatproduce the synthetic spectra and fit them to theobserved spectra are usually undetermined as com-pared to the random errors calculated from the mea-surements of multiple observations of the stars (sect 63in Valenti amp Debra 2005) Unfortunately multipleobservations were not programmed for our stars andwe have only 4 stars in our study (17 19 23 and46) that were observed more than once (four timesfor three and six times for the fourth one) Thismeans that only a rough estimate of the random er-ror can be obtained for our pilot-survey by calculat-ing for each of these stars the standard deviations ofthe parameters measured applying the same spectralanalysis as for the other stars In table 4 we compareour mean uncertainties as obtained with iSpec withthe mean of the standard deviations for the multi-ply observed stars in our sample Except for V sin ithe mean empirical errors are much larger than theiSpec values In particular our empirical errors arelarger than the empirical uncertainties calculated byValenti amp Debra (Figure 9 in 2005) being compara-ble to their 2 sigma probabilities (the values in thetable correspond to 1 sigma the threshold that in-cludes 683 of their error measurements)
Comparing with the Exoplanetsorg andSWEETcat mean uncertainties our mean errors(standard deviations of multiple stars) are slightlylarger although still comparable to those reportedin these studies Although preliminary this resultis important as it suggests that our results based oniSpec analysis of low resolution spectra (R asymp 20 000)are in good agreement with results obtained usinghigher resolution spectra (R higher than 50000)
Another way to verify the consistency of ourdata is to compare our results with those publishedin Exoplanetsorg (on the left in Figure 5) and inSWEET-Cat (on the right) Taken as a whole ourresults seem compatible with the data reported inthese two catalogs (note that the uncertainties arethose of iSpec) although there are also slight no-table differences In Figure 5a our values for Teffare slightly higher below 5800 K than the values re-ported by Exoplanetsorg and SWEET-Cat How-ever above 6000 K our temperatures are compa-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
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50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
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1213
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5200 5400 5600 5800 6000 6200 6400 6600
4500
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7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
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a)
0 1 2 3 4 50
1
2
3
4
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V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
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5
6
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3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
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89
10 11
12
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41
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46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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51
10
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21
57
01
15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
copy C
op
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gh
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02
1 In
stitu
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stro
no
miacutea
U
niv
ers
ida
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ac
ion
al A
utoacute
no
ma
de
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xic
oD
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ttp
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10
22
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10
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15
214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 215
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Blanco-Cuaresma S Soubiran C Heiter U amp JofreP 2014 AampA 569 111
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AJ 154 123Gray D F 1984a ApJ 277 640
1984b ApJ 281 719Gray R O amp Corbally C J 1994 AJ 107 742Grevesse N Asplund M Sauval A J amp Scott P
2010 ApampSS 328 179Han E Wang S X Wright J T et al 2014 PASP
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Hellier C Anderson D R Collier Cameron A et al2015 AJ 150 18
Hempelmann A Mittag M Gonzalez-Perez J N et al2016 AampA 586 14
Henry G W Marcy G W Butler R P amp Vogt SS 2000 ApJ 529 41
Herbst W Eisloeffel J Mundt R amp Scholz A 2007in Protostars and Planets V ed V B Reipurth DJewitt amp K Keil (Tuczon AZ UAP) 927
Hestroffer D amp Magnan C 1998 AampA 333 338Hinkel N R Timmes F X Young P A et al 2014
AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
ApJS 226 4Howard A W Johnson J A Marcy G W et al
2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
Planetary Systems and Host Stars PhD Thesis Col-lege of Science at Florida Institute of Technology
Jofre P Heiter U Soubiran C et al 2014 AampA 564133
Johns-Krull C M McCullough P R Burke C J etal 2008 ApJ 677 657
Johnson J A Marcy G W Fischer D A et al 2006ApJ 647 600
Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
Joshi Y C Pollacco D Collier Cameron A et al2009 MNRAS 392 1532
Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
H C amp Weiss W W 1999 AampAS 138 119Kupka F amp Dubernet M-L 2011 BaltA 20 503Kurucz R L 2005 MSAIS 8 14Kuzuhara M Tamura M Kudo T et al 2013 ApJ
774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
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ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
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ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
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Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
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15
216 FLOR-TORRES ET AL
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Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
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439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
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Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
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copy C
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200 FLOR-TORRES ET AL
common around Sun-like stars suggesting that largescale migration is a standard feature of the planetformation process (Butler et al 2000 Udry amp San-tos 2007)
Two other new types of planets discovered are theldquoSuper-Earthsrdquo (Leconte et al 2009 Valencia et al2006 Martin amp Livio 2015 Chabrier et al 2009) andthe ldquomini-Neptunesrdquo (Gandolfi et al 2017) Thesetoo were found to be common and very close to theirstars which consequently also makes them ldquohotrdquoTheir discoveries are important for two reasons Thefirst reason is that it makes the alternative ldquoin siturdquomodel for the formation of HJs (eg Boss 1997)a special model since it cannot explain the largemass range and diversity of the ldquohotrdquo exoplanetsobserved (Super-Earths and mini-Neptunes in situmodels are discussed in Raymond et al 2008 Chi-ang amp Laughlin 2013) The second reason is thatit was recently established by Lee et al (2017) thattheir numbers around their host stars fall rapidly forperiods P lt 10 days (asymp 009 AU) which assumingKeplerian orbits clearly implies they all formed far-ther out (beyond 01 AU) and have migrated inwardbut with a good many disappearing into their starsThis once again puts large scale migration at thefront scene of the planet formation process
This brings us to the present fundamental ques-tion in planet formation theory (McBride amp Gilmour2004) what explains the fact that large scale migra-tion did not happen in the Solar System Or inother words assuming all planets form in a PPDaround a low mass star (Nomura et al 2016 van derMarel et al 2018 Perez et al 2019) what differ-ence would make migration more important in onecase and less important in another (see discussion inWalsh et al 2011)
Integrating the migration process into a consis-tent model of planet formation is an extremely activeand fast evolving field of research (a recent review ofthis important subject can be found in Raymond ampMorbidelli 2020) In the case of the HJs two mi-gration mechanisms are accepted now as most prob-able (Dawson amp Johnson 2018)(1) disk migrationwhere the planet forms beyond the ice-line and thenmigrates inward by loosing its orbit angular momen-tum to the PPD (see thorough reviews in Baruteauet al 2014 Armitage 2020) and (2) high-eccentricitymigration according to which the planet first gainsa high eccentricity through interactions with otherplanets which makes it to pass very close to itsstar where it looses its orbit angular momentum bytidal interactions (this is a more complicated pro-cess involving different mechanisms eg Rasio amp
Ford 1996 Weidenschilling amp Marzari 1996 Marzariamp Weidenschilling 2002 Chatterjee et al 2008 Na-gasawa et al 2008 Beauge amp Nesvorny 2012) How-ever what is not clear in these two models is whatimportance must be put on the characteristics of thePPD its mass size depth and composition
According to PPD formation theory there aretwo possible mass scenarios (Armitage 2020) theminimum mass model between 001 to 002 Mwhich suggests that the PPD initial mass is onlysufficient to explain the masses of the planets thatformed within it and the maximum mass modelwhich suggests the mass could have been muchhigher close to 05 M Consequently more mas-sive PPD (compared to the Solar System) might haveeither favored the formation of more massive plan-ets (consistent with PPD observations see Figure 2and discussion in Raymond amp Morbidelli 2020) or alarger number of planets The problem is that thismakes both migration mechanisms equally probable(also the masses observed seem too low also relatedto Figure 2 in Raymond amp Morbidelli 2020) An-other caveat is that the Solar System is a multipleplanet system where migration on large scale did nothappen
In terms of angular momentum the differencesbetween the minimum and maximum mass modelfor the PPD might also be important By definitionthe angular momentum of a planet is given by therelation (eg Berget amp Durrance 2010)
Jp = Mp
radicGMlowastap(1minus e2
p) (1)
where Mp and Mlowast are the masses of the planet andits host star ap is the semi-major axis of the planetand ep its eccentricity This suggests that within themaximum mass model more massive planets wouldalso be expected to have higher orbital angular mo-mentum (through their PPD) and consequently tohave lost a larger amount of their angular momen-tum during large scale migration (ap rarr 0) This im-plies that the efficiency of the migration mechanismmust increase with the mass of the planet (or itsPPD) In principle such requirement might be oneway to distinguish which migration process is morerealistic However the problem is bound to be morecomplicated First stars rotate much more slowlythan expected assuming conservation of angular mo-mentum during their formation (McKee amp Ostriker2007) Second defining the angular momentum of aplanetary system as Jsys = Jlowast+ΣJp where ΣJp is thesum of the angular momentum of all the planets andJlowast the angular momentum of the host star (cf Berget
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 201
amp Durrance 2010) the angular momentum of mas-sive planets (even after migration assuming ap 6= 0)will always dominate over the angular momentum ofits host stars That is JlowastΣJp lt 1 and this is de-spite the enormous loss of angular momentum of thestar during its formation This implies that a sort ofcoupling must exist between the angular momentumof the stars and their planets through their PPDsUnderstanding the nature of this coupling thereforeis an important step in understanding how the PPDand the planets forming in it are connected to theformation of their stars This on the other handrequires completing our information about the starsand the planets rotating around them
In the case of the planets the two most success-ful detection techniques the radial velocity (RV) andtransit (Tr) methods yield estimates of the mass ofa planet Mp and its radius Rp as well as the semi-major axis ap and the eccentricity of its orbit epThe first two parameters constrain their composi-tion and formation process in the PPD while thelast two give information about their migration Bycombining the four parameters we can also retrievethe angular momentum of the orbits of the planets(cf equation 1) In the case of the stars the most im-portant characteristics that can be derived from theirspectra are the effective temperature Teff the sur-face gravity log g the metallicities [MH] or [FeH]and the rotational velocity V sin i The first two canbe used in combination with their magnitudes anddistances (using GAIA parallaxes) to determine theirradii and masses which taken in combination withthe rotational velocity yield the angular momentum(or spin) of the star Jlowast
Jlowast = γlowastMlowastRlowastVrotlowast (2)
where Mlowast Rlowast and γlowast are the star mass radius andmoment of inertia (which depends on the mass of thestar cf Irwin 2015) and V rotlowast = V sin i sin i is theequatorial rotation velocity (where i is the inclina-tion angle of the rotation axis relative to our line ofsight)
To understand how the formation of planets isconnected with the formation of their host stars wemust consequently make an effort to determine inparallel with the discovery of the former the physicalcharacteristics of the latter Present data banks forexoplanets (eg Kepler and now TESS with 51 con-firmed discoveries and future surveys like PLATO)5
require follow-up observations and analysis for the
5httpstessmitedu about PLATO see httpsplatomissioncomabout
host stars which are usually done with large diame-ter telescopes equipped with high resolution spectro-graphs However for the brightest stars (TESS tar-gets for example being 30-100 times brighter thanKEPLER stars) the use of smaller diameter tele-scopes equipped with lower resolution spectrographsmight be more efficient in acquiring the informationMoreover although high resolution spectra is jus-tified when one uses the standard spectral analysismethod which is based on modeling the equivalentwidth (EW) of spectral lines this might not be nec-essary when one uses the synthetic spectral analysis(eg Valenti amp Debra 2005) which consists in fit-ting observed spectra to grids of synthetic spectrawith well determined physical characteristics thatcan be produced at different spectral resolutionsAnother problem in using large aperture telescopesfor host stars follow-up is that since these telescopesare in high demand (for faint objects) data are col-lected on short duration runs by different groupsusing different techniques and codes (although thesame analysis method) which introduces discrepan-cies between the results (Hinkel et al 2014 2016Blanco-Cuaresma 2014 Jofre et al 2017) This sug-gests that a follow-up using a dedicated telescopeand applying only one method of analysis could pro-duce more homegeneous data (one effort to homog-enize data is the Stars With ExoplanETs CATalogor SWEET-Cat for short Sousa et al 2008) Forthese reasons we developed a new method based onstellar spectral analysis for data obtained with theTIGRE telescope (Telescopio Internacional de Gua-najuato Robotico Espectroscopico) that is installedat our institution in Guanajuato
TIGRE is a 12 m fully robotic telescope lo-cated at the La Luz Observatory (in central Mex-ico) at an altitude of 2400 m a more detailed de-scription can be found in Schmitt et al (2014) Itsprincipal instrument is the fibre-fed echelle spectro-graph HEROS (Heidelberg Extended Range Opti-cal Spectrograph) which yields a spectral resolu-tion R asymp 20 000 covering a spectral range from3800 A to 8800 A The queue observing mode and au-tomatic reduction pipeline already implemented forthis telescope allow to optimize the observation andreduction process producing highly homogeneousdata rapidly and confidently To optimize the anal-ysis process we developed a semi-automatic methodthat allows us to derive efficiently the most impor-tant physical characteristics of the stars Teff log g[MH] [FeH] and V sin i This was done by apply-ing the synthetic spectral fitting technique as offeredby the code iSpec (Blanco-Cuaresma 2014) which
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202 FLOR-TORRES ET AL
was shown to yield results that are comparable toresults in the literature obtained through differentmethods and codes (Blanco-Cuaresma 2019)
The goal of this first article is to explain our spec-tral analysis method based on iSpec and to compareresults obtained by TIGRE with data taken from theliterature In an accompanying paper (Flor-Torres etal hereinafter Paper II) we will present a prelimi-nary study based on our own observational resultsabout the coupling of the angular momentum of theexoplanets and their host stars
2 SAMPLE OF HOST STARS WITHEXOPLANETS OBSERVED WITH TIGRE
Our initial target list for a pilot project was builtfrom the revised compendium of confirmed exoplan-ets in the Exoplanet Orbit Database (hereinafter Ex-oplanetsorg6) selecting all stars with spectral typesF G or K located on the main sequence (based ontheir luminosities and colors) and for which a con-firmed planet with well determined mass radius andsemi-major axis was reported Note that we did notapply a restriction to single systems since from thepoint of view of the angular momentum we verifiedthat only the major planet of a system counts (likeJupiter in our solar system) To optimize our obser-vation with TIGRE we restricted further our targetlist by retaining only host stars that have a magni-tude V le 105 obtaining a much shorter list of 65targets
Our observed sample consists of 46 stars hostsof 59 exoplanets which were observed by TIGREin queue mode In Table 1 the stars observed aregiven a running number (Column 1) which is usedto identify them in the different graphics The Vmagnitude of each star and its distance as calculatedfrom Gaia parallaxes are listed in Columns 3 and4 respectively Also shown are the exposure timesin Column 5 and the signal to noise ratio (SN)in Column 6 as measured in the red part of thespectrum The last column lists the main referencesfound in the literature with data about the host starsand their planetary systems
The HEROS spectrograph on TIGRE is cou-pled to two ANDOR CCDs cooled by thermocou-ple (Peltier cooling to -100 C) blue iKon-L cameraDZ936N-BBB and red iKon-L camera DZ936N-BVThis yields for each star two spectra one in the bluecovering a spectral range from 3800 A to 5750 A andone in the red covering a spectral range from 5850 Ato 8750 A All the data were automatically reduced
6httpexoplanetsorg
50 100 150 200 250
05
01
00
15
0
SN
Exp
tim
e (
min
)
magv
105
9
75
6
45
Fig 1 SN as a function of exposure time for our samplelimited to stars with magnitude limit V le 105 Notethat the exposure time was adjusted to reach SN ge 60in less than two hours
by the TIGREHEROS standard pipeline which ap-plies automatically all the necessary steps to extractEchelle spectra (Hempelmann et al 2016 Mittag etal 2016) bias subtraction flat fielding cosmic raycorrection order definition and extraction and wave-length calibration which was carried out by means ofTh-Ar lamp spectra taken at the beginning and endof each night Finally we applied a barycentric cor-rection and as a final reduction step corrected eachspectrum for telluric lines using the code Molecfitdeveloped by Smette et al (2015) After verificationof the results of the reduction process we decidedto concentrate our spectral analysis only on the redpart of the spectra where the SN is higher
In Figure 1 we show the SN obtained as a func-tion of the exposure time For each star the totalexposure time during observation was adjusted toreach SN ge 60 Note that this result only dependson the telescope diameter the fiber transmissionthe spectrograph resolution (we used R = 20 000but the resolution is adjustable in iSpec) and thephotometric conditions (explaining most of the vari-ance)The average exposure time was 74 s for anaverage SN asymp 87 which makes observation withTIGRE a very efficient process
To determine how faint a follow-up with TIGREcould be done efficiently we traced in Figure 2 anexponential growth curve based on our data deter-mining the SN expected in one hour for stars withdifferent magnitudes One can see that a star with105 mag in V would be expected to have a SNnear 30 (or 60 in 2 hours) The lowest we could go
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 203
TABLE 1
STARS OBSERVED WITH THE TIGRE
Id Star Magnitude Distance Exp time SN Ref
(V) (pc) (min) (as found in exoplanetsorg)
1 KELT-6 103 2424 971 54 Damasso et al (2015)
2 HD 219134 56 65 80 139 Motalebi et al (2015)
3 KEPLER-37 98 640 932 75 Batalha et al (2013)
4 HD 46375 78 296 1080 107 Marcy et al (2000)
5 HD 75289 64 291 378 99 Udry et al (2000)
6 HD 88133 80 738 1160 94 Fischer et al (2005)
7 HD 149143 79 734 1080 93 Fischer et al (2006) da Silva et al (2006)
8 HAT-P-30 104 2153 1009 59 Johnson et al (2011)
9 KELT-3 98 2113 925 68 Pepper et al (2013)
10 KEPLER-21 83 1089 294 83 Borucki et al (2011)
11 KELT-2A 87 1346 543 95 Beatty et al (2012)
12 HD86081 87 1042 614 100 Johnson et al (2006)
13 WASP-74 98 1498 965 73 Hellier et al (2015)
14 HD 149026 81 760 374 98 Sato et al (2005)
15 HD 209458 76 484 400 98 Henry et al (2000) Charbonneau et al (2000)
16 BD-10 3166 100 846 1008 72 Butler et al (2000)
17 HD 189733 76 198 331 102 Bouchy et al (2005)
18 HD 97658 77 216 350 123 Howard et al (2011)
19 HAT-P-7 105 3445 435 32 Pal et al (2008)
20 KELT-7 85 1372 472 93 Bieryla et al (2015)
21 HAT-P-14 100 2241 840 57 Torres et al (2010)
22 WASP-14 97 1628 746 66 Joshi et al (2009)
23 HAT-P-2 87 1282 700 69 Bakos et al (2007)
24 WASP-38 94 1368 758 82 Barros et al (2011)
25 HD 118203 81 925 415 92 da Silva et al (2006)
26 HD 2638 94 550 1046 82 Moutou et al (2005)
27 WASP-13 104 2290 1237 51 Skillen et al (2009)
28 WASP-34 103 1326 1368 62 Smalley et al (2011)
29 WASP-82 101 2778 981 51 West et al (2016)
30 HD17156 82 783 463 98 Fischer et al (2007)
31 XO-3 99 2143 708 60 Johns-Krull et al (2008)
32 HD 33283 80 901 534 101 Johnson et al (2006)
33 HD 217014 55 155 400 254 Mayor amp Queloz (1995)
34 HD 115383 52 175 40 105 Kuzuhara et al (2013)
35 HAT-P-6 105 2775 1250 49 Noyes et al (2008)
36 HD 75732 60 126 287 141 Marcy et al (2002)
37 HD 120136 45 157 93 174 Butler et al (2000)
38 WASP-76 95 1953 911 73 West et al (2016)
39 Hn-Peg 60 181 80 99 Luhman et al (2007)
40 WASP-8 99 902 1500 81 Queloz et al (2010)
41 WASP-69 99 500 900 76 Anderson et al (2014)
42 HAT-P-34 104 2511 1050 56 Bakos et al (2012)
43 HAT-P-1 99 1597 750 60 Bakos et al (2007)
44 WASP-94 A 101 2125 1050 58 Neveu-VanMalle et al (2014)
45 WASP-111 103 3005 900 58 Anderson et al (2014)
46 HAT-P-8 104 2128 1500 74 Latham et al (2009)
An in front of the name of the star identifies multiple planetary systems
would be SN asymp 10 which would be reached in onehour for a 125 mag star (or 2 hours for a 13 magstar) Since it is not clear how low the SN of astar could be to be efficiently analysed using thesynthetic-spectra method we judged safer to adopta limit SN of 60 which can be reached within twohours using TIGRE This justifies the magnitudelimit V le 105 adopted for this pilot project Ourobservations suggest that a 12 m telescope couldcontribute significantly to the follow-up of exoplanetsurveys like TESS searching for small rocky plan-
ets around bright stars (stars much brighter thanKEPLER stars) and in the near future PLATOwhich will search for Earth-like planets in the habit-able zones of one million nearby Solar type stars
3 SPECTRAL ANALYSIS USING ISPEC
Our spectral analysis was developed using the syn-thetic spectral fitting technique offered by the codeiSpec (version 20161118 Blanco-Cuaresma 20142019) In brief this technique consists in compar-
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204 FLOR-TORRES ET AL
4 5 6 7 8 9 10 11 120
200
400
600
800
1000
1200
1400
1600
Mag V
SN
(t e
xp =
1 h
ou
r)
Fig 2 Exponential growth curve giving the SN ex-pected after one hour exposure time for stars with differ-ent magnitudes
ing an observed spectrum with synthetic spectra in-terpolated from pre-computed grids calculated us-ing different radiative transfer codes and applyinga least-squares minimization algorithm to convergetowards the closest approximation possible In Fig-ure 3 we show one example of a synthetic spectralfit for the star HD 46375 The fit has a rms 00319which is relatively good considering HEROS inter-mediate resolution (Piskunov amp Valenti 2017) Dueto the low resolution of our spectra we can fit at thesame time in a homogeneous manner the intensityand spectral profiles of more than 100 lines (com-pared to a few 10s at high resolution eg Valenti ampDebra 2005) The best fit then allows to determinefive important atmospheric parameters ie the ef-fective temperature Teff the surface gravity log gtwo indexes of metallicities [MH] and [FeH] andthe rotational velocity V sin i
To optimize our analysis a crucial step of ourmethod consisted in applying iSpec to a TIGREspectrum from the Sun (as reflected by the Moon)Our main goal was to determine a subset of spectrallines and segments that best reproduced the physi-cal characteristics of our star Although this step istime consuming because each line and segment has tobe tested incrementally by running iSpec once theselines and segments are established the analysis ofstars becomes straightforward and efficient the fullprocess taking only a few minutes to converge on amodern desktop computer Starting with the wholeline-list available in the VALD database (Kupka etal 1999 2011) we kept only 122 lines in the redfor which we defined specific segments in Table 6 ofAppendix A As we already verified in Eisner et al(2020) these lines and segments can also be used iniSpec as a standard basis for observations obtained
5880 5885 5890 5895 5900 5905
00
02
04
06
08
10
12
Wavelength [nm]
Flu
x [photsm
2micro
ma
s2 ]
Fe I Fe I Na I Na IFe I Fe I Fe IFe IFe ITi I Ti I
Observed spectrum
iSpec synthethic spectrum
Fig 3 Example of the result for the synthetic spec-tral fitting method in iSpec The star is HD 46375 theobserved spectrum is shown in blue and the fitted spec-trum in red with a rms of 00319 The color figure canbe viewed online
with different telescopes and (once adjusted for theresolution) other spectrographs
Our initial analysis of the Sun also allowedus to decide which solar abundance atmosphericmodel and radiative transfer code were optimalWe adopted the solar abundance of Asplund et al(2009) the ATLAS atmospheric model of Kurucz(2005) and the radiative transfer code SPECTRUM ofGray amp Corbally (1994) Another parameter thatturned out to be important using iSpec is a correc-tion for limb darkening which we fixed to a valueof 06 (Hestroffer amp Magnan 1998 Blanco-Cuaresma2019)
After working out the analysis of the Sun wefound an unexpected difficulty in obtaining the ro-tation velocity V sin i for our stars The problemcomes from the fact that in low mass stars the tur-bulence velocity Vmic and Vmac have values com-parable to V sin i (Doyle et al 2014) and there isconsequently no fail-proof recipe how to ldquoconstrainrdquothese velocities using the synthetic method Oneway to approach this problem (following differentresearchers in the field) is to adopt ad hoc valuesbased on theory or observation (Gray 1984ab Fis-cher amp Valenti 2005 Bruntt et al 2010 Tsantaki etal 2014 Doyle et al 2014) For our analysis we de-cided to adopt empirical values For Vmac we usedthe relation (Doyle et al 2014)
Vmac = a+ b∆T + c∆T 2 minus 200(log g minus 444) (3)
where ∆T = (Teffminus5777) a = 321 b = 233times10minus3
and c = 200 times 10minus6 For Vmic we used the relation
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 205
6500 6000 5500 5000
02
46
8
Teff (K)
vm
ac (
km
sminus1
)
Gray (1984)Valenti amp Fischer (2005)Doyle et al (2014)Bruntt et al (2010)
log g
49
455
42
385
35
Fig 4 Values of Vmac adopted for our analysis withiSpec as a function of our results for Teff
(Tsantaki et al 2014)
Vmic = 6932times 10minus4Teff minus 0348 log g minus 1437 (4)
Note that neither authors give uncertainties on thesevalues However Doyle et al (2014) suggest genericuncertainties of the order of plusmn 027 kms and plusmn 015for Vmac and Vmic respectively which we adopted forour study
In Figure 4 we show the final values of Vmac ob-tained in our analysis Traced over the data wedraw the different relations proposed in the litera-ture to fix this parameter At high temperatures(Teff gt 5800 K) one can see that our values forVmac are well above the upper limit determined byValenti amp Fischer (2005) while at low temperaturesthe values are well above the lower limit determinedby Bruntt et al (2010) In general our results forVmac are consistent with the values expected basedon the relation proposed by Gray (1984b)
Our final result for the Sun is shown in Table 2These values were obtained after only ten iterationsusing the parameters of the Sun as initial guess andfixing Vmac and Vmic using equation 3 and equa-tion 4 For comparison we also included in Table 2the values adopted for the Gaia Benchmark starsAlthough our best fit reproduces well the physicalcharacteristics of the Sun the uncertainty estimatedby iSpec for V sin i is relatively high But this as wealready explained is expected considering the prob-lem related to Vmic and Vmac The different solutions(as shown in Figure 4) to this problem might explainfor example why the macro turbulence we used forthe Sun is lower than what was used by Gaia In
TABLE 2
RESULTS FOR THE SOLAR SPECTRUMUSING ISPEC
Char iSpec Sun
Teff 5571 plusmn 30 K 5571 K
log g 444 plusmn 004 dex 444 dex
[MH] 000 plusmn 003 0
[FeH] 000 plusmn 003 0
V sin i 160 plusmn 145 kms 160 kms
Vmic 102 kms 107 kms
Vmac 319 kms 421 kms
rms of fit 00289
Gaia benchmark Stars values(Blanco-Cuaresma 2019)
Doyle et al (2014) the authors already noted a simi-lar difference by comparing the values they obtainedby their relation with results reported by Fischer ampValenti (2005) where the Vmac were systematicallyhigher by as much as 054 km sminus1 However addingthis difference (as a systematic correction) to bringour result for Vmac closer to the value proposed inthe Gaia Benchmark did not lower the uncertaintieson V sin i obtained with iSpec Therefore consider-ing that our method easily reproduces the value ofV sin i for the Sun we judged more realistic to keepa high uncertainty on this parameter Besides thequestion is possibly more complex considering theuncertainty on the existence of a J minus M relationJlowast prop Mα for low mass stars (Herbst et al 2007)and taking into account that V sin i might also de-pend on the age of the star (that is decreasing withthe age Kraft 1967 Wilson 1963 Skumanich 1972)
For the analysis of the stars our semi-automaticmethod can be summarized in the following way Wefirst run iSpec using the parameters of the Sun asinitial input This implies calculating Vmac and Vmicusing equation 3 and equation 4 keeping these valuesfixed and leaving all the other parameters free Theresults of the first run give us new values of Teff andlog g based on which we calculate new initial valuesfor Vmac and Vmic before running iSpec a secondtime
To verify our solutions for each star we use thefinal value of Teff to calculate its mass and radius(first we get the mass then the corresponding ra-dius) using the mass-luminosity relation for starswith masses between 043 M and 2 M (Wang ampZhong 2018)
M
M=
(L
L
)14
=TeffT
(R
R
)12
(5)
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206 FLOR-TORRES ET AL
where L is the bolometric luminosity as determinedfrom its magnitude in V and its distance calculatedfrom Gaia in Table 1 Then we verify that the valueof log g given by iSpec is consistent with the massand radius obtained using the relation (equation 7in Valenti amp Debra 2005)
log(MM) = log(glowast) + 2 log(RR)minus 4437 (6)
In general we obtained consistent values forlog g within the generic errors suggested by Doyleet al (2014) However for eight stars we founddiscrepant masses the masses obtained using equa-tion 6 being higher than the masses using equation 5To solve this problem we found it important to bet-ter constrain the initial value of log g before runningiSpec a second time The reason for this constraint isphysically clear since as shown by equation 5 andequation 6 log g is coupled to Teff In Valenti ampDebra (2005) for example the authors took into ac-count this coupling by first fixing the initial valueof Teff related to the B minus V color of the star thenused a generic log g consistent with this temperatureIn our case we decided to use as initial parametersfor the second run the value of Teff obtained fromthe first run with iSpec (which uses the values ofthe Sun as first guesses) and to use as second guessthe value of log g given by equation 6 that makesthe two masses consistent This also implies recal-culating Vmac and Vmic for these new values whichas before are kept fixed running iSpec The uniqueconsequence of adding this constraint for the eightstars with discrepant masses was to lower the finalvalues of their log(g) all the other parameters beingequal For each star our method requires only tworuns of ten iterations each which amounts to about30 minutes CPU time on a fast desktop computerThis makes our analysis process quite efficient
4 RESULTS CHARACTERIZATION OF THEHOST STARS OF EXOPLANETS OBSERVED
WITH TIGRE
Our measurements for the physical parameters of thehost stars as determined with our semi-automaticmethod are presented in Table 3 Note that for themetallicities [MH] and [FeH] an extra correc-tion was needed following Valenti amp Debra (2005)to eliminate spurious abundance trends (see theirexplanations in sect 64) This correction is based onthe assumption that the ratio of one elemental abun-dance to another must not vary systematically withthe temperature The correction then is simple itconsists in tracing the metallicities as a function of
Teff fitting a second order relation then subtract-ing this spurious relation from the data All theuncertainties reported in Table 3 were calculated byiSpec while the errors of the radii and masses arethe quadratic sums of the uncertainties of the pa-rameters used to calculate these values (see sect 72in Valenti amp Debra 2005) As explained in Valentiamp Debra (2005) and in Piskunov amp Valenti (2017)the uncertainties estimated by the algorithms thatproduce the synthetic spectra and fit them to theobserved spectra are usually undetermined as com-pared to the random errors calculated from the mea-surements of multiple observations of the stars (sect 63in Valenti amp Debra 2005) Unfortunately multipleobservations were not programmed for our stars andwe have only 4 stars in our study (17 19 23 and46) that were observed more than once (four timesfor three and six times for the fourth one) Thismeans that only a rough estimate of the random er-ror can be obtained for our pilot-survey by calculat-ing for each of these stars the standard deviations ofthe parameters measured applying the same spectralanalysis as for the other stars In table 4 we compareour mean uncertainties as obtained with iSpec withthe mean of the standard deviations for the multi-ply observed stars in our sample Except for V sin ithe mean empirical errors are much larger than theiSpec values In particular our empirical errors arelarger than the empirical uncertainties calculated byValenti amp Debra (Figure 9 in 2005) being compara-ble to their 2 sigma probabilities (the values in thetable correspond to 1 sigma the threshold that in-cludes 683 of their error measurements)
Comparing with the Exoplanetsorg andSWEETcat mean uncertainties our mean errors(standard deviations of multiple stars) are slightlylarger although still comparable to those reportedin these studies Although preliminary this resultis important as it suggests that our results based oniSpec analysis of low resolution spectra (R asymp 20 000)are in good agreement with results obtained usinghigher resolution spectra (R higher than 50000)
Another way to verify the consistency of ourdata is to compare our results with those publishedin Exoplanetsorg (on the left in Figure 5) and inSWEET-Cat (on the right) Taken as a whole ourresults seem compatible with the data reported inthese two catalogs (note that the uncertainties arethose of iSpec) although there are also slight no-table differences In Figure 5a our values for Teffare slightly higher below 5800 K than the values re-ported by Exoplanetsorg and SWEET-Cat How-ever above 6000 K our temperatures are compa-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
5
6
7
8
10
11
1213
1415
16
17
18
19
21
22
23
24
27
28
2930
31
3233
35
36
37
38
4041
42
43
44
45 46
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
12
13
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16
17
18
19
21
22
24
25
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2728 29
30
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33
34
36
38
40
41
43
44
a)
0 1 2 3 4 50
1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
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24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 201
amp Durrance 2010) the angular momentum of mas-sive planets (even after migration assuming ap 6= 0)will always dominate over the angular momentum ofits host stars That is JlowastΣJp lt 1 and this is de-spite the enormous loss of angular momentum of thestar during its formation This implies that a sort ofcoupling must exist between the angular momentumof the stars and their planets through their PPDsUnderstanding the nature of this coupling thereforeis an important step in understanding how the PPDand the planets forming in it are connected to theformation of their stars This on the other handrequires completing our information about the starsand the planets rotating around them
In the case of the planets the two most success-ful detection techniques the radial velocity (RV) andtransit (Tr) methods yield estimates of the mass ofa planet Mp and its radius Rp as well as the semi-major axis ap and the eccentricity of its orbit epThe first two parameters constrain their composi-tion and formation process in the PPD while thelast two give information about their migration Bycombining the four parameters we can also retrievethe angular momentum of the orbits of the planets(cf equation 1) In the case of the stars the most im-portant characteristics that can be derived from theirspectra are the effective temperature Teff the sur-face gravity log g the metallicities [MH] or [FeH]and the rotational velocity V sin i The first two canbe used in combination with their magnitudes anddistances (using GAIA parallaxes) to determine theirradii and masses which taken in combination withthe rotational velocity yield the angular momentum(or spin) of the star Jlowast
Jlowast = γlowastMlowastRlowastVrotlowast (2)
where Mlowast Rlowast and γlowast are the star mass radius andmoment of inertia (which depends on the mass of thestar cf Irwin 2015) and V rotlowast = V sin i sin i is theequatorial rotation velocity (where i is the inclina-tion angle of the rotation axis relative to our line ofsight)
To understand how the formation of planets isconnected with the formation of their host stars wemust consequently make an effort to determine inparallel with the discovery of the former the physicalcharacteristics of the latter Present data banks forexoplanets (eg Kepler and now TESS with 51 con-firmed discoveries and future surveys like PLATO)5
require follow-up observations and analysis for the
5httpstessmitedu about PLATO see httpsplatomissioncomabout
host stars which are usually done with large diame-ter telescopes equipped with high resolution spectro-graphs However for the brightest stars (TESS tar-gets for example being 30-100 times brighter thanKEPLER stars) the use of smaller diameter tele-scopes equipped with lower resolution spectrographsmight be more efficient in acquiring the informationMoreover although high resolution spectra is jus-tified when one uses the standard spectral analysismethod which is based on modeling the equivalentwidth (EW) of spectral lines this might not be nec-essary when one uses the synthetic spectral analysis(eg Valenti amp Debra 2005) which consists in fit-ting observed spectra to grids of synthetic spectrawith well determined physical characteristics thatcan be produced at different spectral resolutionsAnother problem in using large aperture telescopesfor host stars follow-up is that since these telescopesare in high demand (for faint objects) data are col-lected on short duration runs by different groupsusing different techniques and codes (although thesame analysis method) which introduces discrepan-cies between the results (Hinkel et al 2014 2016Blanco-Cuaresma 2014 Jofre et al 2017) This sug-gests that a follow-up using a dedicated telescopeand applying only one method of analysis could pro-duce more homegeneous data (one effort to homog-enize data is the Stars With ExoplanETs CATalogor SWEET-Cat for short Sousa et al 2008) Forthese reasons we developed a new method based onstellar spectral analysis for data obtained with theTIGRE telescope (Telescopio Internacional de Gua-najuato Robotico Espectroscopico) that is installedat our institution in Guanajuato
TIGRE is a 12 m fully robotic telescope lo-cated at the La Luz Observatory (in central Mex-ico) at an altitude of 2400 m a more detailed de-scription can be found in Schmitt et al (2014) Itsprincipal instrument is the fibre-fed echelle spectro-graph HEROS (Heidelberg Extended Range Opti-cal Spectrograph) which yields a spectral resolu-tion R asymp 20 000 covering a spectral range from3800 A to 8800 A The queue observing mode and au-tomatic reduction pipeline already implemented forthis telescope allow to optimize the observation andreduction process producing highly homogeneousdata rapidly and confidently To optimize the anal-ysis process we developed a semi-automatic methodthat allows us to derive efficiently the most impor-tant physical characteristics of the stars Teff log g[MH] [FeH] and V sin i This was done by apply-ing the synthetic spectral fitting technique as offeredby the code iSpec (Blanco-Cuaresma 2014) which
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202 FLOR-TORRES ET AL
was shown to yield results that are comparable toresults in the literature obtained through differentmethods and codes (Blanco-Cuaresma 2019)
The goal of this first article is to explain our spec-tral analysis method based on iSpec and to compareresults obtained by TIGRE with data taken from theliterature In an accompanying paper (Flor-Torres etal hereinafter Paper II) we will present a prelimi-nary study based on our own observational resultsabout the coupling of the angular momentum of theexoplanets and their host stars
2 SAMPLE OF HOST STARS WITHEXOPLANETS OBSERVED WITH TIGRE
Our initial target list for a pilot project was builtfrom the revised compendium of confirmed exoplan-ets in the Exoplanet Orbit Database (hereinafter Ex-oplanetsorg6) selecting all stars with spectral typesF G or K located on the main sequence (based ontheir luminosities and colors) and for which a con-firmed planet with well determined mass radius andsemi-major axis was reported Note that we did notapply a restriction to single systems since from thepoint of view of the angular momentum we verifiedthat only the major planet of a system counts (likeJupiter in our solar system) To optimize our obser-vation with TIGRE we restricted further our targetlist by retaining only host stars that have a magni-tude V le 105 obtaining a much shorter list of 65targets
Our observed sample consists of 46 stars hostsof 59 exoplanets which were observed by TIGREin queue mode In Table 1 the stars observed aregiven a running number (Column 1) which is usedto identify them in the different graphics The Vmagnitude of each star and its distance as calculatedfrom Gaia parallaxes are listed in Columns 3 and4 respectively Also shown are the exposure timesin Column 5 and the signal to noise ratio (SN)in Column 6 as measured in the red part of thespectrum The last column lists the main referencesfound in the literature with data about the host starsand their planetary systems
The HEROS spectrograph on TIGRE is cou-pled to two ANDOR CCDs cooled by thermocou-ple (Peltier cooling to -100 C) blue iKon-L cameraDZ936N-BBB and red iKon-L camera DZ936N-BVThis yields for each star two spectra one in the bluecovering a spectral range from 3800 A to 5750 A andone in the red covering a spectral range from 5850 Ato 8750 A All the data were automatically reduced
6httpexoplanetsorg
50 100 150 200 250
05
01
00
15
0
SN
Exp
tim
e (
min
)
magv
105
9
75
6
45
Fig 1 SN as a function of exposure time for our samplelimited to stars with magnitude limit V le 105 Notethat the exposure time was adjusted to reach SN ge 60in less than two hours
by the TIGREHEROS standard pipeline which ap-plies automatically all the necessary steps to extractEchelle spectra (Hempelmann et al 2016 Mittag etal 2016) bias subtraction flat fielding cosmic raycorrection order definition and extraction and wave-length calibration which was carried out by means ofTh-Ar lamp spectra taken at the beginning and endof each night Finally we applied a barycentric cor-rection and as a final reduction step corrected eachspectrum for telluric lines using the code Molecfitdeveloped by Smette et al (2015) After verificationof the results of the reduction process we decidedto concentrate our spectral analysis only on the redpart of the spectra where the SN is higher
In Figure 1 we show the SN obtained as a func-tion of the exposure time For each star the totalexposure time during observation was adjusted toreach SN ge 60 Note that this result only dependson the telescope diameter the fiber transmissionthe spectrograph resolution (we used R = 20 000but the resolution is adjustable in iSpec) and thephotometric conditions (explaining most of the vari-ance)The average exposure time was 74 s for anaverage SN asymp 87 which makes observation withTIGRE a very efficient process
To determine how faint a follow-up with TIGREcould be done efficiently we traced in Figure 2 anexponential growth curve based on our data deter-mining the SN expected in one hour for stars withdifferent magnitudes One can see that a star with105 mag in V would be expected to have a SNnear 30 (or 60 in 2 hours) The lowest we could go
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 203
TABLE 1
STARS OBSERVED WITH THE TIGRE
Id Star Magnitude Distance Exp time SN Ref
(V) (pc) (min) (as found in exoplanetsorg)
1 KELT-6 103 2424 971 54 Damasso et al (2015)
2 HD 219134 56 65 80 139 Motalebi et al (2015)
3 KEPLER-37 98 640 932 75 Batalha et al (2013)
4 HD 46375 78 296 1080 107 Marcy et al (2000)
5 HD 75289 64 291 378 99 Udry et al (2000)
6 HD 88133 80 738 1160 94 Fischer et al (2005)
7 HD 149143 79 734 1080 93 Fischer et al (2006) da Silva et al (2006)
8 HAT-P-30 104 2153 1009 59 Johnson et al (2011)
9 KELT-3 98 2113 925 68 Pepper et al (2013)
10 KEPLER-21 83 1089 294 83 Borucki et al (2011)
11 KELT-2A 87 1346 543 95 Beatty et al (2012)
12 HD86081 87 1042 614 100 Johnson et al (2006)
13 WASP-74 98 1498 965 73 Hellier et al (2015)
14 HD 149026 81 760 374 98 Sato et al (2005)
15 HD 209458 76 484 400 98 Henry et al (2000) Charbonneau et al (2000)
16 BD-10 3166 100 846 1008 72 Butler et al (2000)
17 HD 189733 76 198 331 102 Bouchy et al (2005)
18 HD 97658 77 216 350 123 Howard et al (2011)
19 HAT-P-7 105 3445 435 32 Pal et al (2008)
20 KELT-7 85 1372 472 93 Bieryla et al (2015)
21 HAT-P-14 100 2241 840 57 Torres et al (2010)
22 WASP-14 97 1628 746 66 Joshi et al (2009)
23 HAT-P-2 87 1282 700 69 Bakos et al (2007)
24 WASP-38 94 1368 758 82 Barros et al (2011)
25 HD 118203 81 925 415 92 da Silva et al (2006)
26 HD 2638 94 550 1046 82 Moutou et al (2005)
27 WASP-13 104 2290 1237 51 Skillen et al (2009)
28 WASP-34 103 1326 1368 62 Smalley et al (2011)
29 WASP-82 101 2778 981 51 West et al (2016)
30 HD17156 82 783 463 98 Fischer et al (2007)
31 XO-3 99 2143 708 60 Johns-Krull et al (2008)
32 HD 33283 80 901 534 101 Johnson et al (2006)
33 HD 217014 55 155 400 254 Mayor amp Queloz (1995)
34 HD 115383 52 175 40 105 Kuzuhara et al (2013)
35 HAT-P-6 105 2775 1250 49 Noyes et al (2008)
36 HD 75732 60 126 287 141 Marcy et al (2002)
37 HD 120136 45 157 93 174 Butler et al (2000)
38 WASP-76 95 1953 911 73 West et al (2016)
39 Hn-Peg 60 181 80 99 Luhman et al (2007)
40 WASP-8 99 902 1500 81 Queloz et al (2010)
41 WASP-69 99 500 900 76 Anderson et al (2014)
42 HAT-P-34 104 2511 1050 56 Bakos et al (2012)
43 HAT-P-1 99 1597 750 60 Bakos et al (2007)
44 WASP-94 A 101 2125 1050 58 Neveu-VanMalle et al (2014)
45 WASP-111 103 3005 900 58 Anderson et al (2014)
46 HAT-P-8 104 2128 1500 74 Latham et al (2009)
An in front of the name of the star identifies multiple planetary systems
would be SN asymp 10 which would be reached in onehour for a 125 mag star (or 2 hours for a 13 magstar) Since it is not clear how low the SN of astar could be to be efficiently analysed using thesynthetic-spectra method we judged safer to adopta limit SN of 60 which can be reached within twohours using TIGRE This justifies the magnitudelimit V le 105 adopted for this pilot project Ourobservations suggest that a 12 m telescope couldcontribute significantly to the follow-up of exoplanetsurveys like TESS searching for small rocky plan-
ets around bright stars (stars much brighter thanKEPLER stars) and in the near future PLATOwhich will search for Earth-like planets in the habit-able zones of one million nearby Solar type stars
3 SPECTRAL ANALYSIS USING ISPEC
Our spectral analysis was developed using the syn-thetic spectral fitting technique offered by the codeiSpec (version 20161118 Blanco-Cuaresma 20142019) In brief this technique consists in compar-
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204 FLOR-TORRES ET AL
4 5 6 7 8 9 10 11 120
200
400
600
800
1000
1200
1400
1600
Mag V
SN
(t e
xp =
1 h
ou
r)
Fig 2 Exponential growth curve giving the SN ex-pected after one hour exposure time for stars with differ-ent magnitudes
ing an observed spectrum with synthetic spectra in-terpolated from pre-computed grids calculated us-ing different radiative transfer codes and applyinga least-squares minimization algorithm to convergetowards the closest approximation possible In Fig-ure 3 we show one example of a synthetic spectralfit for the star HD 46375 The fit has a rms 00319which is relatively good considering HEROS inter-mediate resolution (Piskunov amp Valenti 2017) Dueto the low resolution of our spectra we can fit at thesame time in a homogeneous manner the intensityand spectral profiles of more than 100 lines (com-pared to a few 10s at high resolution eg Valenti ampDebra 2005) The best fit then allows to determinefive important atmospheric parameters ie the ef-fective temperature Teff the surface gravity log gtwo indexes of metallicities [MH] and [FeH] andthe rotational velocity V sin i
To optimize our analysis a crucial step of ourmethod consisted in applying iSpec to a TIGREspectrum from the Sun (as reflected by the Moon)Our main goal was to determine a subset of spectrallines and segments that best reproduced the physi-cal characteristics of our star Although this step istime consuming because each line and segment has tobe tested incrementally by running iSpec once theselines and segments are established the analysis ofstars becomes straightforward and efficient the fullprocess taking only a few minutes to converge on amodern desktop computer Starting with the wholeline-list available in the VALD database (Kupka etal 1999 2011) we kept only 122 lines in the redfor which we defined specific segments in Table 6 ofAppendix A As we already verified in Eisner et al(2020) these lines and segments can also be used iniSpec as a standard basis for observations obtained
5880 5885 5890 5895 5900 5905
00
02
04
06
08
10
12
Wavelength [nm]
Flu
x [photsm
2micro
ma
s2 ]
Fe I Fe I Na I Na IFe I Fe I Fe IFe IFe ITi I Ti I
Observed spectrum
iSpec synthethic spectrum
Fig 3 Example of the result for the synthetic spec-tral fitting method in iSpec The star is HD 46375 theobserved spectrum is shown in blue and the fitted spec-trum in red with a rms of 00319 The color figure canbe viewed online
with different telescopes and (once adjusted for theresolution) other spectrographs
Our initial analysis of the Sun also allowedus to decide which solar abundance atmosphericmodel and radiative transfer code were optimalWe adopted the solar abundance of Asplund et al(2009) the ATLAS atmospheric model of Kurucz(2005) and the radiative transfer code SPECTRUM ofGray amp Corbally (1994) Another parameter thatturned out to be important using iSpec is a correc-tion for limb darkening which we fixed to a valueof 06 (Hestroffer amp Magnan 1998 Blanco-Cuaresma2019)
After working out the analysis of the Sun wefound an unexpected difficulty in obtaining the ro-tation velocity V sin i for our stars The problemcomes from the fact that in low mass stars the tur-bulence velocity Vmic and Vmac have values com-parable to V sin i (Doyle et al 2014) and there isconsequently no fail-proof recipe how to ldquoconstrainrdquothese velocities using the synthetic method Oneway to approach this problem (following differentresearchers in the field) is to adopt ad hoc valuesbased on theory or observation (Gray 1984ab Fis-cher amp Valenti 2005 Bruntt et al 2010 Tsantaki etal 2014 Doyle et al 2014) For our analysis we de-cided to adopt empirical values For Vmac we usedthe relation (Doyle et al 2014)
Vmac = a+ b∆T + c∆T 2 minus 200(log g minus 444) (3)
where ∆T = (Teffminus5777) a = 321 b = 233times10minus3
and c = 200 times 10minus6 For Vmic we used the relation
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 205
6500 6000 5500 5000
02
46
8
Teff (K)
vm
ac (
km
sminus1
)
Gray (1984)Valenti amp Fischer (2005)Doyle et al (2014)Bruntt et al (2010)
log g
49
455
42
385
35
Fig 4 Values of Vmac adopted for our analysis withiSpec as a function of our results for Teff
(Tsantaki et al 2014)
Vmic = 6932times 10minus4Teff minus 0348 log g minus 1437 (4)
Note that neither authors give uncertainties on thesevalues However Doyle et al (2014) suggest genericuncertainties of the order of plusmn 027 kms and plusmn 015for Vmac and Vmic respectively which we adopted forour study
In Figure 4 we show the final values of Vmac ob-tained in our analysis Traced over the data wedraw the different relations proposed in the litera-ture to fix this parameter At high temperatures(Teff gt 5800 K) one can see that our values forVmac are well above the upper limit determined byValenti amp Fischer (2005) while at low temperaturesthe values are well above the lower limit determinedby Bruntt et al (2010) In general our results forVmac are consistent with the values expected basedon the relation proposed by Gray (1984b)
Our final result for the Sun is shown in Table 2These values were obtained after only ten iterationsusing the parameters of the Sun as initial guess andfixing Vmac and Vmic using equation 3 and equa-tion 4 For comparison we also included in Table 2the values adopted for the Gaia Benchmark starsAlthough our best fit reproduces well the physicalcharacteristics of the Sun the uncertainty estimatedby iSpec for V sin i is relatively high But this as wealready explained is expected considering the prob-lem related to Vmic and Vmac The different solutions(as shown in Figure 4) to this problem might explainfor example why the macro turbulence we used forthe Sun is lower than what was used by Gaia In
TABLE 2
RESULTS FOR THE SOLAR SPECTRUMUSING ISPEC
Char iSpec Sun
Teff 5571 plusmn 30 K 5571 K
log g 444 plusmn 004 dex 444 dex
[MH] 000 plusmn 003 0
[FeH] 000 plusmn 003 0
V sin i 160 plusmn 145 kms 160 kms
Vmic 102 kms 107 kms
Vmac 319 kms 421 kms
rms of fit 00289
Gaia benchmark Stars values(Blanco-Cuaresma 2019)
Doyle et al (2014) the authors already noted a simi-lar difference by comparing the values they obtainedby their relation with results reported by Fischer ampValenti (2005) where the Vmac were systematicallyhigher by as much as 054 km sminus1 However addingthis difference (as a systematic correction) to bringour result for Vmac closer to the value proposed inthe Gaia Benchmark did not lower the uncertaintieson V sin i obtained with iSpec Therefore consider-ing that our method easily reproduces the value ofV sin i for the Sun we judged more realistic to keepa high uncertainty on this parameter Besides thequestion is possibly more complex considering theuncertainty on the existence of a J minus M relationJlowast prop Mα for low mass stars (Herbst et al 2007)and taking into account that V sin i might also de-pend on the age of the star (that is decreasing withthe age Kraft 1967 Wilson 1963 Skumanich 1972)
For the analysis of the stars our semi-automaticmethod can be summarized in the following way Wefirst run iSpec using the parameters of the Sun asinitial input This implies calculating Vmac and Vmicusing equation 3 and equation 4 keeping these valuesfixed and leaving all the other parameters free Theresults of the first run give us new values of Teff andlog g based on which we calculate new initial valuesfor Vmac and Vmic before running iSpec a secondtime
To verify our solutions for each star we use thefinal value of Teff to calculate its mass and radius(first we get the mass then the corresponding ra-dius) using the mass-luminosity relation for starswith masses between 043 M and 2 M (Wang ampZhong 2018)
M
M=
(L
L
)14
=TeffT
(R
R
)12
(5)
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206 FLOR-TORRES ET AL
where L is the bolometric luminosity as determinedfrom its magnitude in V and its distance calculatedfrom Gaia in Table 1 Then we verify that the valueof log g given by iSpec is consistent with the massand radius obtained using the relation (equation 7in Valenti amp Debra 2005)
log(MM) = log(glowast) + 2 log(RR)minus 4437 (6)
In general we obtained consistent values forlog g within the generic errors suggested by Doyleet al (2014) However for eight stars we founddiscrepant masses the masses obtained using equa-tion 6 being higher than the masses using equation 5To solve this problem we found it important to bet-ter constrain the initial value of log g before runningiSpec a second time The reason for this constraint isphysically clear since as shown by equation 5 andequation 6 log g is coupled to Teff In Valenti ampDebra (2005) for example the authors took into ac-count this coupling by first fixing the initial valueof Teff related to the B minus V color of the star thenused a generic log g consistent with this temperatureIn our case we decided to use as initial parametersfor the second run the value of Teff obtained fromthe first run with iSpec (which uses the values ofthe Sun as first guesses) and to use as second guessthe value of log g given by equation 6 that makesthe two masses consistent This also implies recal-culating Vmac and Vmic for these new values whichas before are kept fixed running iSpec The uniqueconsequence of adding this constraint for the eightstars with discrepant masses was to lower the finalvalues of their log(g) all the other parameters beingequal For each star our method requires only tworuns of ten iterations each which amounts to about30 minutes CPU time on a fast desktop computerThis makes our analysis process quite efficient
4 RESULTS CHARACTERIZATION OF THEHOST STARS OF EXOPLANETS OBSERVED
WITH TIGRE
Our measurements for the physical parameters of thehost stars as determined with our semi-automaticmethod are presented in Table 3 Note that for themetallicities [MH] and [FeH] an extra correc-tion was needed following Valenti amp Debra (2005)to eliminate spurious abundance trends (see theirexplanations in sect 64) This correction is based onthe assumption that the ratio of one elemental abun-dance to another must not vary systematically withthe temperature The correction then is simple itconsists in tracing the metallicities as a function of
Teff fitting a second order relation then subtract-ing this spurious relation from the data All theuncertainties reported in Table 3 were calculated byiSpec while the errors of the radii and masses arethe quadratic sums of the uncertainties of the pa-rameters used to calculate these values (see sect 72in Valenti amp Debra 2005) As explained in Valentiamp Debra (2005) and in Piskunov amp Valenti (2017)the uncertainties estimated by the algorithms thatproduce the synthetic spectra and fit them to theobserved spectra are usually undetermined as com-pared to the random errors calculated from the mea-surements of multiple observations of the stars (sect 63in Valenti amp Debra 2005) Unfortunately multipleobservations were not programmed for our stars andwe have only 4 stars in our study (17 19 23 and46) that were observed more than once (four timesfor three and six times for the fourth one) Thismeans that only a rough estimate of the random er-ror can be obtained for our pilot-survey by calculat-ing for each of these stars the standard deviations ofthe parameters measured applying the same spectralanalysis as for the other stars In table 4 we compareour mean uncertainties as obtained with iSpec withthe mean of the standard deviations for the multi-ply observed stars in our sample Except for V sin ithe mean empirical errors are much larger than theiSpec values In particular our empirical errors arelarger than the empirical uncertainties calculated byValenti amp Debra (Figure 9 in 2005) being compara-ble to their 2 sigma probabilities (the values in thetable correspond to 1 sigma the threshold that in-cludes 683 of their error measurements)
Comparing with the Exoplanetsorg andSWEETcat mean uncertainties our mean errors(standard deviations of multiple stars) are slightlylarger although still comparable to those reportedin these studies Although preliminary this resultis important as it suggests that our results based oniSpec analysis of low resolution spectra (R asymp 20 000)are in good agreement with results obtained usinghigher resolution spectra (R higher than 50000)
Another way to verify the consistency of ourdata is to compare our results with those publishedin Exoplanetsorg (on the left in Figure 5) and inSWEET-Cat (on the right) Taken as a whole ourresults seem compatible with the data reported inthese two catalogs (note that the uncertainties arethose of iSpec) although there are also slight no-table differences In Figure 5a our values for Teffare slightly higher below 5800 K than the values re-ported by Exoplanetsorg and SWEET-Cat How-ever above 6000 K our temperatures are compa-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
5
6
7
8
10
11
1213
1415
16
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24
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4041
42
43
44
45 46
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
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V sin i (kms)
V s
in i V
mac
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a)
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1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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216 FLOR-TORRES ET AL
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Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
673 79Moutou C Mayor M Bouchy F et al 2005 AampA
439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
S Blanco-Cuaresma Harvard-Smithsonian Center for Astrophysics Cambridge MA USAR Coziol L M Flor-Torres D Jack and K-P Schroder Departamento de Astronomıa Universidad de
Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
AampA 502 391Skumanich A 1972 ApJ 171 565Smalley B Anderson D R Collier Cameron A et al
2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
2008 AampA 620 58Stauffer J R amp Hartman L W 1986 PASP 98 1233Tassoul J-L 2000 Stellar Rotation (New York NY
CUP) doi101017CBO9780511546044Torres G Bakos G A Hartman J et al 2010 ApJ
715 458Tsantaki M Sousa S G Santos N C et al 2014
AampA 570 80Udry S Mayor M Naef D et al 2000 AampA 356
590Udry S amp Santos N C 2007 ARAampA 45 397Uzdensky D A Konigl A amp Litwin C 2002 ApJ
565 1191Valencia D OrsquoConnell R J amp Sasselov D 2006 Icar
181 545Valenti J A amp Debra A 2005 ApJS 159 141van der Marel N Williams J P amp Bruderer S 2018
ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
D P amp Mandell A M 2011 Natur 475 206Wang J amp Zhong Z 2018 AampA 619 1Weidenschilling S J amp Marzari F 1996 Natur 384
619West R G Hellier C Almenara J-M et al 2016
AampA 585 126Wilson O C 1963 ApJ 138 832Wolff S amp Simon T 1997 PASP 109 759
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202 FLOR-TORRES ET AL
was shown to yield results that are comparable toresults in the literature obtained through differentmethods and codes (Blanco-Cuaresma 2019)
The goal of this first article is to explain our spec-tral analysis method based on iSpec and to compareresults obtained by TIGRE with data taken from theliterature In an accompanying paper (Flor-Torres etal hereinafter Paper II) we will present a prelimi-nary study based on our own observational resultsabout the coupling of the angular momentum of theexoplanets and their host stars
2 SAMPLE OF HOST STARS WITHEXOPLANETS OBSERVED WITH TIGRE
Our initial target list for a pilot project was builtfrom the revised compendium of confirmed exoplan-ets in the Exoplanet Orbit Database (hereinafter Ex-oplanetsorg6) selecting all stars with spectral typesF G or K located on the main sequence (based ontheir luminosities and colors) and for which a con-firmed planet with well determined mass radius andsemi-major axis was reported Note that we did notapply a restriction to single systems since from thepoint of view of the angular momentum we verifiedthat only the major planet of a system counts (likeJupiter in our solar system) To optimize our obser-vation with TIGRE we restricted further our targetlist by retaining only host stars that have a magni-tude V le 105 obtaining a much shorter list of 65targets
Our observed sample consists of 46 stars hostsof 59 exoplanets which were observed by TIGREin queue mode In Table 1 the stars observed aregiven a running number (Column 1) which is usedto identify them in the different graphics The Vmagnitude of each star and its distance as calculatedfrom Gaia parallaxes are listed in Columns 3 and4 respectively Also shown are the exposure timesin Column 5 and the signal to noise ratio (SN)in Column 6 as measured in the red part of thespectrum The last column lists the main referencesfound in the literature with data about the host starsand their planetary systems
The HEROS spectrograph on TIGRE is cou-pled to two ANDOR CCDs cooled by thermocou-ple (Peltier cooling to -100 C) blue iKon-L cameraDZ936N-BBB and red iKon-L camera DZ936N-BVThis yields for each star two spectra one in the bluecovering a spectral range from 3800 A to 5750 A andone in the red covering a spectral range from 5850 Ato 8750 A All the data were automatically reduced
6httpexoplanetsorg
50 100 150 200 250
05
01
00
15
0
SN
Exp
tim
e (
min
)
magv
105
9
75
6
45
Fig 1 SN as a function of exposure time for our samplelimited to stars with magnitude limit V le 105 Notethat the exposure time was adjusted to reach SN ge 60in less than two hours
by the TIGREHEROS standard pipeline which ap-plies automatically all the necessary steps to extractEchelle spectra (Hempelmann et al 2016 Mittag etal 2016) bias subtraction flat fielding cosmic raycorrection order definition and extraction and wave-length calibration which was carried out by means ofTh-Ar lamp spectra taken at the beginning and endof each night Finally we applied a barycentric cor-rection and as a final reduction step corrected eachspectrum for telluric lines using the code Molecfitdeveloped by Smette et al (2015) After verificationof the results of the reduction process we decidedto concentrate our spectral analysis only on the redpart of the spectra where the SN is higher
In Figure 1 we show the SN obtained as a func-tion of the exposure time For each star the totalexposure time during observation was adjusted toreach SN ge 60 Note that this result only dependson the telescope diameter the fiber transmissionthe spectrograph resolution (we used R = 20 000but the resolution is adjustable in iSpec) and thephotometric conditions (explaining most of the vari-ance)The average exposure time was 74 s for anaverage SN asymp 87 which makes observation withTIGRE a very efficient process
To determine how faint a follow-up with TIGREcould be done efficiently we traced in Figure 2 anexponential growth curve based on our data deter-mining the SN expected in one hour for stars withdifferent magnitudes One can see that a star with105 mag in V would be expected to have a SNnear 30 (or 60 in 2 hours) The lowest we could go
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 203
TABLE 1
STARS OBSERVED WITH THE TIGRE
Id Star Magnitude Distance Exp time SN Ref
(V) (pc) (min) (as found in exoplanetsorg)
1 KELT-6 103 2424 971 54 Damasso et al (2015)
2 HD 219134 56 65 80 139 Motalebi et al (2015)
3 KEPLER-37 98 640 932 75 Batalha et al (2013)
4 HD 46375 78 296 1080 107 Marcy et al (2000)
5 HD 75289 64 291 378 99 Udry et al (2000)
6 HD 88133 80 738 1160 94 Fischer et al (2005)
7 HD 149143 79 734 1080 93 Fischer et al (2006) da Silva et al (2006)
8 HAT-P-30 104 2153 1009 59 Johnson et al (2011)
9 KELT-3 98 2113 925 68 Pepper et al (2013)
10 KEPLER-21 83 1089 294 83 Borucki et al (2011)
11 KELT-2A 87 1346 543 95 Beatty et al (2012)
12 HD86081 87 1042 614 100 Johnson et al (2006)
13 WASP-74 98 1498 965 73 Hellier et al (2015)
14 HD 149026 81 760 374 98 Sato et al (2005)
15 HD 209458 76 484 400 98 Henry et al (2000) Charbonneau et al (2000)
16 BD-10 3166 100 846 1008 72 Butler et al (2000)
17 HD 189733 76 198 331 102 Bouchy et al (2005)
18 HD 97658 77 216 350 123 Howard et al (2011)
19 HAT-P-7 105 3445 435 32 Pal et al (2008)
20 KELT-7 85 1372 472 93 Bieryla et al (2015)
21 HAT-P-14 100 2241 840 57 Torres et al (2010)
22 WASP-14 97 1628 746 66 Joshi et al (2009)
23 HAT-P-2 87 1282 700 69 Bakos et al (2007)
24 WASP-38 94 1368 758 82 Barros et al (2011)
25 HD 118203 81 925 415 92 da Silva et al (2006)
26 HD 2638 94 550 1046 82 Moutou et al (2005)
27 WASP-13 104 2290 1237 51 Skillen et al (2009)
28 WASP-34 103 1326 1368 62 Smalley et al (2011)
29 WASP-82 101 2778 981 51 West et al (2016)
30 HD17156 82 783 463 98 Fischer et al (2007)
31 XO-3 99 2143 708 60 Johns-Krull et al (2008)
32 HD 33283 80 901 534 101 Johnson et al (2006)
33 HD 217014 55 155 400 254 Mayor amp Queloz (1995)
34 HD 115383 52 175 40 105 Kuzuhara et al (2013)
35 HAT-P-6 105 2775 1250 49 Noyes et al (2008)
36 HD 75732 60 126 287 141 Marcy et al (2002)
37 HD 120136 45 157 93 174 Butler et al (2000)
38 WASP-76 95 1953 911 73 West et al (2016)
39 Hn-Peg 60 181 80 99 Luhman et al (2007)
40 WASP-8 99 902 1500 81 Queloz et al (2010)
41 WASP-69 99 500 900 76 Anderson et al (2014)
42 HAT-P-34 104 2511 1050 56 Bakos et al (2012)
43 HAT-P-1 99 1597 750 60 Bakos et al (2007)
44 WASP-94 A 101 2125 1050 58 Neveu-VanMalle et al (2014)
45 WASP-111 103 3005 900 58 Anderson et al (2014)
46 HAT-P-8 104 2128 1500 74 Latham et al (2009)
An in front of the name of the star identifies multiple planetary systems
would be SN asymp 10 which would be reached in onehour for a 125 mag star (or 2 hours for a 13 magstar) Since it is not clear how low the SN of astar could be to be efficiently analysed using thesynthetic-spectra method we judged safer to adopta limit SN of 60 which can be reached within twohours using TIGRE This justifies the magnitudelimit V le 105 adopted for this pilot project Ourobservations suggest that a 12 m telescope couldcontribute significantly to the follow-up of exoplanetsurveys like TESS searching for small rocky plan-
ets around bright stars (stars much brighter thanKEPLER stars) and in the near future PLATOwhich will search for Earth-like planets in the habit-able zones of one million nearby Solar type stars
3 SPECTRAL ANALYSIS USING ISPEC
Our spectral analysis was developed using the syn-thetic spectral fitting technique offered by the codeiSpec (version 20161118 Blanco-Cuaresma 20142019) In brief this technique consists in compar-
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204 FLOR-TORRES ET AL
4 5 6 7 8 9 10 11 120
200
400
600
800
1000
1200
1400
1600
Mag V
SN
(t e
xp =
1 h
ou
r)
Fig 2 Exponential growth curve giving the SN ex-pected after one hour exposure time for stars with differ-ent magnitudes
ing an observed spectrum with synthetic spectra in-terpolated from pre-computed grids calculated us-ing different radiative transfer codes and applyinga least-squares minimization algorithm to convergetowards the closest approximation possible In Fig-ure 3 we show one example of a synthetic spectralfit for the star HD 46375 The fit has a rms 00319which is relatively good considering HEROS inter-mediate resolution (Piskunov amp Valenti 2017) Dueto the low resolution of our spectra we can fit at thesame time in a homogeneous manner the intensityand spectral profiles of more than 100 lines (com-pared to a few 10s at high resolution eg Valenti ampDebra 2005) The best fit then allows to determinefive important atmospheric parameters ie the ef-fective temperature Teff the surface gravity log gtwo indexes of metallicities [MH] and [FeH] andthe rotational velocity V sin i
To optimize our analysis a crucial step of ourmethod consisted in applying iSpec to a TIGREspectrum from the Sun (as reflected by the Moon)Our main goal was to determine a subset of spectrallines and segments that best reproduced the physi-cal characteristics of our star Although this step istime consuming because each line and segment has tobe tested incrementally by running iSpec once theselines and segments are established the analysis ofstars becomes straightforward and efficient the fullprocess taking only a few minutes to converge on amodern desktop computer Starting with the wholeline-list available in the VALD database (Kupka etal 1999 2011) we kept only 122 lines in the redfor which we defined specific segments in Table 6 ofAppendix A As we already verified in Eisner et al(2020) these lines and segments can also be used iniSpec as a standard basis for observations obtained
5880 5885 5890 5895 5900 5905
00
02
04
06
08
10
12
Wavelength [nm]
Flu
x [photsm
2micro
ma
s2 ]
Fe I Fe I Na I Na IFe I Fe I Fe IFe IFe ITi I Ti I
Observed spectrum
iSpec synthethic spectrum
Fig 3 Example of the result for the synthetic spec-tral fitting method in iSpec The star is HD 46375 theobserved spectrum is shown in blue and the fitted spec-trum in red with a rms of 00319 The color figure canbe viewed online
with different telescopes and (once adjusted for theresolution) other spectrographs
Our initial analysis of the Sun also allowedus to decide which solar abundance atmosphericmodel and radiative transfer code were optimalWe adopted the solar abundance of Asplund et al(2009) the ATLAS atmospheric model of Kurucz(2005) and the radiative transfer code SPECTRUM ofGray amp Corbally (1994) Another parameter thatturned out to be important using iSpec is a correc-tion for limb darkening which we fixed to a valueof 06 (Hestroffer amp Magnan 1998 Blanco-Cuaresma2019)
After working out the analysis of the Sun wefound an unexpected difficulty in obtaining the ro-tation velocity V sin i for our stars The problemcomes from the fact that in low mass stars the tur-bulence velocity Vmic and Vmac have values com-parable to V sin i (Doyle et al 2014) and there isconsequently no fail-proof recipe how to ldquoconstrainrdquothese velocities using the synthetic method Oneway to approach this problem (following differentresearchers in the field) is to adopt ad hoc valuesbased on theory or observation (Gray 1984ab Fis-cher amp Valenti 2005 Bruntt et al 2010 Tsantaki etal 2014 Doyle et al 2014) For our analysis we de-cided to adopt empirical values For Vmac we usedthe relation (Doyle et al 2014)
Vmac = a+ b∆T + c∆T 2 minus 200(log g minus 444) (3)
where ∆T = (Teffminus5777) a = 321 b = 233times10minus3
and c = 200 times 10minus6 For Vmic we used the relation
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 205
6500 6000 5500 5000
02
46
8
Teff (K)
vm
ac (
km
sminus1
)
Gray (1984)Valenti amp Fischer (2005)Doyle et al (2014)Bruntt et al (2010)
log g
49
455
42
385
35
Fig 4 Values of Vmac adopted for our analysis withiSpec as a function of our results for Teff
(Tsantaki et al 2014)
Vmic = 6932times 10minus4Teff minus 0348 log g minus 1437 (4)
Note that neither authors give uncertainties on thesevalues However Doyle et al (2014) suggest genericuncertainties of the order of plusmn 027 kms and plusmn 015for Vmac and Vmic respectively which we adopted forour study
In Figure 4 we show the final values of Vmac ob-tained in our analysis Traced over the data wedraw the different relations proposed in the litera-ture to fix this parameter At high temperatures(Teff gt 5800 K) one can see that our values forVmac are well above the upper limit determined byValenti amp Fischer (2005) while at low temperaturesthe values are well above the lower limit determinedby Bruntt et al (2010) In general our results forVmac are consistent with the values expected basedon the relation proposed by Gray (1984b)
Our final result for the Sun is shown in Table 2These values were obtained after only ten iterationsusing the parameters of the Sun as initial guess andfixing Vmac and Vmic using equation 3 and equa-tion 4 For comparison we also included in Table 2the values adopted for the Gaia Benchmark starsAlthough our best fit reproduces well the physicalcharacteristics of the Sun the uncertainty estimatedby iSpec for V sin i is relatively high But this as wealready explained is expected considering the prob-lem related to Vmic and Vmac The different solutions(as shown in Figure 4) to this problem might explainfor example why the macro turbulence we used forthe Sun is lower than what was used by Gaia In
TABLE 2
RESULTS FOR THE SOLAR SPECTRUMUSING ISPEC
Char iSpec Sun
Teff 5571 plusmn 30 K 5571 K
log g 444 plusmn 004 dex 444 dex
[MH] 000 plusmn 003 0
[FeH] 000 plusmn 003 0
V sin i 160 plusmn 145 kms 160 kms
Vmic 102 kms 107 kms
Vmac 319 kms 421 kms
rms of fit 00289
Gaia benchmark Stars values(Blanco-Cuaresma 2019)
Doyle et al (2014) the authors already noted a simi-lar difference by comparing the values they obtainedby their relation with results reported by Fischer ampValenti (2005) where the Vmac were systematicallyhigher by as much as 054 km sminus1 However addingthis difference (as a systematic correction) to bringour result for Vmac closer to the value proposed inthe Gaia Benchmark did not lower the uncertaintieson V sin i obtained with iSpec Therefore consider-ing that our method easily reproduces the value ofV sin i for the Sun we judged more realistic to keepa high uncertainty on this parameter Besides thequestion is possibly more complex considering theuncertainty on the existence of a J minus M relationJlowast prop Mα for low mass stars (Herbst et al 2007)and taking into account that V sin i might also de-pend on the age of the star (that is decreasing withthe age Kraft 1967 Wilson 1963 Skumanich 1972)
For the analysis of the stars our semi-automaticmethod can be summarized in the following way Wefirst run iSpec using the parameters of the Sun asinitial input This implies calculating Vmac and Vmicusing equation 3 and equation 4 keeping these valuesfixed and leaving all the other parameters free Theresults of the first run give us new values of Teff andlog g based on which we calculate new initial valuesfor Vmac and Vmic before running iSpec a secondtime
To verify our solutions for each star we use thefinal value of Teff to calculate its mass and radius(first we get the mass then the corresponding ra-dius) using the mass-luminosity relation for starswith masses between 043 M and 2 M (Wang ampZhong 2018)
M
M=
(L
L
)14
=TeffT
(R
R
)12
(5)
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206 FLOR-TORRES ET AL
where L is the bolometric luminosity as determinedfrom its magnitude in V and its distance calculatedfrom Gaia in Table 1 Then we verify that the valueof log g given by iSpec is consistent with the massand radius obtained using the relation (equation 7in Valenti amp Debra 2005)
log(MM) = log(glowast) + 2 log(RR)minus 4437 (6)
In general we obtained consistent values forlog g within the generic errors suggested by Doyleet al (2014) However for eight stars we founddiscrepant masses the masses obtained using equa-tion 6 being higher than the masses using equation 5To solve this problem we found it important to bet-ter constrain the initial value of log g before runningiSpec a second time The reason for this constraint isphysically clear since as shown by equation 5 andequation 6 log g is coupled to Teff In Valenti ampDebra (2005) for example the authors took into ac-count this coupling by first fixing the initial valueof Teff related to the B minus V color of the star thenused a generic log g consistent with this temperatureIn our case we decided to use as initial parametersfor the second run the value of Teff obtained fromthe first run with iSpec (which uses the values ofthe Sun as first guesses) and to use as second guessthe value of log g given by equation 6 that makesthe two masses consistent This also implies recal-culating Vmac and Vmic for these new values whichas before are kept fixed running iSpec The uniqueconsequence of adding this constraint for the eightstars with discrepant masses was to lower the finalvalues of their log(g) all the other parameters beingequal For each star our method requires only tworuns of ten iterations each which amounts to about30 minutes CPU time on a fast desktop computerThis makes our analysis process quite efficient
4 RESULTS CHARACTERIZATION OF THEHOST STARS OF EXOPLANETS OBSERVED
WITH TIGRE
Our measurements for the physical parameters of thehost stars as determined with our semi-automaticmethod are presented in Table 3 Note that for themetallicities [MH] and [FeH] an extra correc-tion was needed following Valenti amp Debra (2005)to eliminate spurious abundance trends (see theirexplanations in sect 64) This correction is based onthe assumption that the ratio of one elemental abun-dance to another must not vary systematically withthe temperature The correction then is simple itconsists in tracing the metallicities as a function of
Teff fitting a second order relation then subtract-ing this spurious relation from the data All theuncertainties reported in Table 3 were calculated byiSpec while the errors of the radii and masses arethe quadratic sums of the uncertainties of the pa-rameters used to calculate these values (see sect 72in Valenti amp Debra 2005) As explained in Valentiamp Debra (2005) and in Piskunov amp Valenti (2017)the uncertainties estimated by the algorithms thatproduce the synthetic spectra and fit them to theobserved spectra are usually undetermined as com-pared to the random errors calculated from the mea-surements of multiple observations of the stars (sect 63in Valenti amp Debra 2005) Unfortunately multipleobservations were not programmed for our stars andwe have only 4 stars in our study (17 19 23 and46) that were observed more than once (four timesfor three and six times for the fourth one) Thismeans that only a rough estimate of the random er-ror can be obtained for our pilot-survey by calculat-ing for each of these stars the standard deviations ofthe parameters measured applying the same spectralanalysis as for the other stars In table 4 we compareour mean uncertainties as obtained with iSpec withthe mean of the standard deviations for the multi-ply observed stars in our sample Except for V sin ithe mean empirical errors are much larger than theiSpec values In particular our empirical errors arelarger than the empirical uncertainties calculated byValenti amp Debra (Figure 9 in 2005) being compara-ble to their 2 sigma probabilities (the values in thetable correspond to 1 sigma the threshold that in-cludes 683 of their error measurements)
Comparing with the Exoplanetsorg andSWEETcat mean uncertainties our mean errors(standard deviations of multiple stars) are slightlylarger although still comparable to those reportedin these studies Although preliminary this resultis important as it suggests that our results based oniSpec analysis of low resolution spectra (R asymp 20 000)are in good agreement with results obtained usinghigher resolution spectra (R higher than 50000)
Another way to verify the consistency of ourdata is to compare our results with those publishedin Exoplanetsorg (on the left in Figure 5) and inSWEET-Cat (on the right) Taken as a whole ourresults seem compatible with the data reported inthese two catalogs (note that the uncertainties arethose of iSpec) although there are also slight no-table differences In Figure 5a our values for Teffare slightly higher below 5800 K than the values re-ported by Exoplanetsorg and SWEET-Cat How-ever above 6000 K our temperatures are compa-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
5
6
7
8
10
11
1213
1415
16
17
18
19
21
22
23
24
27
28
2930
31
3233
35
36
37
38
4041
42
43
44
45 46
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
12
13
14
15
16
17
18
19
21
22
24
25
26
2728 29
30
32
33
34
36
38
40
41
43
44
a)
0 1 2 3 4 50
1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
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2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
Planetary Systems and Host Stars PhD Thesis Col-lege of Science at Florida Institute of Technology
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Johnson J A Marcy G W Fischer D A et al 2006ApJ 647 600
Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
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Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
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774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
1996 Natur 380 606Luhman K L Patten B M Marengo M et al 2007
ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
536 43Marcy G W Butler R P Fischer D A et al 2002
ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
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McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
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216 FLOR-TORRES ET AL
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Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
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ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
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439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
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773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
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Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
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2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 203
TABLE 1
STARS OBSERVED WITH THE TIGRE
Id Star Magnitude Distance Exp time SN Ref
(V) (pc) (min) (as found in exoplanetsorg)
1 KELT-6 103 2424 971 54 Damasso et al (2015)
2 HD 219134 56 65 80 139 Motalebi et al (2015)
3 KEPLER-37 98 640 932 75 Batalha et al (2013)
4 HD 46375 78 296 1080 107 Marcy et al (2000)
5 HD 75289 64 291 378 99 Udry et al (2000)
6 HD 88133 80 738 1160 94 Fischer et al (2005)
7 HD 149143 79 734 1080 93 Fischer et al (2006) da Silva et al (2006)
8 HAT-P-30 104 2153 1009 59 Johnson et al (2011)
9 KELT-3 98 2113 925 68 Pepper et al (2013)
10 KEPLER-21 83 1089 294 83 Borucki et al (2011)
11 KELT-2A 87 1346 543 95 Beatty et al (2012)
12 HD86081 87 1042 614 100 Johnson et al (2006)
13 WASP-74 98 1498 965 73 Hellier et al (2015)
14 HD 149026 81 760 374 98 Sato et al (2005)
15 HD 209458 76 484 400 98 Henry et al (2000) Charbonneau et al (2000)
16 BD-10 3166 100 846 1008 72 Butler et al (2000)
17 HD 189733 76 198 331 102 Bouchy et al (2005)
18 HD 97658 77 216 350 123 Howard et al (2011)
19 HAT-P-7 105 3445 435 32 Pal et al (2008)
20 KELT-7 85 1372 472 93 Bieryla et al (2015)
21 HAT-P-14 100 2241 840 57 Torres et al (2010)
22 WASP-14 97 1628 746 66 Joshi et al (2009)
23 HAT-P-2 87 1282 700 69 Bakos et al (2007)
24 WASP-38 94 1368 758 82 Barros et al (2011)
25 HD 118203 81 925 415 92 da Silva et al (2006)
26 HD 2638 94 550 1046 82 Moutou et al (2005)
27 WASP-13 104 2290 1237 51 Skillen et al (2009)
28 WASP-34 103 1326 1368 62 Smalley et al (2011)
29 WASP-82 101 2778 981 51 West et al (2016)
30 HD17156 82 783 463 98 Fischer et al (2007)
31 XO-3 99 2143 708 60 Johns-Krull et al (2008)
32 HD 33283 80 901 534 101 Johnson et al (2006)
33 HD 217014 55 155 400 254 Mayor amp Queloz (1995)
34 HD 115383 52 175 40 105 Kuzuhara et al (2013)
35 HAT-P-6 105 2775 1250 49 Noyes et al (2008)
36 HD 75732 60 126 287 141 Marcy et al (2002)
37 HD 120136 45 157 93 174 Butler et al (2000)
38 WASP-76 95 1953 911 73 West et al (2016)
39 Hn-Peg 60 181 80 99 Luhman et al (2007)
40 WASP-8 99 902 1500 81 Queloz et al (2010)
41 WASP-69 99 500 900 76 Anderson et al (2014)
42 HAT-P-34 104 2511 1050 56 Bakos et al (2012)
43 HAT-P-1 99 1597 750 60 Bakos et al (2007)
44 WASP-94 A 101 2125 1050 58 Neveu-VanMalle et al (2014)
45 WASP-111 103 3005 900 58 Anderson et al (2014)
46 HAT-P-8 104 2128 1500 74 Latham et al (2009)
An in front of the name of the star identifies multiple planetary systems
would be SN asymp 10 which would be reached in onehour for a 125 mag star (or 2 hours for a 13 magstar) Since it is not clear how low the SN of astar could be to be efficiently analysed using thesynthetic-spectra method we judged safer to adopta limit SN of 60 which can be reached within twohours using TIGRE This justifies the magnitudelimit V le 105 adopted for this pilot project Ourobservations suggest that a 12 m telescope couldcontribute significantly to the follow-up of exoplanetsurveys like TESS searching for small rocky plan-
ets around bright stars (stars much brighter thanKEPLER stars) and in the near future PLATOwhich will search for Earth-like planets in the habit-able zones of one million nearby Solar type stars
3 SPECTRAL ANALYSIS USING ISPEC
Our spectral analysis was developed using the syn-thetic spectral fitting technique offered by the codeiSpec (version 20161118 Blanco-Cuaresma 20142019) In brief this technique consists in compar-
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204 FLOR-TORRES ET AL
4 5 6 7 8 9 10 11 120
200
400
600
800
1000
1200
1400
1600
Mag V
SN
(t e
xp =
1 h
ou
r)
Fig 2 Exponential growth curve giving the SN ex-pected after one hour exposure time for stars with differ-ent magnitudes
ing an observed spectrum with synthetic spectra in-terpolated from pre-computed grids calculated us-ing different radiative transfer codes and applyinga least-squares minimization algorithm to convergetowards the closest approximation possible In Fig-ure 3 we show one example of a synthetic spectralfit for the star HD 46375 The fit has a rms 00319which is relatively good considering HEROS inter-mediate resolution (Piskunov amp Valenti 2017) Dueto the low resolution of our spectra we can fit at thesame time in a homogeneous manner the intensityand spectral profiles of more than 100 lines (com-pared to a few 10s at high resolution eg Valenti ampDebra 2005) The best fit then allows to determinefive important atmospheric parameters ie the ef-fective temperature Teff the surface gravity log gtwo indexes of metallicities [MH] and [FeH] andthe rotational velocity V sin i
To optimize our analysis a crucial step of ourmethod consisted in applying iSpec to a TIGREspectrum from the Sun (as reflected by the Moon)Our main goal was to determine a subset of spectrallines and segments that best reproduced the physi-cal characteristics of our star Although this step istime consuming because each line and segment has tobe tested incrementally by running iSpec once theselines and segments are established the analysis ofstars becomes straightforward and efficient the fullprocess taking only a few minutes to converge on amodern desktop computer Starting with the wholeline-list available in the VALD database (Kupka etal 1999 2011) we kept only 122 lines in the redfor which we defined specific segments in Table 6 ofAppendix A As we already verified in Eisner et al(2020) these lines and segments can also be used iniSpec as a standard basis for observations obtained
5880 5885 5890 5895 5900 5905
00
02
04
06
08
10
12
Wavelength [nm]
Flu
x [photsm
2micro
ma
s2 ]
Fe I Fe I Na I Na IFe I Fe I Fe IFe IFe ITi I Ti I
Observed spectrum
iSpec synthethic spectrum
Fig 3 Example of the result for the synthetic spec-tral fitting method in iSpec The star is HD 46375 theobserved spectrum is shown in blue and the fitted spec-trum in red with a rms of 00319 The color figure canbe viewed online
with different telescopes and (once adjusted for theresolution) other spectrographs
Our initial analysis of the Sun also allowedus to decide which solar abundance atmosphericmodel and radiative transfer code were optimalWe adopted the solar abundance of Asplund et al(2009) the ATLAS atmospheric model of Kurucz(2005) and the radiative transfer code SPECTRUM ofGray amp Corbally (1994) Another parameter thatturned out to be important using iSpec is a correc-tion for limb darkening which we fixed to a valueof 06 (Hestroffer amp Magnan 1998 Blanco-Cuaresma2019)
After working out the analysis of the Sun wefound an unexpected difficulty in obtaining the ro-tation velocity V sin i for our stars The problemcomes from the fact that in low mass stars the tur-bulence velocity Vmic and Vmac have values com-parable to V sin i (Doyle et al 2014) and there isconsequently no fail-proof recipe how to ldquoconstrainrdquothese velocities using the synthetic method Oneway to approach this problem (following differentresearchers in the field) is to adopt ad hoc valuesbased on theory or observation (Gray 1984ab Fis-cher amp Valenti 2005 Bruntt et al 2010 Tsantaki etal 2014 Doyle et al 2014) For our analysis we de-cided to adopt empirical values For Vmac we usedthe relation (Doyle et al 2014)
Vmac = a+ b∆T + c∆T 2 minus 200(log g minus 444) (3)
where ∆T = (Teffminus5777) a = 321 b = 233times10minus3
and c = 200 times 10minus6 For Vmic we used the relation
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 205
6500 6000 5500 5000
02
46
8
Teff (K)
vm
ac (
km
sminus1
)
Gray (1984)Valenti amp Fischer (2005)Doyle et al (2014)Bruntt et al (2010)
log g
49
455
42
385
35
Fig 4 Values of Vmac adopted for our analysis withiSpec as a function of our results for Teff
(Tsantaki et al 2014)
Vmic = 6932times 10minus4Teff minus 0348 log g minus 1437 (4)
Note that neither authors give uncertainties on thesevalues However Doyle et al (2014) suggest genericuncertainties of the order of plusmn 027 kms and plusmn 015for Vmac and Vmic respectively which we adopted forour study
In Figure 4 we show the final values of Vmac ob-tained in our analysis Traced over the data wedraw the different relations proposed in the litera-ture to fix this parameter At high temperatures(Teff gt 5800 K) one can see that our values forVmac are well above the upper limit determined byValenti amp Fischer (2005) while at low temperaturesthe values are well above the lower limit determinedby Bruntt et al (2010) In general our results forVmac are consistent with the values expected basedon the relation proposed by Gray (1984b)
Our final result for the Sun is shown in Table 2These values were obtained after only ten iterationsusing the parameters of the Sun as initial guess andfixing Vmac and Vmic using equation 3 and equa-tion 4 For comparison we also included in Table 2the values adopted for the Gaia Benchmark starsAlthough our best fit reproduces well the physicalcharacteristics of the Sun the uncertainty estimatedby iSpec for V sin i is relatively high But this as wealready explained is expected considering the prob-lem related to Vmic and Vmac The different solutions(as shown in Figure 4) to this problem might explainfor example why the macro turbulence we used forthe Sun is lower than what was used by Gaia In
TABLE 2
RESULTS FOR THE SOLAR SPECTRUMUSING ISPEC
Char iSpec Sun
Teff 5571 plusmn 30 K 5571 K
log g 444 plusmn 004 dex 444 dex
[MH] 000 plusmn 003 0
[FeH] 000 plusmn 003 0
V sin i 160 plusmn 145 kms 160 kms
Vmic 102 kms 107 kms
Vmac 319 kms 421 kms
rms of fit 00289
Gaia benchmark Stars values(Blanco-Cuaresma 2019)
Doyle et al (2014) the authors already noted a simi-lar difference by comparing the values they obtainedby their relation with results reported by Fischer ampValenti (2005) where the Vmac were systematicallyhigher by as much as 054 km sminus1 However addingthis difference (as a systematic correction) to bringour result for Vmac closer to the value proposed inthe Gaia Benchmark did not lower the uncertaintieson V sin i obtained with iSpec Therefore consider-ing that our method easily reproduces the value ofV sin i for the Sun we judged more realistic to keepa high uncertainty on this parameter Besides thequestion is possibly more complex considering theuncertainty on the existence of a J minus M relationJlowast prop Mα for low mass stars (Herbst et al 2007)and taking into account that V sin i might also de-pend on the age of the star (that is decreasing withthe age Kraft 1967 Wilson 1963 Skumanich 1972)
For the analysis of the stars our semi-automaticmethod can be summarized in the following way Wefirst run iSpec using the parameters of the Sun asinitial input This implies calculating Vmac and Vmicusing equation 3 and equation 4 keeping these valuesfixed and leaving all the other parameters free Theresults of the first run give us new values of Teff andlog g based on which we calculate new initial valuesfor Vmac and Vmic before running iSpec a secondtime
To verify our solutions for each star we use thefinal value of Teff to calculate its mass and radius(first we get the mass then the corresponding ra-dius) using the mass-luminosity relation for starswith masses between 043 M and 2 M (Wang ampZhong 2018)
M
M=
(L
L
)14
=TeffT
(R
R
)12
(5)
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206 FLOR-TORRES ET AL
where L is the bolometric luminosity as determinedfrom its magnitude in V and its distance calculatedfrom Gaia in Table 1 Then we verify that the valueof log g given by iSpec is consistent with the massand radius obtained using the relation (equation 7in Valenti amp Debra 2005)
log(MM) = log(glowast) + 2 log(RR)minus 4437 (6)
In general we obtained consistent values forlog g within the generic errors suggested by Doyleet al (2014) However for eight stars we founddiscrepant masses the masses obtained using equa-tion 6 being higher than the masses using equation 5To solve this problem we found it important to bet-ter constrain the initial value of log g before runningiSpec a second time The reason for this constraint isphysically clear since as shown by equation 5 andequation 6 log g is coupled to Teff In Valenti ampDebra (2005) for example the authors took into ac-count this coupling by first fixing the initial valueof Teff related to the B minus V color of the star thenused a generic log g consistent with this temperatureIn our case we decided to use as initial parametersfor the second run the value of Teff obtained fromthe first run with iSpec (which uses the values ofthe Sun as first guesses) and to use as second guessthe value of log g given by equation 6 that makesthe two masses consistent This also implies recal-culating Vmac and Vmic for these new values whichas before are kept fixed running iSpec The uniqueconsequence of adding this constraint for the eightstars with discrepant masses was to lower the finalvalues of their log(g) all the other parameters beingequal For each star our method requires only tworuns of ten iterations each which amounts to about30 minutes CPU time on a fast desktop computerThis makes our analysis process quite efficient
4 RESULTS CHARACTERIZATION OF THEHOST STARS OF EXOPLANETS OBSERVED
WITH TIGRE
Our measurements for the physical parameters of thehost stars as determined with our semi-automaticmethod are presented in Table 3 Note that for themetallicities [MH] and [FeH] an extra correc-tion was needed following Valenti amp Debra (2005)to eliminate spurious abundance trends (see theirexplanations in sect 64) This correction is based onthe assumption that the ratio of one elemental abun-dance to another must not vary systematically withthe temperature The correction then is simple itconsists in tracing the metallicities as a function of
Teff fitting a second order relation then subtract-ing this spurious relation from the data All theuncertainties reported in Table 3 were calculated byiSpec while the errors of the radii and masses arethe quadratic sums of the uncertainties of the pa-rameters used to calculate these values (see sect 72in Valenti amp Debra 2005) As explained in Valentiamp Debra (2005) and in Piskunov amp Valenti (2017)the uncertainties estimated by the algorithms thatproduce the synthetic spectra and fit them to theobserved spectra are usually undetermined as com-pared to the random errors calculated from the mea-surements of multiple observations of the stars (sect 63in Valenti amp Debra 2005) Unfortunately multipleobservations were not programmed for our stars andwe have only 4 stars in our study (17 19 23 and46) that were observed more than once (four timesfor three and six times for the fourth one) Thismeans that only a rough estimate of the random er-ror can be obtained for our pilot-survey by calculat-ing for each of these stars the standard deviations ofthe parameters measured applying the same spectralanalysis as for the other stars In table 4 we compareour mean uncertainties as obtained with iSpec withthe mean of the standard deviations for the multi-ply observed stars in our sample Except for V sin ithe mean empirical errors are much larger than theiSpec values In particular our empirical errors arelarger than the empirical uncertainties calculated byValenti amp Debra (Figure 9 in 2005) being compara-ble to their 2 sigma probabilities (the values in thetable correspond to 1 sigma the threshold that in-cludes 683 of their error measurements)
Comparing with the Exoplanetsorg andSWEETcat mean uncertainties our mean errors(standard deviations of multiple stars) are slightlylarger although still comparable to those reportedin these studies Although preliminary this resultis important as it suggests that our results based oniSpec analysis of low resolution spectra (R asymp 20 000)are in good agreement with results obtained usinghigher resolution spectra (R higher than 50000)
Another way to verify the consistency of ourdata is to compare our results with those publishedin Exoplanetsorg (on the left in Figure 5) and inSWEET-Cat (on the right) Taken as a whole ourresults seem compatible with the data reported inthese two catalogs (note that the uncertainties arethose of iSpec) although there are also slight no-table differences In Figure 5a our values for Teffare slightly higher below 5800 K than the values re-ported by Exoplanetsorg and SWEET-Cat How-ever above 6000 K our temperatures are compa-
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
5
6
7
8
10
11
1213
1415
16
17
18
19
21
22
23
24
27
28
2930
31
3233
35
36
37
38
4041
42
43
44
45 46
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
12
13
14
15
16
17
18
19
21
22
24
25
26
2728 29
30
32
33
34
36
38
40
41
43
44
a)
0 1 2 3 4 50
1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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216 FLOR-TORRES ET AL
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204 FLOR-TORRES ET AL
4 5 6 7 8 9 10 11 120
200
400
600
800
1000
1200
1400
1600
Mag V
SN
(t e
xp =
1 h
ou
r)
Fig 2 Exponential growth curve giving the SN ex-pected after one hour exposure time for stars with differ-ent magnitudes
ing an observed spectrum with synthetic spectra in-terpolated from pre-computed grids calculated us-ing different radiative transfer codes and applyinga least-squares minimization algorithm to convergetowards the closest approximation possible In Fig-ure 3 we show one example of a synthetic spectralfit for the star HD 46375 The fit has a rms 00319which is relatively good considering HEROS inter-mediate resolution (Piskunov amp Valenti 2017) Dueto the low resolution of our spectra we can fit at thesame time in a homogeneous manner the intensityand spectral profiles of more than 100 lines (com-pared to a few 10s at high resolution eg Valenti ampDebra 2005) The best fit then allows to determinefive important atmospheric parameters ie the ef-fective temperature Teff the surface gravity log gtwo indexes of metallicities [MH] and [FeH] andthe rotational velocity V sin i
To optimize our analysis a crucial step of ourmethod consisted in applying iSpec to a TIGREspectrum from the Sun (as reflected by the Moon)Our main goal was to determine a subset of spectrallines and segments that best reproduced the physi-cal characteristics of our star Although this step istime consuming because each line and segment has tobe tested incrementally by running iSpec once theselines and segments are established the analysis ofstars becomes straightforward and efficient the fullprocess taking only a few minutes to converge on amodern desktop computer Starting with the wholeline-list available in the VALD database (Kupka etal 1999 2011) we kept only 122 lines in the redfor which we defined specific segments in Table 6 ofAppendix A As we already verified in Eisner et al(2020) these lines and segments can also be used iniSpec as a standard basis for observations obtained
5880 5885 5890 5895 5900 5905
00
02
04
06
08
10
12
Wavelength [nm]
Flu
x [photsm
2micro
ma
s2 ]
Fe I Fe I Na I Na IFe I Fe I Fe IFe IFe ITi I Ti I
Observed spectrum
iSpec synthethic spectrum
Fig 3 Example of the result for the synthetic spec-tral fitting method in iSpec The star is HD 46375 theobserved spectrum is shown in blue and the fitted spec-trum in red with a rms of 00319 The color figure canbe viewed online
with different telescopes and (once adjusted for theresolution) other spectrographs
Our initial analysis of the Sun also allowedus to decide which solar abundance atmosphericmodel and radiative transfer code were optimalWe adopted the solar abundance of Asplund et al(2009) the ATLAS atmospheric model of Kurucz(2005) and the radiative transfer code SPECTRUM ofGray amp Corbally (1994) Another parameter thatturned out to be important using iSpec is a correc-tion for limb darkening which we fixed to a valueof 06 (Hestroffer amp Magnan 1998 Blanco-Cuaresma2019)
After working out the analysis of the Sun wefound an unexpected difficulty in obtaining the ro-tation velocity V sin i for our stars The problemcomes from the fact that in low mass stars the tur-bulence velocity Vmic and Vmac have values com-parable to V sin i (Doyle et al 2014) and there isconsequently no fail-proof recipe how to ldquoconstrainrdquothese velocities using the synthetic method Oneway to approach this problem (following differentresearchers in the field) is to adopt ad hoc valuesbased on theory or observation (Gray 1984ab Fis-cher amp Valenti 2005 Bruntt et al 2010 Tsantaki etal 2014 Doyle et al 2014) For our analysis we de-cided to adopt empirical values For Vmac we usedthe relation (Doyle et al 2014)
Vmac = a+ b∆T + c∆T 2 minus 200(log g minus 444) (3)
where ∆T = (Teffminus5777) a = 321 b = 233times10minus3
and c = 200 times 10minus6 For Vmic we used the relation
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 205
6500 6000 5500 5000
02
46
8
Teff (K)
vm
ac (
km
sminus1
)
Gray (1984)Valenti amp Fischer (2005)Doyle et al (2014)Bruntt et al (2010)
log g
49
455
42
385
35
Fig 4 Values of Vmac adopted for our analysis withiSpec as a function of our results for Teff
(Tsantaki et al 2014)
Vmic = 6932times 10minus4Teff minus 0348 log g minus 1437 (4)
Note that neither authors give uncertainties on thesevalues However Doyle et al (2014) suggest genericuncertainties of the order of plusmn 027 kms and plusmn 015for Vmac and Vmic respectively which we adopted forour study
In Figure 4 we show the final values of Vmac ob-tained in our analysis Traced over the data wedraw the different relations proposed in the litera-ture to fix this parameter At high temperatures(Teff gt 5800 K) one can see that our values forVmac are well above the upper limit determined byValenti amp Fischer (2005) while at low temperaturesthe values are well above the lower limit determinedby Bruntt et al (2010) In general our results forVmac are consistent with the values expected basedon the relation proposed by Gray (1984b)
Our final result for the Sun is shown in Table 2These values were obtained after only ten iterationsusing the parameters of the Sun as initial guess andfixing Vmac and Vmic using equation 3 and equa-tion 4 For comparison we also included in Table 2the values adopted for the Gaia Benchmark starsAlthough our best fit reproduces well the physicalcharacteristics of the Sun the uncertainty estimatedby iSpec for V sin i is relatively high But this as wealready explained is expected considering the prob-lem related to Vmic and Vmac The different solutions(as shown in Figure 4) to this problem might explainfor example why the macro turbulence we used forthe Sun is lower than what was used by Gaia In
TABLE 2
RESULTS FOR THE SOLAR SPECTRUMUSING ISPEC
Char iSpec Sun
Teff 5571 plusmn 30 K 5571 K
log g 444 plusmn 004 dex 444 dex
[MH] 000 plusmn 003 0
[FeH] 000 plusmn 003 0
V sin i 160 plusmn 145 kms 160 kms
Vmic 102 kms 107 kms
Vmac 319 kms 421 kms
rms of fit 00289
Gaia benchmark Stars values(Blanco-Cuaresma 2019)
Doyle et al (2014) the authors already noted a simi-lar difference by comparing the values they obtainedby their relation with results reported by Fischer ampValenti (2005) where the Vmac were systematicallyhigher by as much as 054 km sminus1 However addingthis difference (as a systematic correction) to bringour result for Vmac closer to the value proposed inthe Gaia Benchmark did not lower the uncertaintieson V sin i obtained with iSpec Therefore consider-ing that our method easily reproduces the value ofV sin i for the Sun we judged more realistic to keepa high uncertainty on this parameter Besides thequestion is possibly more complex considering theuncertainty on the existence of a J minus M relationJlowast prop Mα for low mass stars (Herbst et al 2007)and taking into account that V sin i might also de-pend on the age of the star (that is decreasing withthe age Kraft 1967 Wilson 1963 Skumanich 1972)
For the analysis of the stars our semi-automaticmethod can be summarized in the following way Wefirst run iSpec using the parameters of the Sun asinitial input This implies calculating Vmac and Vmicusing equation 3 and equation 4 keeping these valuesfixed and leaving all the other parameters free Theresults of the first run give us new values of Teff andlog g based on which we calculate new initial valuesfor Vmac and Vmic before running iSpec a secondtime
To verify our solutions for each star we use thefinal value of Teff to calculate its mass and radius(first we get the mass then the corresponding ra-dius) using the mass-luminosity relation for starswith masses between 043 M and 2 M (Wang ampZhong 2018)
M
M=
(L
L
)14
=TeffT
(R
R
)12
(5)
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206 FLOR-TORRES ET AL
where L is the bolometric luminosity as determinedfrom its magnitude in V and its distance calculatedfrom Gaia in Table 1 Then we verify that the valueof log g given by iSpec is consistent with the massand radius obtained using the relation (equation 7in Valenti amp Debra 2005)
log(MM) = log(glowast) + 2 log(RR)minus 4437 (6)
In general we obtained consistent values forlog g within the generic errors suggested by Doyleet al (2014) However for eight stars we founddiscrepant masses the masses obtained using equa-tion 6 being higher than the masses using equation 5To solve this problem we found it important to bet-ter constrain the initial value of log g before runningiSpec a second time The reason for this constraint isphysically clear since as shown by equation 5 andequation 6 log g is coupled to Teff In Valenti ampDebra (2005) for example the authors took into ac-count this coupling by first fixing the initial valueof Teff related to the B minus V color of the star thenused a generic log g consistent with this temperatureIn our case we decided to use as initial parametersfor the second run the value of Teff obtained fromthe first run with iSpec (which uses the values ofthe Sun as first guesses) and to use as second guessthe value of log g given by equation 6 that makesthe two masses consistent This also implies recal-culating Vmac and Vmic for these new values whichas before are kept fixed running iSpec The uniqueconsequence of adding this constraint for the eightstars with discrepant masses was to lower the finalvalues of their log(g) all the other parameters beingequal For each star our method requires only tworuns of ten iterations each which amounts to about30 minutes CPU time on a fast desktop computerThis makes our analysis process quite efficient
4 RESULTS CHARACTERIZATION OF THEHOST STARS OF EXOPLANETS OBSERVED
WITH TIGRE
Our measurements for the physical parameters of thehost stars as determined with our semi-automaticmethod are presented in Table 3 Note that for themetallicities [MH] and [FeH] an extra correc-tion was needed following Valenti amp Debra (2005)to eliminate spurious abundance trends (see theirexplanations in sect 64) This correction is based onthe assumption that the ratio of one elemental abun-dance to another must not vary systematically withthe temperature The correction then is simple itconsists in tracing the metallicities as a function of
Teff fitting a second order relation then subtract-ing this spurious relation from the data All theuncertainties reported in Table 3 were calculated byiSpec while the errors of the radii and masses arethe quadratic sums of the uncertainties of the pa-rameters used to calculate these values (see sect 72in Valenti amp Debra 2005) As explained in Valentiamp Debra (2005) and in Piskunov amp Valenti (2017)the uncertainties estimated by the algorithms thatproduce the synthetic spectra and fit them to theobserved spectra are usually undetermined as com-pared to the random errors calculated from the mea-surements of multiple observations of the stars (sect 63in Valenti amp Debra 2005) Unfortunately multipleobservations were not programmed for our stars andwe have only 4 stars in our study (17 19 23 and46) that were observed more than once (four timesfor three and six times for the fourth one) Thismeans that only a rough estimate of the random er-ror can be obtained for our pilot-survey by calculat-ing for each of these stars the standard deviations ofthe parameters measured applying the same spectralanalysis as for the other stars In table 4 we compareour mean uncertainties as obtained with iSpec withthe mean of the standard deviations for the multi-ply observed stars in our sample Except for V sin ithe mean empirical errors are much larger than theiSpec values In particular our empirical errors arelarger than the empirical uncertainties calculated byValenti amp Debra (Figure 9 in 2005) being compara-ble to their 2 sigma probabilities (the values in thetable correspond to 1 sigma the threshold that in-cludes 683 of their error measurements)
Comparing with the Exoplanetsorg andSWEETcat mean uncertainties our mean errors(standard deviations of multiple stars) are slightlylarger although still comparable to those reportedin these studies Although preliminary this resultis important as it suggests that our results based oniSpec analysis of low resolution spectra (R asymp 20 000)are in good agreement with results obtained usinghigher resolution spectra (R higher than 50000)
Another way to verify the consistency of ourdata is to compare our results with those publishedin Exoplanetsorg (on the left in Figure 5) and inSWEET-Cat (on the right) Taken as a whole ourresults seem compatible with the data reported inthese two catalogs (note that the uncertainties arethose of iSpec) although there are also slight no-table differences In Figure 5a our values for Teffare slightly higher below 5800 K than the values re-ported by Exoplanetsorg and SWEET-Cat How-ever above 6000 K our temperatures are compa-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
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Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
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log(g) [this work]
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) [E
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]
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-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
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[E
xopla
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org
]
e)
0 5 10 15 20 25 300
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15
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V sin i (kms) [this work]
V s
in i (
km
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[Exopla
nets
org
]
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Teff (K) [this work]
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[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
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V sin i (kms)
V s
in i V
mac
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a)
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V sin i (kms) [this work]
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in i (
km
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[Exopla
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org
]
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3336
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b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
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03
04
05
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Teff (K)
V s
in i (
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log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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02
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stitu
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no
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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AJ 154 123Gray D F 1984a ApJ 277 640
1984b ApJ 281 719Gray R O amp Corbally C J 1994 AJ 107 742Grevesse N Asplund M Sauval A J amp Scott P
2010 ApampSS 328 179Han E Wang S X Wright J T et al 2014 PASP
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Hellier C Anderson D R Collier Cameron A et al2015 AJ 150 18
Hempelmann A Mittag M Gonzalez-Perez J N et al2016 AampA 586 14
Henry G W Marcy G W Butler R P amp Vogt SS 2000 ApJ 529 41
Herbst W Eisloeffel J Mundt R amp Scholz A 2007in Protostars and Planets V ed V B Reipurth DJewitt amp K Keil (Tuczon AZ UAP) 927
Hestroffer D amp Magnan C 1998 AampA 333 338Hinkel N R Timmes F X Young P A et al 2014
AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
ApJS 226 4Howard A W Johnson J A Marcy G W et al
2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
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Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
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Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
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ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
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Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
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216 FLOR-TORRES ET AL
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2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
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773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
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Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
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2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
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ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 205
6500 6000 5500 5000
02
46
8
Teff (K)
vm
ac (
km
sminus1
)
Gray (1984)Valenti amp Fischer (2005)Doyle et al (2014)Bruntt et al (2010)
log g
49
455
42
385
35
Fig 4 Values of Vmac adopted for our analysis withiSpec as a function of our results for Teff
(Tsantaki et al 2014)
Vmic = 6932times 10minus4Teff minus 0348 log g minus 1437 (4)
Note that neither authors give uncertainties on thesevalues However Doyle et al (2014) suggest genericuncertainties of the order of plusmn 027 kms and plusmn 015for Vmac and Vmic respectively which we adopted forour study
In Figure 4 we show the final values of Vmac ob-tained in our analysis Traced over the data wedraw the different relations proposed in the litera-ture to fix this parameter At high temperatures(Teff gt 5800 K) one can see that our values forVmac are well above the upper limit determined byValenti amp Fischer (2005) while at low temperaturesthe values are well above the lower limit determinedby Bruntt et al (2010) In general our results forVmac are consistent with the values expected basedon the relation proposed by Gray (1984b)
Our final result for the Sun is shown in Table 2These values were obtained after only ten iterationsusing the parameters of the Sun as initial guess andfixing Vmac and Vmic using equation 3 and equa-tion 4 For comparison we also included in Table 2the values adopted for the Gaia Benchmark starsAlthough our best fit reproduces well the physicalcharacteristics of the Sun the uncertainty estimatedby iSpec for V sin i is relatively high But this as wealready explained is expected considering the prob-lem related to Vmic and Vmac The different solutions(as shown in Figure 4) to this problem might explainfor example why the macro turbulence we used forthe Sun is lower than what was used by Gaia In
TABLE 2
RESULTS FOR THE SOLAR SPECTRUMUSING ISPEC
Char iSpec Sun
Teff 5571 plusmn 30 K 5571 K
log g 444 plusmn 004 dex 444 dex
[MH] 000 plusmn 003 0
[FeH] 000 plusmn 003 0
V sin i 160 plusmn 145 kms 160 kms
Vmic 102 kms 107 kms
Vmac 319 kms 421 kms
rms of fit 00289
Gaia benchmark Stars values(Blanco-Cuaresma 2019)
Doyle et al (2014) the authors already noted a simi-lar difference by comparing the values they obtainedby their relation with results reported by Fischer ampValenti (2005) where the Vmac were systematicallyhigher by as much as 054 km sminus1 However addingthis difference (as a systematic correction) to bringour result for Vmac closer to the value proposed inthe Gaia Benchmark did not lower the uncertaintieson V sin i obtained with iSpec Therefore consider-ing that our method easily reproduces the value ofV sin i for the Sun we judged more realistic to keepa high uncertainty on this parameter Besides thequestion is possibly more complex considering theuncertainty on the existence of a J minus M relationJlowast prop Mα for low mass stars (Herbst et al 2007)and taking into account that V sin i might also de-pend on the age of the star (that is decreasing withthe age Kraft 1967 Wilson 1963 Skumanich 1972)
For the analysis of the stars our semi-automaticmethod can be summarized in the following way Wefirst run iSpec using the parameters of the Sun asinitial input This implies calculating Vmac and Vmicusing equation 3 and equation 4 keeping these valuesfixed and leaving all the other parameters free Theresults of the first run give us new values of Teff andlog g based on which we calculate new initial valuesfor Vmac and Vmic before running iSpec a secondtime
To verify our solutions for each star we use thefinal value of Teff to calculate its mass and radius(first we get the mass then the corresponding ra-dius) using the mass-luminosity relation for starswith masses between 043 M and 2 M (Wang ampZhong 2018)
M
M=
(L
L
)14
=TeffT
(R
R
)12
(5)
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206 FLOR-TORRES ET AL
where L is the bolometric luminosity as determinedfrom its magnitude in V and its distance calculatedfrom Gaia in Table 1 Then we verify that the valueof log g given by iSpec is consistent with the massand radius obtained using the relation (equation 7in Valenti amp Debra 2005)
log(MM) = log(glowast) + 2 log(RR)minus 4437 (6)
In general we obtained consistent values forlog g within the generic errors suggested by Doyleet al (2014) However for eight stars we founddiscrepant masses the masses obtained using equa-tion 6 being higher than the masses using equation 5To solve this problem we found it important to bet-ter constrain the initial value of log g before runningiSpec a second time The reason for this constraint isphysically clear since as shown by equation 5 andequation 6 log g is coupled to Teff In Valenti ampDebra (2005) for example the authors took into ac-count this coupling by first fixing the initial valueof Teff related to the B minus V color of the star thenused a generic log g consistent with this temperatureIn our case we decided to use as initial parametersfor the second run the value of Teff obtained fromthe first run with iSpec (which uses the values ofthe Sun as first guesses) and to use as second guessthe value of log g given by equation 6 that makesthe two masses consistent This also implies recal-culating Vmac and Vmic for these new values whichas before are kept fixed running iSpec The uniqueconsequence of adding this constraint for the eightstars with discrepant masses was to lower the finalvalues of their log(g) all the other parameters beingequal For each star our method requires only tworuns of ten iterations each which amounts to about30 minutes CPU time on a fast desktop computerThis makes our analysis process quite efficient
4 RESULTS CHARACTERIZATION OF THEHOST STARS OF EXOPLANETS OBSERVED
WITH TIGRE
Our measurements for the physical parameters of thehost stars as determined with our semi-automaticmethod are presented in Table 3 Note that for themetallicities [MH] and [FeH] an extra correc-tion was needed following Valenti amp Debra (2005)to eliminate spurious abundance trends (see theirexplanations in sect 64) This correction is based onthe assumption that the ratio of one elemental abun-dance to another must not vary systematically withthe temperature The correction then is simple itconsists in tracing the metallicities as a function of
Teff fitting a second order relation then subtract-ing this spurious relation from the data All theuncertainties reported in Table 3 were calculated byiSpec while the errors of the radii and masses arethe quadratic sums of the uncertainties of the pa-rameters used to calculate these values (see sect 72in Valenti amp Debra 2005) As explained in Valentiamp Debra (2005) and in Piskunov amp Valenti (2017)the uncertainties estimated by the algorithms thatproduce the synthetic spectra and fit them to theobserved spectra are usually undetermined as com-pared to the random errors calculated from the mea-surements of multiple observations of the stars (sect 63in Valenti amp Debra 2005) Unfortunately multipleobservations were not programmed for our stars andwe have only 4 stars in our study (17 19 23 and46) that were observed more than once (four timesfor three and six times for the fourth one) Thismeans that only a rough estimate of the random er-ror can be obtained for our pilot-survey by calculat-ing for each of these stars the standard deviations ofthe parameters measured applying the same spectralanalysis as for the other stars In table 4 we compareour mean uncertainties as obtained with iSpec withthe mean of the standard deviations for the multi-ply observed stars in our sample Except for V sin ithe mean empirical errors are much larger than theiSpec values In particular our empirical errors arelarger than the empirical uncertainties calculated byValenti amp Debra (Figure 9 in 2005) being compara-ble to their 2 sigma probabilities (the values in thetable correspond to 1 sigma the threshold that in-cludes 683 of their error measurements)
Comparing with the Exoplanetsorg andSWEETcat mean uncertainties our mean errors(standard deviations of multiple stars) are slightlylarger although still comparable to those reportedin these studies Although preliminary this resultis important as it suggests that our results based oniSpec analysis of low resolution spectra (R asymp 20 000)are in good agreement with results obtained usinghigher resolution spectra (R higher than 50000)
Another way to verify the consistency of ourdata is to compare our results with those publishedin Exoplanetsorg (on the left in Figure 5) and inSWEET-Cat (on the right) Taken as a whole ourresults seem compatible with the data reported inthese two catalogs (note that the uncertainties arethose of iSpec) although there are also slight no-table differences In Figure 5a our values for Teffare slightly higher below 5800 K than the values re-ported by Exoplanetsorg and SWEET-Cat How-ever above 6000 K our temperatures are compa-
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
5
6
7
8
10
11
1213
1415
16
17
18
19
21
22
23
24
27
28
2930
31
3233
35
36
37
38
4041
42
43
44
45 46
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
12
13
14
15
16
17
18
19
21
22
24
25
26
2728 29
30
32
33
34
36
38
40
41
43
44
a)
0 1 2 3 4 50
1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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206 FLOR-TORRES ET AL
where L is the bolometric luminosity as determinedfrom its magnitude in V and its distance calculatedfrom Gaia in Table 1 Then we verify that the valueof log g given by iSpec is consistent with the massand radius obtained using the relation (equation 7in Valenti amp Debra 2005)
log(MM) = log(glowast) + 2 log(RR)minus 4437 (6)
In general we obtained consistent values forlog g within the generic errors suggested by Doyleet al (2014) However for eight stars we founddiscrepant masses the masses obtained using equa-tion 6 being higher than the masses using equation 5To solve this problem we found it important to bet-ter constrain the initial value of log g before runningiSpec a second time The reason for this constraint isphysically clear since as shown by equation 5 andequation 6 log g is coupled to Teff In Valenti ampDebra (2005) for example the authors took into ac-count this coupling by first fixing the initial valueof Teff related to the B minus V color of the star thenused a generic log g consistent with this temperatureIn our case we decided to use as initial parametersfor the second run the value of Teff obtained fromthe first run with iSpec (which uses the values ofthe Sun as first guesses) and to use as second guessthe value of log g given by equation 6 that makesthe two masses consistent This also implies recal-culating Vmac and Vmic for these new values whichas before are kept fixed running iSpec The uniqueconsequence of adding this constraint for the eightstars with discrepant masses was to lower the finalvalues of their log(g) all the other parameters beingequal For each star our method requires only tworuns of ten iterations each which amounts to about30 minutes CPU time on a fast desktop computerThis makes our analysis process quite efficient
4 RESULTS CHARACTERIZATION OF THEHOST STARS OF EXOPLANETS OBSERVED
WITH TIGRE
Our measurements for the physical parameters of thehost stars as determined with our semi-automaticmethod are presented in Table 3 Note that for themetallicities [MH] and [FeH] an extra correc-tion was needed following Valenti amp Debra (2005)to eliminate spurious abundance trends (see theirexplanations in sect 64) This correction is based onthe assumption that the ratio of one elemental abun-dance to another must not vary systematically withthe temperature The correction then is simple itconsists in tracing the metallicities as a function of
Teff fitting a second order relation then subtract-ing this spurious relation from the data All theuncertainties reported in Table 3 were calculated byiSpec while the errors of the radii and masses arethe quadratic sums of the uncertainties of the pa-rameters used to calculate these values (see sect 72in Valenti amp Debra 2005) As explained in Valentiamp Debra (2005) and in Piskunov amp Valenti (2017)the uncertainties estimated by the algorithms thatproduce the synthetic spectra and fit them to theobserved spectra are usually undetermined as com-pared to the random errors calculated from the mea-surements of multiple observations of the stars (sect 63in Valenti amp Debra 2005) Unfortunately multipleobservations were not programmed for our stars andwe have only 4 stars in our study (17 19 23 and46) that were observed more than once (four timesfor three and six times for the fourth one) Thismeans that only a rough estimate of the random er-ror can be obtained for our pilot-survey by calculat-ing for each of these stars the standard deviations ofthe parameters measured applying the same spectralanalysis as for the other stars In table 4 we compareour mean uncertainties as obtained with iSpec withthe mean of the standard deviations for the multi-ply observed stars in our sample Except for V sin ithe mean empirical errors are much larger than theiSpec values In particular our empirical errors arelarger than the empirical uncertainties calculated byValenti amp Debra (Figure 9 in 2005) being compara-ble to their 2 sigma probabilities (the values in thetable correspond to 1 sigma the threshold that in-cludes 683 of their error measurements)
Comparing with the Exoplanetsorg andSWEETcat mean uncertainties our mean errors(standard deviations of multiple stars) are slightlylarger although still comparable to those reportedin these studies Although preliminary this resultis important as it suggests that our results based oniSpec analysis of low resolution spectra (R asymp 20 000)are in good agreement with results obtained usinghigher resolution spectra (R higher than 50000)
Another way to verify the consistency of ourdata is to compare our results with those publishedin Exoplanetsorg (on the left in Figure 5) and inSWEET-Cat (on the right) Taken as a whole ourresults seem compatible with the data reported inthese two catalogs (note that the uncertainties arethose of iSpec) although there are also slight no-table differences In Figure 5a our values for Teffare slightly higher below 5800 K than the values re-ported by Exoplanetsorg and SWEET-Cat How-ever above 6000 K our temperatures are compa-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
5
6
7
8
10
11
1213
1415
16
17
18
19
21
22
23
24
27
28
2930
31
3233
35
36
37
38
4041
42
43
44
45 46
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
12
13
14
15
16
17
18
19
21
22
24
25
26
2728 29
30
32
33
34
36
38
40
41
43
44
a)
0 1 2 3 4 50
1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 207
TABLE 3
PHYSICAL PARAMETERS OF THE HOST STARS OF EXOPLANETS IN OUR SAMPLEAS DETERMINED WITH ISPEC
No Name Teff ∆Teff log g ∆log g [MH] ∆[MH ] [FeH ] ∆[FeH ] V sin i ∆V sin i Vmic Vmac rms Rlowast ∆Rlowast Mlowast ∆Mlowastof star (K) (K) (kms) (kms) (kms) (kms) (R) (R) (M) (M)
1 KELT-6 6176 24 403 005 minus038 002 minus014 003 652 082 144 528 00292 171 020 122 020
2 HD 219134 5209 13 490 000 000 002 002 001 709 030 047 161 00318 054 009 077 009
3 KEPLER-37 5520 19 450 004 minus040 002 minus028 002 662 050 082 262 00317 071 015 088 015
4 HD 46375 5345 22 447 004 minus005 001 011 001 201 073 071 252 00319 083 001 088 002
5 HD 75289 6196 23 416 006 016 002 042 002 411 056 141 510 00291 127 001 114 003
6 HD 88133 5582 16 405 003 015 001 034 001 198 076 102 361 00344 180 001 112 002
7 HD 149143 6067 20 436 004 017 002 048 002 353 061 125 422 00316 164 010 119 010
8 HAT-P-30 6177 30 381 008 006 004 015 003 888 060 152 572 00324 151 019 119 019
9 KELT-3 6404 26 420 005 002 003 024 002 851 057 154 593 00294 177 016 128 016
10 KEPLER-21 6256 31 402 006 minus007 003 011 003 738 057 150 563 00317 196 010 128 010
11 KELT-2A 6164 22 374 005 minus004 003 019 002 728 051 153 581 00315 201 010 127 010
12 HD86081 6015 19 394 006 014 002 038 002 401 057 136 488 00314 163 013 118 013
13 WASP-74 5727 14 370 003 014 002 022 002 824 038 125 458 00341 157 015 111 016
14 HD 149026 6096 14 406 002 025 002 038 002 528 049 138 492 00302 151 010 117 010
15 HD 209458 5988 17 417 006 minus022 003 minus001 002 296 086 126 433 00282 125 010 110 010
16 BD-10 3166 5578 23 464 004 022 001 039 002 688 038 082 243 00361 082 017 092 017
17 HD 189733 5374 18 489 004 minus004 001 009 001 275 060 059 170 00287 060 001 082 002
18 HD 97658 5468 20 468 004 minus039 001 minus017 001 187 085 072 220 00320 062 001 084 002
19 HAT-P-7 6270 46 395 012 minus001 007 043 005 570 144 153 582 00312 221 019 132 020
20 KELT-7 6508 38 395 013 minus019 001 015 004 452 139 170 696 00269 201 015 134 017
21 HAT-P-14 6490 35 412 007 minus011 004 009 003 886 065 163 653 00293 169 015 128 016
22 WASP-14 6195 24 360 004 minus033 003 minus023 003 147 211 160 621 00298 150 015 119 015
23 HAT-P-2 6439 24 405 005 015 003 029 003 2066 058 162 641 00254 179 010 129 010
24 WASP-38 6178 18 395 004 minus010 003 015 002 747 054 147 544 00301 149 013 118 013
25 HD 118203 5847 31 406 006 004 001 019 002 416 058 120 414 00321 204 010 121 010
26 HD 2638 5564 18 490 000 014 002 038 002 330 062 071 188 00355 072 013 089 013
27 WASP-13 6025 29 389 003 minus001 003 012 003 235 130 139 501 00344 162 020 118 020
28 WASP-34 5771 27 444 004 minus031 003 000 003 160 139 102 320 00326 108 020 102 020
29 WASP-82 6257 28 396 008 minus005 004 022 003 286 123 152 575 00331 216 017 131 018
30 HD17156 5985 22 410 005 minus006 001 009 002 302 078 129 446 00303 158 010 116 010
31 XO-3 6281 30 416 010 minus012 004 minus019 003 202 073 147 545 00270 183 016 127 016
32 HD 33283 5877 16 381 003 005 002 032 002 439 047 131 472 00320 199 009 121 009
33 HD 217014 5755 12 443 003 minus030 001 minus001 002 040 143 101 318 00312 116 019 104 019
34 HD 115383 5891 19 419 004 minus016 002 022 002 811 040 119 400 00285 141 001 111 002
35 HAT-P-6 6442 34 405 005 004 002 minus010 003 117 071 162 643 00440 170 017 128 018
36 HD 75732 5548 17 489 003 019 001 038 001 017 161 071 188 00338 080 019 091 019
37 HD 120136 6210 17 379 004 020 002 020 002 1514 036 155 589 00292 161 019 121 019
38 WASP-76 6133 21 390 004 010 002 040 002 224 100 146 537 00301 203 016 127 016
39 HN-PEG 5853 18 441 004 minus037 002 003 002 1002 041 109 346 00337 103 001 102 002
40 WASP-8 5735 55 462 013 010 002 039 004 645 107 093 276 00308 089 019 097 020
41 WASP-69 5197 15 490 000 022 001 030 001 118 107 046 161 00360 058 015 078 015
42 HAT-P-34 6494 33 422 007 014 004 038 004 2532 080 160 635 00287 157 019 126 019
43 HAT-P-1 6142 24 415 006 014 002 021 003 565 066 138 491 00330 141 010 116 010
44 WASP-94A 5988 23 376 004 017 003 038 002 555 060 141 515 00338 180 017 120 018
45 WASP-111 6312 32 394 008 005 004 030 003 1157 054 157 603 00308 212 018 132 018
46 HAT-P-8 6009 60 406 009 015 005 minus012 007 1368 109 132 462 00365 155 016 116 016
rable with those in Exoplanetsorg while clearlylower compared to SWEET-Cat The largest dif-ference between our results and those of the twoother surveys is for log g Compared with Exoplan-etsorg (Figure 5c) our values for log g are com-parable within the range 4-47 dex only slightly
underestimated Above 47 dex our values tendto be overestimated while below 4 dex they areunderestimated These differences are amplifiedcomparing with SWEET-Cat in Figure 5d Onceagain however we must conclude that these dif-ferences already existed comparing Exoplanetsorg
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
5
6
7
8
10
11
1213
1415
16
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22
23
24
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2930
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3233
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4041
42
43
44
45 46
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
12
13
14
15
16
17
18
19
21
22
24
25
26
2728 29
30
32
33
34
36
38
40
41
43
44
a)
0 1 2 3 4 50
1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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10
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57
01
15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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1 In
stitu
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
Joshi Y C Pollacco D Collier Cameron A et al2009 MNRAS 392 1532
Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
H C amp Weiss W W 1999 AampAS 138 119Kupka F amp Dubernet M-L 2011 BaltA 20 503Kurucz R L 2005 MSAIS 8 14Kuzuhara M Tamura M Kudo T et al 2013 ApJ
774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
1996 Natur 380 606Luhman K L Patten B M Marengo M et al 2007
ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
536 43Marcy G W Butler R P Fischer D A et al 2002
ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
2015 ApJ 810 105Marzari F amp Weidenschilling S J 2002 Icar 156 570Mayor M amp Queloz D 1995 Natur 378 355McBride N amp Gilmour I 2004 An Introduction to the
Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
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216 FLOR-TORRES ET AL
Mittag M Schroder K-P Hempelmann A Gonzalez-Perez J N amp Schmitt J H M M 2016 AampA 59189
Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
673 79Moutou C Mayor M Bouchy F et al 2005 AampA
439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
S Blanco-Cuaresma Harvard-Smithsonian Center for Astrophysics Cambridge MA USAR Coziol L M Flor-Torres D Jack and K-P Schroder Departamento de Astronomıa Universidad de
Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
AampA 502 391Skumanich A 1972 ApJ 171 565Smalley B Anderson D R Collier Cameron A et al
2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
2008 AampA 620 58Stauffer J R amp Hartman L W 1986 PASP 98 1233Tassoul J-L 2000 Stellar Rotation (New York NY
CUP) doi101017CBO9780511546044Torres G Bakos G A Hartman J et al 2010 ApJ
715 458Tsantaki M Sousa S G Santos N C et al 2014
AampA 570 80Udry S Mayor M Naef D et al 2000 AampA 356
590Udry S amp Santos N C 2007 ARAampA 45 397Uzdensky D A Konigl A amp Litwin C 2002 ApJ
565 1191Valencia D OrsquoConnell R J amp Sasselov D 2006 Icar
181 545Valenti J A amp Debra A 2005 ApJS 159 141van der Marel N Williams J P amp Bruderer S 2018
ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
D P amp Mandell A M 2011 Natur 475 206Wang J amp Zhong Z 2018 AampA 619 1Weidenschilling S J amp Marzari F 1996 Natur 384
619West R G Hellier C Almenara J-M et al 2016
AampA 585 126Wilson O C 1963 ApJ 138 832Wolff S amp Simon T 1997 PASP 109 759
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208 FLOR-TORRES ET AL
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[Exopla
nets
org
]
a)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [E
xopla
nets
org
]
c)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[E
xopla
nets
org
]
e)
0 5 10 15 20 25 300
5
10
15
20
25
30
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
1
234
5
6
7
8
10
11
1213
1415
16
17
18
19
21
22
23
24
27
28
2930
31
3233
35
36
37
38
4041
42
43
44
45 46
5200 5400 5600 5800 6000 6200 6400 6600
4500
5000
5500
6000
6500
7000
Teff (K) [this work]
Teff (
K)
[S
WE
ET-C
at]
b)
35 40 45 50
35
40
45
50
log(g) [this work]
log(g
) [S
WE
ET-C
at]
d)
-04 -02 00 02 04 06
-04
-02
00
02
04
06
FeH [this work]
FeH
[S
WE
ET-C
at]
f)
06 08 10 12 14 16
06
08
10
12
14
16
MM
[this work]
MM
[S
WE
ET-C
at]
h)
Exoplanetsorg
Fig 5 Comparison of our results with those in Exoplanetsorg (left) and SWEET-Cat (right) a) and b) Teff c) andd) log g e) and f) [FeH] g) V sin i h) the mass of the stars Mlowast with data for Exoplanetsorg included
with SWEET-Cat Despite the above differencesour metallicities in Figure 5e and Figure 5f are com-parable with those published both by Exoplanetsorgand SWEET-Cat Once again our results seem moresimilar to the former than to the latter
The most important comparison for the purposeof our survey is for V sin i in Figure 5g Unfortu-nately we can only compare with Exoplanetsorgsince SWEET-Cat did not publish their resultsWhat we find is a very good agreement with only aslight trend for our values to be higher This trend
is most probably due to our lower resolution andto the different way we determined Vmic and Vmac(more about that will be said later) In Figure 5hwe compare the masses of the stars to those reportedby SWEET-Cat This time we observe a much bet-ter consistency Note that we have also included thevalues given by Exoplanetsorg (as open circles) Ingeneral our masses show a weak trend to be smalleralthough well within the uncertainties
To quantify the differences between our val-ues and those reported in Exoplanetsorg and
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
12
13
14
15
16
17
18
19
21
22
24
25
26
2728 29
30
32
33
34
36
38
40
41
43
44
a)
0 1 2 3 4 50
1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
copy C
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1 In
stitu
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15
214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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Batalha N M Rowe J F Bryson S T et al 2013ApJS 204 24
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stitu
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 215
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Beauge C amp Nesvorny D 2012 ApJ 751 119Berget D J amp Durrance S T 2010 Journal of the
Southeastern Association for Research in Astronomy3 32
Bieryla A Collins K Beatty T G et al 2015 AJ150 12
Blanco-Cuaresma S Soubiran C Heiter U amp JofreP 2014 AampA 569 111
Blanco-Cuaresma S 2019 MNRAS 486 2075Bland A P amp Schwenzer S P 2004 in An Introduction
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Borucki W J Koch D G Basri G et al 2011 ApJ736 19
Boss A P 1997 Sci 276 1836Bouchy F Udry S Mayor M et al 2005 AampA 444
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MNRAS 405 1907Butler R P Vogt S S Marcy G W et al 2000 ApJ
545 504Chabrier G Baraffe I Leconte J Gallardo J amp Bar-
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Charbonneau D B Brown T M Latham D W andMayor M 2000 ApJ 529 45
Chatterjee S Ford E B Matsumura S amp Rasio AF 2008 ApJ 686 580
Chiang E amp Laughlin G 2013 MNRAS 431 3444da Silva R Udry S Bouchy F et al 2006 AampA 446
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AampA 581 6Dawson R I amp Johnson J A 2018 ARAampA 56 175Doyle A P Davies G R Smalley B Chaplin W J
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MNRAS 494 750Fischer D A Laughlin G Butler P et al 2005 ApJ
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ApJ 637 1094Fischer D A Vogt S S Marcy G W et al 2007
ApJ 669 1336Gandolfi D Barragan O Hatzes A P et al 2017
AJ 154 123Gray D F 1984a ApJ 277 640
1984b ApJ 281 719Gray R O amp Corbally C J 1994 AJ 107 742Grevesse N Asplund M Sauval A J amp Scott P
2010 ApampSS 328 179Han E Wang S X Wright J T et al 2014 PASP
126 827
Hellier C Anderson D R Collier Cameron A et al2015 AJ 150 18
Hempelmann A Mittag M Gonzalez-Perez J N et al2016 AampA 586 14
Henry G W Marcy G W Butler R P amp Vogt SS 2000 ApJ 529 41
Herbst W Eisloeffel J Mundt R amp Scholz A 2007in Protostars and Planets V ed V B Reipurth DJewitt amp K Keil (Tuczon AZ UAP) 927
Hestroffer D amp Magnan C 1998 AampA 333 338Hinkel N R Timmes F X Young P A et al 2014
AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
ApJS 226 4Howard A W Johnson J A Marcy G W et al
2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
Planetary Systems and Host Stars PhD Thesis Col-lege of Science at Florida Institute of Technology
Jofre P Heiter U Soubiran C et al 2014 AampA 564133
Johns-Krull C M McCullough P R Burke C J etal 2008 ApJ 677 657
Johnson J A Marcy G W Fischer D A et al 2006ApJ 647 600
Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
Joshi Y C Pollacco D Collier Cameron A et al2009 MNRAS 392 1532
Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
H C amp Weiss W W 1999 AampAS 138 119Kupka F amp Dubernet M-L 2011 BaltA 20 503Kurucz R L 2005 MSAIS 8 14Kuzuhara M Tamura M Kudo T et al 2013 ApJ
774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
1996 Natur 380 606Luhman K L Patten B M Marengo M et al 2007
ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
536 43Marcy G W Butler R P Fischer D A et al 2002
ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
2015 ApJ 810 105Marzari F amp Weidenschilling S J 2002 Icar 156 570Mayor M amp Queloz D 1995 Natur 378 355McBride N amp Gilmour I 2004 An Introduction to the
Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
copy C
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216 FLOR-TORRES ET AL
Mittag M Schroder K-P Hempelmann A Gonzalez-Perez J N amp Schmitt J H M M 2016 AampA 59189
Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
673 79Moutou C Mayor M Bouchy F et al 2005 AampA
439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
S Blanco-Cuaresma Harvard-Smithsonian Center for Astrophysics Cambridge MA USAR Coziol L M Flor-Torres D Jack and K-P Schroder Departamento de Astronomıa Universidad de
Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
AampA 502 391Skumanich A 1972 ApJ 171 565Smalley B Anderson D R Collier Cameron A et al
2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
2008 AampA 620 58Stauffer J R amp Hartman L W 1986 PASP 98 1233Tassoul J-L 2000 Stellar Rotation (New York NY
CUP) doi101017CBO9780511546044Torres G Bakos G A Hartman J et al 2010 ApJ
715 458Tsantaki M Sousa S G Santos N C et al 2014
AampA 570 80Udry S Mayor M Naef D et al 2000 AampA 356
590Udry S amp Santos N C 2007 ARAampA 45 397Uzdensky D A Konigl A amp Litwin C 2002 ApJ
565 1191Valencia D OrsquoConnell R J amp Sasselov D 2006 Icar
181 545Valenti J A amp Debra A 2005 ApJS 159 141van der Marel N Williams J P amp Bruderer S 2018
ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
D P amp Mandell A M 2011 Natur 475 206Wang J amp Zhong Z 2018 AampA 619 1Weidenschilling S J amp Marzari F 1996 Natur 384
619West R G Hellier C Almenara J-M et al 2016
AampA 585 126Wilson O C 1963 ApJ 138 832Wolff S amp Simon T 1997 PASP 109 759
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 209
TABLE 4
COMPARISON OF ERRORS
Errors Teff log g [FeH] V sin i
(K) (dex) (dex) (kms)
Standard deviations 73 014 008 08
iSpec 25 005 002 08
Valenti amp Fischer 44 006 003 05
Exoplanetsorg 66 006 007 07
SWEET-Cat 52 010 004
SWEET-Cat we compare in Table 5 the medians andmeans (note that since the numbers of stars in thecomparisons vary the means and medians are notthe same) In both cases we also determined if thedifferences were statistically significant using non-parametric Mann-Whitney tests (Dalgaard 2008)The last two columns in Table 5 report the p-valuesof the tests and the level of significance of the differ-ences (at a level of confidence of 95) As one cansee the only parameter distributions that are sig-nificantly different are the surface gravity which isslightly lower in our work than in Exoplanetsorg andSWEET-Cat The statistical test also confirms thatthe difference is more significant comparing our datawith SWEET-Cat than with Exoplanetsorg (p-value00008 instead of 00195) Considered as a wholetherefore these tests suggest that our results arequite comparable with those reported in the liter-ature
As we mentioned before as the temperature ofthe stars goes down Vmic and Vmac become compa-rable to V sin i and thus it is more complicated toseparate one from the others In the Valenti amp De-bra (2005) spectral synthesis analysis the authorsrecognized this problem stating in particular thatldquoadopting a global macroturbulence relationshipshould yield more accurate results than solving forVmac in each individual spectrumrdquo To determinesuch relation they fixed V sin i = 0 obtaining themaximum values Vmac could have at different tem-peratures Note that these authors did not reportany dependence on the spectral resolution althoughthey used spectra with R between 50000 and almost100000 The maximum relation they deduced can beseen in Figure 4 According to these authors belowTeff = 5800 K V sin i becomes negligible and whatwe measure then must be the ldquorealrdquo Vmac Howeverthis conclusion contradicts what was expected basedon the semi-empirical relation established by Gray(1984b) and later the minimum relation for Vmac ob-tained by Bruntt et al (2010) by line modeling (the
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
V sin i (kms)
V s
in i V
mac
1
2
3
4 5
6
7
8
910
11
12
13
14
15
16
17
18
19
21
22
24
25
26
2728 29
30
32
33
34
36
38
40
41
43
44
a)
0 1 2 3 4 50
1
2
3
4
5
V sin i (kms) [this work]
V s
in i (
km
s)
[Exopla
nets
org
]
4
5
6
7
12
15
17
18
22
28
29
30
32
3336
38
41
b)
Fig 6 a) The ratio V sin iVmac as a function of V sin iBelow V sin i = 4 the ratios are lower than 1 Three stars33 36 and 22 have iSpec have values with uncertaintiesthat include zero b) Zoom of the region in Figure 5gwith V sin i lt 5 kms
two relations can also be seen in Figure 4) Theseresults suggest that applying the right macro (andmicro) turbulence relationship one could obtain avalue of V sin i 6= 0 below Teff = 5800 K In fact inour analysis of the Sun we did reproduce the valueof V sin i using the relations for Vmic obtained byTsantaki et al (2014) and Vmac determined by Doyleet al (2014) both depending not only on Teff butalso on log g and where V sin i lt Vmac The ques-tion then is how low can V sin i be compared to Vmacand still be distinguishable by iSpec
In Figure 6a we compare V sin i with the ra-tio V sin iVmac What we observe is that belowV sin i = 4 kms the ratio is lower than one Asone can see in Figure 4 a value of Vmac = 4 kms(V sin iVmac = 1) corresponds to Teff asymp 5800 KTherefore our results are at the same time consis-tent with the conclusion of Valenti amp Debra (2005)since below Teff = 5800 K V sin i is lower thanVmac and consistent with Gray (1984a) Bruntt et
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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216 FLOR-TORRES ET AL
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210 FLOR-TORRES ET AL
TABLE 5
COMPARISON WITH LITERATURE
TIGRE (45 stars) Exoplanets p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6025 5975 6095 5952 07679 ns
log g 406 418 426 428 00195
[FeH] 007 012 020 018 01638 ns
V sin i (kms) 555 739 410 692 02732 ns
Mlowast (M) 118 113 122 119 01010 ns
Rlowast (R) 157 147 134 136 00868 ns
TIGRE (44 stars) SWEET-Cat p-value sl
Parameter Units Median Mean Median Mean
Teff (K) 6046 5977 6133 6036 02936 ns
log g 406 418 433 434 00008
[FeH] 008 012 020 017 01973 ns
Mlowast (M) 118 113 124 118 00700 ns
al (2010) and Doyle et al (2014) since V sin i 6= 0But how low could a value of V sin i below Vmacbe We already answered this question in Figure 5gwhere we compared our values of V sin i with thevalues reported by Exoplanetsorg To get a bet-ter view in Figure 6b we zoom in on values ofV sin i le 5 kms Except for three stars 22 33and 36 with V sin iVmac lt 04 all the other starshave V sin i comparable to the values reported in Ex-oplanetsorg (in fact two of the stars 4 and 16 havehigher values) In Figure 6a note that the iSpec un-certainty increases as V sin i goes down As a con-sequence the possible values for stars 22 33 and 36include zero However could stars with V sin i = 0exist physically Considering that the loss of angularmomentum plays an important role in the formationof stars this would seem difficult to explain (notethat we did obtained V sin i = 0 for some stars in ourinitial list but they were not included in our study)Since the Gray (1984b) study the problem seemsclear how can we measure the rotation of a starwhere Vmac is as high or even higher than V sin i Itseems that the best approach is to assume an a pri-ori global relation and to see what comes out fromthe residual (Gray 1984ab Fischer amp Valenti 2005Bruntt et al 2010 Tsantaki et al 2014 Doyle et al2014) However to stay safe due to their higher un-certainties we should not consider stars 22 33 and36 in our statistical analysis for V sin i
Considering the results above one expects therotation to decrease with the temperature but stillbe above zero for cool stars Moreover since Tsan-
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
12
3
4
5
6
7
89
10 11
12
13
14
15
16
1718
19
20
21
22
23
24
2526
2728
29 30
31
32
33
34
35
36
37
38
39
40
41
42
43 44
45
46
log g
49
455
42
385
35
Fig 7 Exponential relation between the rotational ve-locity the temperature and the surface gravity for the46 stars in our sample The black triangle representsthe Sun The gray area corresponds to the interval ofconfidence and the dashed curves delimit the predictioninterval
taki et al (2014) and Doyle et al (2014) have foundrelations for Vmic and Vmac that depend not only onTeff but also on on log g we might expect a similarrelation for V sin i Teff and log g In Figure 7 weshow the diagram of V sin i and Teff for our starsThe dependence on log g is shown by the gray-scalebar In Figure 7 we also traced over our data the bi-exponential relation we obtained together with theinterval of confidence (in gray) and the prediction in-
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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1 In
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22
20
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51
10
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21
57
01
15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
copy C
op
yri
gh
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02
1 In
stitu
to d
e A
stro
no
miacutea
U
niv
ers
ida
d N
ac
ion
al A
utoacute
no
ma
de
Meacute
xic
oD
OI h
ttp
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10
22
20
1i
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10
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01
15
214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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op
yri
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t 2
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1 In
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20
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57
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 215
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Beauge C amp Nesvorny D 2012 ApJ 751 119Berget D J amp Durrance S T 2010 Journal of the
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Bieryla A Collins K Beatty T G et al 2015 AJ150 12
Blanco-Cuaresma S Soubiran C Heiter U amp JofreP 2014 AampA 569 111
Blanco-Cuaresma S 2019 MNRAS 486 2075Bland A P amp Schwenzer S P 2004 in An Introduction
to the Solar System ed D A Rothery N McBrideand I Gilmour (New York NY CUP) 129
Borucki W J Koch D G Basri G et al 2011 ApJ736 19
Boss A P 1997 Sci 276 1836Bouchy F Udry S Mayor M et al 2005 AampA 444
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MNRAS 405 1907Butler R P Vogt S S Marcy G W et al 2000 ApJ
545 504Chabrier G Baraffe I Leconte J Gallardo J amp Bar-
man T 2009 AIPC 1094 Cool Stars Stellar Systemsand the Sun 1094 12
Charbonneau D B Brown T M Latham D W andMayor M 2000 ApJ 529 45
Chatterjee S Ford E B Matsumura S amp Rasio AF 2008 ApJ 686 580
Chiang E amp Laughlin G 2013 MNRAS 431 3444da Silva R Udry S Bouchy F et al 2006 AampA 446
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York NY Springer) doi101007978-0-387-79054-1Damasso M Esposito M Nascimbeni V et al 2015
AampA 581 6Dawson R I amp Johnson J A 2018 ARAampA 56 175Doyle A P Davies G R Smalley B Chaplin W J
amp Elsworth Y 2014 MNRAS 444 3592Eisner N L Barragan O Aigrain S et al 2020
MNRAS 494 750Fischer D A Laughlin G Butler P et al 2005 ApJ
620 481Fischer D A amp Valenti J 2005 ApJ 622 1102Fischer D A Laughlin G Marcy G W et al 2006
ApJ 637 1094Fischer D A Vogt S S Marcy G W et al 2007
ApJ 669 1336Gandolfi D Barragan O Hatzes A P et al 2017
AJ 154 123Gray D F 1984a ApJ 277 640
1984b ApJ 281 719Gray R O amp Corbally C J 1994 AJ 107 742Grevesse N Asplund M Sauval A J amp Scott P
2010 ApampSS 328 179Han E Wang S X Wright J T et al 2014 PASP
126 827
Hellier C Anderson D R Collier Cameron A et al2015 AJ 150 18
Hempelmann A Mittag M Gonzalez-Perez J N et al2016 AampA 586 14
Henry G W Marcy G W Butler R P amp Vogt SS 2000 ApJ 529 41
Herbst W Eisloeffel J Mundt R amp Scholz A 2007in Protostars and Planets V ed V B Reipurth DJewitt amp K Keil (Tuczon AZ UAP) 927
Hestroffer D amp Magnan C 1998 AampA 333 338Hinkel N R Timmes F X Young P A et al 2014
AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
ApJS 226 4Howard A W Johnson J A Marcy G W et al
2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
Planetary Systems and Host Stars PhD Thesis Col-lege of Science at Florida Institute of Technology
Jofre P Heiter U Soubiran C et al 2014 AampA 564133
Johns-Krull C M McCullough P R Burke C J etal 2008 ApJ 677 657
Johnson J A Marcy G W Fischer D A et al 2006ApJ 647 600
Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
Joshi Y C Pollacco D Collier Cameron A et al2009 MNRAS 392 1532
Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
H C amp Weiss W W 1999 AampAS 138 119Kupka F amp Dubernet M-L 2011 BaltA 20 503Kurucz R L 2005 MSAIS 8 14Kuzuhara M Tamura M Kudo T et al 2013 ApJ
774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
1996 Natur 380 606Luhman K L Patten B M Marengo M et al 2007
ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
536 43Marcy G W Butler R P Fischer D A et al 2002
ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
2015 ApJ 810 105Marzari F amp Weidenschilling S J 2002 Icar 156 570Mayor M amp Queloz D 1995 Natur 378 355McBride N amp Gilmour I 2004 An Introduction to the
Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
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t 2
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1 In
stitu
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20
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18
51
10
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20
21
57
01
15
216 FLOR-TORRES ET AL
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Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
673 79Moutou C Mayor M Bouchy F et al 2005 AampA
439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
S Blanco-Cuaresma Harvard-Smithsonian Center for Astrophysics Cambridge MA USAR Coziol L M Flor-Torres D Jack and K-P Schroder Departamento de Astronomıa Universidad de
Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
AampA 502 391Skumanich A 1972 ApJ 171 565Smalley B Anderson D R Collier Cameron A et al
2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
2008 AampA 620 58Stauffer J R amp Hartman L W 1986 PASP 98 1233Tassoul J-L 2000 Stellar Rotation (New York NY
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715 458Tsantaki M Sousa S G Santos N C et al 2014
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590Udry S amp Santos N C 2007 ARAampA 45 397Uzdensky D A Konigl A amp Litwin C 2002 ApJ
565 1191Valencia D OrsquoConnell R J amp Sasselov D 2006 Icar
181 545Valenti J A amp Debra A 2005 ApJS 159 141van der Marel N Williams J P amp Bruderer S 2018
ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
D P amp Mandell A M 2011 Natur 475 206Wang J amp Zhong Z 2018 AampA 619 1Weidenschilling S J amp Marzari F 1996 Natur 384
619West R G Hellier C Almenara J-M et al 2016
AampA 585 126Wilson O C 1963 ApJ 138 832Wolff S amp Simon T 1997 PASP 109 759
copy C
op
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1 In
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 211
8000 7000 6000 5000 4000 3000
1eminus
02
1eminus
01
1e+
00
1e+
01
1e+
02
Teff (K)
LL
su
nlog g
49
455
42
385
35
Fig 8 HR diagram of our 46 stars overlaid on the mainsequence of Hipparchos stars
terval (dashed curves) which takes into account theuncertainty of each measurement The final relationwe obtained is the following
V sin i
kms= exp
[A
(Teff
1000K
)+B log g minus C
] (7)
where A = 220 plusmn 036 B = 030 plusmn 046 andC = 1291plusmn 359 and which has a multiple corre-lation coefficient of r2 = 06329 Except for stars 23 13 and 16 and the three stars with highest un-certainties (22 33 and 36 not considered in thisrelation) all our data fit well inside the predictioninterval
Note that in order to obtain the highest corre-lation coefficient possible 8 stars suspected to havepeculiarly high rotation for their temperature wereconsidered as outliers They are from right to leftin Figure 7 2 3 16 13 40 39 46 and 37 Differentreasons were explored that could explain why thesestars would be outliers One is the age of the stars(eg Stauffer amp Hartman 1986) younger stars ro-tating faster than older stars (see Figure 16 in Tas-soul 2000) In Tassoul (2000) it was also shown thatyoung stars trace the same relation of V sin i withTeff as old stars only with higher velocities form-ing an upper sequence (or upper envelope) Thiscould be what we see in Figure 7 However in Fig-ure 8 the HR diagram for our stars compared to Hip-parchos stars suggests that except for three starswith slightly higher luminosity for their temperature(6 25 and 32 none of these stars forming the en-velope) all of the stars more luminous than the Sunare clearly on the main sequence This eliminates theyoung age hypothesis Another explanation could be
6500 6000 5500 5000
01
02
03
04
05
0
Teff (K)
V s
in i (
km
s)
log g
49
455
42
385
35
Fig 9 Data as found in Exoplanetsorg
peculiar surface activity Since more than one phe-nomenon can cause such activities the expected ef-fect would be pure random dispersion Checking theliterature for each of the stars in our sample we didfind 8 stars with reported peculiarities 2 3 17 2633 37 39 and 46 The type of peculiarities encoun-tered included ldquoFlare starrdquo ldquoRotationally variablerdquoldquoVariable BY DRardquo and ldquoDouble or Multiple starrdquoOf these ldquoactiverdquo stars only five in Figure 7 have ahigher V sin i for their temperature 2 3 37 39 and46 This leaves three stars (13 16 and 40) with unex-plained relatively high V sin i values In fact check-ing their Vmac we found these stars have lower valuesthan stars with comparable temperatures Howeverin our various attempts to get the higher highest cor-relation coefficient possible we judged better to keepthem as outliers
To verify our relation in Figure 9 we traced itover the distribution of the rotational velocities andtemperatures of the stars that were in our initialsample based on Exoplanetsorg As one can seeexcept for a few stars below Teff = 5500 K withhigher velocities and stars below Teff = 5500 Kwith lower velocities (some with V sin i = 0) themajority of the stars in this sample fall well betweenthe prediction interval of our empirical relation Thisresult suggests that the decrease in angular momen-tum of low mass stars is a non-aleatory phenomenonmost probably reflecting the action of one specificmechanism like for example magnetic braking orstellar wind (Wolff amp Simon 1997 Tassoul 2000 Uz-densky et al 2002) An exciting possibility howevercould be that this relation somehow is coupled to theformation of planets Although this hypothesis pro-
copy C
op
yri
gh
t 2
02
1 In
stitu
to d
e A
stro
no
miacutea
U
niv
ers
ida
d N
ac
ion
al A
utoacute
no
ma
de
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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216 FLOR-TORRES ET AL
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212 FLOR-TORRES ET AL
posed in the late 1960s was rapidly rejected since noplanet outside the Solar System was known at thetime the discovery of exoplanets allows us today totest this idea anew (eg Berget amp Durrance 2010)This will be the subject of Paper II in search of aconnection between the formation of stars and plan-ets
5 CONCLUSIONSIn this study we have shown that our method of anal-ysis developed for the TIGRE telescope using iSpecon intermediate Echelle resolution spectra yields re-sults about the physical characteristics of stars host-ing exoplanets that are comparable to those obtainedusing bigger telescopes and standard spectra analy-sis methods with high resolution spectra Our resultsshow that TIGRE can provide a helpful contributionin the follow-up of exoplanet surveys around brightstars like TESS and PLATO Such follow-up studiesare essential in order to understand how the forma-tion of planets is connected to the formation of theirhost stars (Eisner et al 2020)
We like to thank an anonymous referee for a care-ful revision of our results and for comments andsuggestions that helped us to improve our workL M F T would like to thank the CONACyT forits support through grant CVU 555458 She also ac-knowledges CONACyT for travel support (bilateralConacyt-DFG projects 192334 207772 and 278156)as well as the Universidad de Guanajuato (Direccionde Apoyo a la Investigacion y al Posgrado DAIP andCampus Guanajuato) for support given for confer-ence participation and international collaborationsL M F T also thanks the time request commit-tee of the TIGRE for granting her the observationsand the whole observing team for their support ingetting the data that were used in this study Morepersonally she thanks Sebastian Kohl for his helpwith MOLECFIT This research has made use of theExoplanet Orbit Database the Exoplanet Data Ex-plorer at exoplanetsorg (Han et al 2014) the exo-planetseu (Schneider et al 2011) and the NASArsquosAstrophysics Data System
APPENDIX
A LIST OF SPECTRAL LINES AND SEGMENTS DEFINED FOR OUR ANALYSIS
TABLE 6
LINES AND SEGMENTS DEFINED IN THIS WORK
Line Wave Peak Wave Base Wave Top Segm Wave base Segm Wave top
Na 1 5889959 5889422 5890422 5888922 5890922
Na 1 5895916 5895411 5896411 5894911 5896911
Fe 1 5930186 5929859 5930539 5929359 5931039
Fe 1 5934665 5934289 5935059 5933789 5935559
No ident 5956706 5956206 5957206 5955706 5957706
Fe 1 5975341 5974898 5975898 5974398 5977729
Fe 1 5976777 5976299 5977229 - -
Fe 1 5984831 5984319 5985689 5983819 5988099
Fe 1 5987088 5986449 5987599 - -
Fe 1 6002986 6002519 6003509 6002019 6004009
Fe 1 6008552 6008249 6008989 6007749 6009489
Mn 1 6016628 6016110 6017110 6015610 6017610
Fe 1 6020142 6019637 6020637 6019137 6021137
Fe 1 6024066 6023579 6024639 6023079 6025139
Fe 1 6056032 6055599 6056809 6055099 6057309
Fe 1 6065494 6065009 6065919 6064509 6066419
Fe 1 6078490 6077729 6078769 6077229 6079269
Fe 1 6082757 6082180 6083180 6081680 6083680
Fe 1 6085228 6084775 6085775 6084275 6086275
Ca 1 6122225 6121703 6122703 6121203 6123203
No ident 6151608 6151108 6152108 6150608 6152608
Ca 1 6162171 6161690 6162690 6161190 6163190
Fe 1 6170503 6170028 6171168 6169528 6171668
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
REFERENCES
Anderson D R Collier Cameron A Delrez L et al2014 MNRAS 445 1114
Armitage P J 2020 Astrophysics of Planet Formation(2nd ed Cambridge UK CUP)
Asplund M Grevesse N Sauval A J amp Scott P2009 Annu Rev Astron Astrophys 47 481
Bakos G A Kovacs G Torres G et al 2007 ApJ670 826
Bakos G A Hartman J D Torres G et al 2012 AJ144 19
Barros S C C Faedi F Collier Cameron A et al2011 AampA 525 54
Baruteau C Crida A Paardekooper S-J et al 2014in Protostars and Planets VI ed H Beuther R SKlessen C P Dullemond and T Henning (TucsonAZ UAP) 667
Batalha N M Rowe J F Bryson S T et al 2013ApJS 204 24
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15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 215
Beatty T G Pepper J Siverd R J et al 2012 ApJ756 39
Beauge C amp Nesvorny D 2012 ApJ 751 119Berget D J amp Durrance S T 2010 Journal of the
Southeastern Association for Research in Astronomy3 32
Bieryla A Collins K Beatty T G et al 2015 AJ150 12
Blanco-Cuaresma S Soubiran C Heiter U amp JofreP 2014 AampA 569 111
Blanco-Cuaresma S 2019 MNRAS 486 2075Bland A P amp Schwenzer S P 2004 in An Introduction
to the Solar System ed D A Rothery N McBrideand I Gilmour (New York NY CUP) 129
Borucki W J Koch D G Basri G et al 2011 ApJ736 19
Boss A P 1997 Sci 276 1836Bouchy F Udry S Mayor M et al 2005 AampA 444
15Bruntt H Bedding T R Quirion P-O et al 2010
MNRAS 405 1907Butler R P Vogt S S Marcy G W et al 2000 ApJ
545 504Chabrier G Baraffe I Leconte J Gallardo J amp Bar-
man T 2009 AIPC 1094 Cool Stars Stellar Systemsand the Sun 1094 12
Charbonneau D B Brown T M Latham D W andMayor M 2000 ApJ 529 45
Chatterjee S Ford E B Matsumura S amp Rasio AF 2008 ApJ 686 580
Chiang E amp Laughlin G 2013 MNRAS 431 3444da Silva R Udry S Bouchy F et al 2006 AampA 446
717Dalgaard P 2008 Introductory statistics with R (New
York NY Springer) doi101007978-0-387-79054-1Damasso M Esposito M Nascimbeni V et al 2015
AampA 581 6Dawson R I amp Johnson J A 2018 ARAampA 56 175Doyle A P Davies G R Smalley B Chaplin W J
amp Elsworth Y 2014 MNRAS 444 3592Eisner N L Barragan O Aigrain S et al 2020
MNRAS 494 750Fischer D A Laughlin G Butler P et al 2005 ApJ
620 481Fischer D A amp Valenti J 2005 ApJ 622 1102Fischer D A Laughlin G Marcy G W et al 2006
ApJ 637 1094Fischer D A Vogt S S Marcy G W et al 2007
ApJ 669 1336Gandolfi D Barragan O Hatzes A P et al 2017
AJ 154 123Gray D F 1984a ApJ 277 640
1984b ApJ 281 719Gray R O amp Corbally C J 1994 AJ 107 742Grevesse N Asplund M Sauval A J amp Scott P
2010 ApampSS 328 179Han E Wang S X Wright J T et al 2014 PASP
126 827
Hellier C Anderson D R Collier Cameron A et al2015 AJ 150 18
Hempelmann A Mittag M Gonzalez-Perez J N et al2016 AampA 586 14
Henry G W Marcy G W Butler R P amp Vogt SS 2000 ApJ 529 41
Herbst W Eisloeffel J Mundt R amp Scholz A 2007in Protostars and Planets V ed V B Reipurth DJewitt amp K Keil (Tuczon AZ UAP) 927
Hestroffer D amp Magnan C 1998 AampA 333 338Hinkel N R Timmes F X Young P A et al 2014
AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
ApJS 226 4Howard A W Johnson J A Marcy G W et al
2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
Planetary Systems and Host Stars PhD Thesis Col-lege of Science at Florida Institute of Technology
Jofre P Heiter U Soubiran C et al 2014 AampA 564133
Johns-Krull C M McCullough P R Burke C J etal 2008 ApJ 677 657
Johnson J A Marcy G W Fischer D A et al 2006ApJ 647 600
Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
Joshi Y C Pollacco D Collier Cameron A et al2009 MNRAS 392 1532
Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
H C amp Weiss W W 1999 AampAS 138 119Kupka F amp Dubernet M-L 2011 BaltA 20 503Kurucz R L 2005 MSAIS 8 14Kuzuhara M Tamura M Kudo T et al 2013 ApJ
774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
1996 Natur 380 606Luhman K L Patten B M Marengo M et al 2007
ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
536 43Marcy G W Butler R P Fischer D A et al 2002
ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
2015 ApJ 810 105Marzari F amp Weidenschilling S J 2002 Icar 156 570Mayor M amp Queloz D 1995 Natur 378 355McBride N amp Gilmour I 2004 An Introduction to the
Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
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216 FLOR-TORRES ET AL
Mittag M Schroder K-P Hempelmann A Gonzalez-Perez J N amp Schmitt J H M M 2016 AampA 59189
Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
673 79Moutou C Mayor M Bouchy F et al 2005 AampA
439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
S Blanco-Cuaresma Harvard-Smithsonian Center for Astrophysics Cambridge MA USAR Coziol L M Flor-Torres D Jack and K-P Schroder Departamento de Astronomıa Universidad de
Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
AampA 502 391Skumanich A 1972 ApJ 171 565Smalley B Anderson D R Collier Cameron A et al
2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
2008 AampA 620 58Stauffer J R amp Hartman L W 1986 PASP 98 1233Tassoul J-L 2000 Stellar Rotation (New York NY
CUP) doi101017CBO9780511546044Torres G Bakos G A Hartman J et al 2010 ApJ
715 458Tsantaki M Sousa S G Santos N C et al 2014
AampA 570 80Udry S Mayor M Naef D et al 2000 AampA 356
590Udry S amp Santos N C 2007 ARAampA 45 397Uzdensky D A Konigl A amp Litwin C 2002 ApJ
565 1191Valencia D OrsquoConnell R J amp Sasselov D 2006 Icar
181 545Valenti J A amp Debra A 2005 ApJS 159 141van der Marel N Williams J P amp Bruderer S 2018
ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
D P amp Mandell A M 2011 Natur 475 206Wang J amp Zhong Z 2018 AampA 619 1Weidenschilling S J amp Marzari F 1996 Natur 384
619West R G Hellier C Almenara J-M et al 2016
AampA 585 126Wilson O C 1963 ApJ 138 832Wolff S amp Simon T 1997 PASP 109 759
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SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 213
TABLE 6 CONTINUED
Fe 1 6173340 6172828 6173838 6172328 6174338
Fe 1 6213421 6212988 6213958 6212488 6214458
Fe 1 6219270 6218418 6219698 6217918 6220198
Fe 1 6230722 6230278 6231868 6229778 6233578
Fe 1 6232644 6231868 6233078 - -
Fe 1 6246326 6245898 6246868 6245398 6247368
Fe 1 6252564 6252108 6253108 6251608 6257298
Fe 1 6254240 6253298 6255098 - -
Fe 1 6256343 6255628 6256798 - -
Fe 1 6290951 6290473 6291473 6289973 6291973
Fe 1 6297808 6297138 6298548 6296638 6299048
Fe 1 6301508 6300898 6302028 6300398 6303528
Fe 1 6302514 6302028 6303028 - -
Fe 1 6322710 6322228 6323128 6321728 6323628
Fe 1 6335331 6334658 6335888 6334158 6337978
Fe 1 6336827 6336388 6337478 - -
Fe 1 6355038 6354468 6355768 6353968 6356268
Fe 1 6358671 6358128 6359258 6357628 6359758
Fe 1 6380743 6380264 6381264 6379764 6381764
Fe 1 6393612 6392968 6394278 6392468 6394778
Fe 1 6408011 6407578 6409138 6407078 6409638
Fe 1 6411646 6410878 6412198 6410378 6412698
Fe 2 6416962 6416449 6417449 6415949 6417949
Fe 1 6419949 6419428 6420408 6418928 6422598
Fe 1 6421377 6420758 6422098 - -
Fe 1 6430851 6430158 6431528 6429658 6433681
Fe 2 6432663 6432181 6433181 - -
Ca 1 6439063 6438572 6439572 6438072 6440072
Fe 2 6456405 6455866 6456866 6455366 6457366
Ca 1 6462606 6462081 6463081 6461581 6463581
Fe 1 6469200 6468711 6469711 6468211 6470211
Fe 1 6475657 6475117 6476117 6474617 6476617
Fe 1 6481882 6481362 6482362 6480862 6482862
Fe 1 6494989 6494197 6495437 6493697 6495937
Fe 2 6516098 6515587 6516587 6515087 6517087
Fe 1 6518385 6517868 6518868 6517368 6519368
Fe 1 6546245 6545757 6546967 6545257 6547467
H 1 6562808 6555483 6566832 6551934 6567340
Fe 1 6575003 6574507 6575507 6574007 6576007
Fe 1 6593887 6593417 6594537 6592917 6595037
Fe 1 6597585 6597073 6598073 6596573 6598573
Fe 1 6609067 6608605 6609605 6608105 6610105
Ni 1 6643626 6643139 6644139 6642639 6644639
Fe 1 6677983 6677297 6678707 6676797 6679207
Fe 1 6705134 6704570 6705570 6704070 6706070
No ident 6713073 6712573 6713573 6712073 6714073
Ca 1 6717701 6717138 6718138 6716638 6718638
Fe 1 6726657 6726178 6727178 6725678 6727678
Fe 1 6750182 6749653 6750653 6749153 6751153
Fe 1 6806856 6806358 6807358 6805858 6807858
Fe 1 6820359 6819894 6820894 6819394 6821394
Fe 1 6828620 6828085 6829085 6827585 6829585
No ident 6839811 6839311 6840311 6838811 6840811
Fe 1 6843658 6843150 6844150 6842650 6844650
Fe 1 6916669 6916218 6917218 6915718 6917718
No ident 6933635 6933135 6934135 6932635 6934635
copy C
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214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
REFERENCES
Anderson D R Collier Cameron A Delrez L et al2014 MNRAS 445 1114
Armitage P J 2020 Astrophysics of Planet Formation(2nd ed Cambridge UK CUP)
Asplund M Grevesse N Sauval A J amp Scott P2009 Annu Rev Astron Astrophys 47 481
Bakos G A Kovacs G Torres G et al 2007 ApJ670 826
Bakos G A Hartman J D Torres G et al 2012 AJ144 19
Barros S C C Faedi F Collier Cameron A et al2011 AampA 525 54
Baruteau C Crida A Paardekooper S-J et al 2014in Protostars and Planets VI ed H Beuther R SKlessen C P Dullemond and T Henning (TucsonAZ UAP) 667
Batalha N M Rowe J F Bryson S T et al 2013ApJS 204 24
copy C
op
yri
gh
t 2
02
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stitu
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stro
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miacutea
U
niv
ers
ida
d N
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ion
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utoacute
no
ma
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22
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a0
18
51
10
1p
20
21
57
01
15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 215
Beatty T G Pepper J Siverd R J et al 2012 ApJ756 39
Beauge C amp Nesvorny D 2012 ApJ 751 119Berget D J amp Durrance S T 2010 Journal of the
Southeastern Association for Research in Astronomy3 32
Bieryla A Collins K Beatty T G et al 2015 AJ150 12
Blanco-Cuaresma S Soubiran C Heiter U amp JofreP 2014 AampA 569 111
Blanco-Cuaresma S 2019 MNRAS 486 2075Bland A P amp Schwenzer S P 2004 in An Introduction
to the Solar System ed D A Rothery N McBrideand I Gilmour (New York NY CUP) 129
Borucki W J Koch D G Basri G et al 2011 ApJ736 19
Boss A P 1997 Sci 276 1836Bouchy F Udry S Mayor M et al 2005 AampA 444
15Bruntt H Bedding T R Quirion P-O et al 2010
MNRAS 405 1907Butler R P Vogt S S Marcy G W et al 2000 ApJ
545 504Chabrier G Baraffe I Leconte J Gallardo J amp Bar-
man T 2009 AIPC 1094 Cool Stars Stellar Systemsand the Sun 1094 12
Charbonneau D B Brown T M Latham D W andMayor M 2000 ApJ 529 45
Chatterjee S Ford E B Matsumura S amp Rasio AF 2008 ApJ 686 580
Chiang E amp Laughlin G 2013 MNRAS 431 3444da Silva R Udry S Bouchy F et al 2006 AampA 446
717Dalgaard P 2008 Introductory statistics with R (New
York NY Springer) doi101007978-0-387-79054-1Damasso M Esposito M Nascimbeni V et al 2015
AampA 581 6Dawson R I amp Johnson J A 2018 ARAampA 56 175Doyle A P Davies G R Smalley B Chaplin W J
amp Elsworth Y 2014 MNRAS 444 3592Eisner N L Barragan O Aigrain S et al 2020
MNRAS 494 750Fischer D A Laughlin G Butler P et al 2005 ApJ
620 481Fischer D A amp Valenti J 2005 ApJ 622 1102Fischer D A Laughlin G Marcy G W et al 2006
ApJ 637 1094Fischer D A Vogt S S Marcy G W et al 2007
ApJ 669 1336Gandolfi D Barragan O Hatzes A P et al 2017
AJ 154 123Gray D F 1984a ApJ 277 640
1984b ApJ 281 719Gray R O amp Corbally C J 1994 AJ 107 742Grevesse N Asplund M Sauval A J amp Scott P
2010 ApampSS 328 179Han E Wang S X Wright J T et al 2014 PASP
126 827
Hellier C Anderson D R Collier Cameron A et al2015 AJ 150 18
Hempelmann A Mittag M Gonzalez-Perez J N et al2016 AampA 586 14
Henry G W Marcy G W Butler R P amp Vogt SS 2000 ApJ 529 41
Herbst W Eisloeffel J Mundt R amp Scholz A 2007in Protostars and Planets V ed V B Reipurth DJewitt amp K Keil (Tuczon AZ UAP) 927
Hestroffer D amp Magnan C 1998 AampA 333 338Hinkel N R Timmes F X Young P A et al 2014
AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
ApJS 226 4Howard A W Johnson J A Marcy G W et al
2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
Planetary Systems and Host Stars PhD Thesis Col-lege of Science at Florida Institute of Technology
Jofre P Heiter U Soubiran C et al 2014 AampA 564133
Johns-Krull C M McCullough P R Burke C J etal 2008 ApJ 677 657
Johnson J A Marcy G W Fischer D A et al 2006ApJ 647 600
Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
Joshi Y C Pollacco D Collier Cameron A et al2009 MNRAS 392 1532
Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
H C amp Weiss W W 1999 AampAS 138 119Kupka F amp Dubernet M-L 2011 BaltA 20 503Kurucz R L 2005 MSAIS 8 14Kuzuhara M Tamura M Kudo T et al 2013 ApJ
774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
1996 Natur 380 606Luhman K L Patten B M Marengo M et al 2007
ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
536 43Marcy G W Butler R P Fischer D A et al 2002
ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
2015 ApJ 810 105Marzari F amp Weidenschilling S J 2002 Icar 156 570Mayor M amp Queloz D 1995 Natur 378 355McBride N amp Gilmour I 2004 An Introduction to the
Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
copy C
op
yri
gh
t 2
02
1 In
stitu
to d
e A
stro
no
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U
niv
ers
ida
d N
ac
ion
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1p
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01
15
216 FLOR-TORRES ET AL
Mittag M Schroder K-P Hempelmann A Gonzalez-Perez J N amp Schmitt J H M M 2016 AampA 59189
Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
673 79Moutou C Mayor M Bouchy F et al 2005 AampA
439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
S Blanco-Cuaresma Harvard-Smithsonian Center for Astrophysics Cambridge MA USAR Coziol L M Flor-Torres D Jack and K-P Schroder Departamento de Astronomıa Universidad de
Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
AampA 502 391Skumanich A 1972 ApJ 171 565Smalley B Anderson D R Collier Cameron A et al
2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
2008 AampA 620 58Stauffer J R amp Hartman L W 1986 PASP 98 1233Tassoul J-L 2000 Stellar Rotation (New York NY
CUP) doi101017CBO9780511546044Torres G Bakos G A Hartman J et al 2010 ApJ
715 458Tsantaki M Sousa S G Santos N C et al 2014
AampA 570 80Udry S Mayor M Naef D et al 2000 AampA 356
590Udry S amp Santos N C 2007 ARAampA 45 397Uzdensky D A Konigl A amp Litwin C 2002 ApJ
565 1191Valencia D OrsquoConnell R J amp Sasselov D 2006 Icar
181 545Valenti J A amp Debra A 2005 ApJS 159 141van der Marel N Williams J P amp Bruderer S 2018
ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
D P amp Mandell A M 2011 Natur 475 206Wang J amp Zhong Z 2018 AampA 619 1Weidenschilling S J amp Marzari F 1996 Natur 384
619West R G Hellier C Almenara J-M et al 2016
AampA 585 126Wilson O C 1963 ApJ 138 832Wolff S amp Simon T 1997 PASP 109 759
copy C
op
yri
gh
t 2
02
1 In
stitu
to d
e A
stro
no
miacutea
U
niv
ers
ida
d N
ac
ion
al A
utoacute
no
ma
de
Meacute
xic
oD
OI h
ttp
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do
iorg
10
22
20
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18
51
10
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20
21
57
01
15
214 FLOR-TORRES ET AL
TABLE 6 CONTINUED
Fe 1 6945196 6944703 6945703 6944203 6946203
- - - - 6946410 6948410
Fe 1 6951251 6950721 6951721 6950221 6952221
Fe 1 7038209 7037718 7038718 7037218 7039218
Fe 1 7068440 7067918 7068918 7067418 7069418
Fe 1 7090378 7089850 7090850 7089350 7091350
Fe 1 7130900 7130451 7131451 7129951 7131951
Fe 1 7133001 7132453 7133453 7131953 7133953
CN 1 7145241 7144768 7145768 7144268 7146268
Ca 1 7148155 7147666 7148666 7147166 7149166
Fe 1 7155670 7155125 7156125 7154625 7156625
No ident 7164473 7163185 7165085 7162685 7165585
Fe 1 7175970 7175403 7176403 7174903 7176903
Fe 1 7219712 7219134 7220134 7218634 7222190
CN 1 7221100 7220690 7221690 - -
No ident 7244812 7244312 7245312 7243812 7245812
Fe 1 7320693 7320178 7321178 7319678 7321678
Fe 1 7386353 7385818 7386818 7385318 7387318
Fe 1 7389363 7388454 7389974 7387954 7390474
Fe 1 7411151 7410394 7411764 7409894 7412264
Ni 1 7422264 7421770 7422770 7421270 7423270
No ident 7440877 7440377 7441377 7439877 7441877
Fe 1 7445740 7445174 7446654 7444674 7447154
Fe 1 7495088 7494484 7495724 7493984 7496224
Fe 1 7511024 7510024 7511854 7509524 7512354
Fe 1 7710389 7709827 7710827 7709327 7711327
Fe 1 7723237 7722724 7723724 7722224 7724224
Fe 1 7748304 7747653 7748613 7747153 7749113
Ni 1 7751163 7750625 7751625 7750125 7752125
Fe 1 7780562 7779613 7781263 7779113 7781763
Fe 1 7832221 7831453 7833183 7830953 7833683
Fe 1 7937145 7936112 7937802 7935612 7938302
Fe 1 7945839 7945132 7946502 7944632 7947002
Fe 1 7998967 7998112 7999622 7997612 8000122
No ident 8046052 8045282 8047002 8044782 8047502
No ident 8085170 8084442 8086012 8083942 8086512
Fe 1 8207791 8207284 8208284 8206784 8208784
Fe 1 8327062 8326341 8327711 8325841 8328211
Fe 1 8387760 8387061 8388521 8386561 8389021
Fe 1 8468392 8467820 8468930 8467320 8469430
Fe 1 8514073 8513290 8514650 8512790 8515150
Fe 1 8688639 8687760 8689430 8687260 8689930
No ident 8710395 8709895 8710895 8709395 8711395
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Anderson D R Collier Cameron A Delrez L et al2014 MNRAS 445 1114
Armitage P J 2020 Astrophysics of Planet Formation(2nd ed Cambridge UK CUP)
Asplund M Grevesse N Sauval A J amp Scott P2009 Annu Rev Astron Astrophys 47 481
Bakos G A Kovacs G Torres G et al 2007 ApJ670 826
Bakos G A Hartman J D Torres G et al 2012 AJ144 19
Barros S C C Faedi F Collier Cameron A et al2011 AampA 525 54
Baruteau C Crida A Paardekooper S-J et al 2014in Protostars and Planets VI ed H Beuther R SKlessen C P Dullemond and T Henning (TucsonAZ UAP) 667
Batalha N M Rowe J F Bryson S T et al 2013ApJS 204 24
copy C
op
yri
gh
t 2
02
1 In
stitu
to d
e A
stro
no
miacutea
U
niv
ers
ida
d N
ac
ion
al A
utoacute
no
ma
de
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xic
oD
OI h
ttp
s
do
iorg
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22
20
1i
a0
18
51
10
1p
20
21
57
01
15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 215
Beatty T G Pepper J Siverd R J et al 2012 ApJ756 39
Beauge C amp Nesvorny D 2012 ApJ 751 119Berget D J amp Durrance S T 2010 Journal of the
Southeastern Association for Research in Astronomy3 32
Bieryla A Collins K Beatty T G et al 2015 AJ150 12
Blanco-Cuaresma S Soubiran C Heiter U amp JofreP 2014 AampA 569 111
Blanco-Cuaresma S 2019 MNRAS 486 2075Bland A P amp Schwenzer S P 2004 in An Introduction
to the Solar System ed D A Rothery N McBrideand I Gilmour (New York NY CUP) 129
Borucki W J Koch D G Basri G et al 2011 ApJ736 19
Boss A P 1997 Sci 276 1836Bouchy F Udry S Mayor M et al 2005 AampA 444
15Bruntt H Bedding T R Quirion P-O et al 2010
MNRAS 405 1907Butler R P Vogt S S Marcy G W et al 2000 ApJ
545 504Chabrier G Baraffe I Leconte J Gallardo J amp Bar-
man T 2009 AIPC 1094 Cool Stars Stellar Systemsand the Sun 1094 12
Charbonneau D B Brown T M Latham D W andMayor M 2000 ApJ 529 45
Chatterjee S Ford E B Matsumura S amp Rasio AF 2008 ApJ 686 580
Chiang E amp Laughlin G 2013 MNRAS 431 3444da Silva R Udry S Bouchy F et al 2006 AampA 446
717Dalgaard P 2008 Introductory statistics with R (New
York NY Springer) doi101007978-0-387-79054-1Damasso M Esposito M Nascimbeni V et al 2015
AampA 581 6Dawson R I amp Johnson J A 2018 ARAampA 56 175Doyle A P Davies G R Smalley B Chaplin W J
amp Elsworth Y 2014 MNRAS 444 3592Eisner N L Barragan O Aigrain S et al 2020
MNRAS 494 750Fischer D A Laughlin G Butler P et al 2005 ApJ
620 481Fischer D A amp Valenti J 2005 ApJ 622 1102Fischer D A Laughlin G Marcy G W et al 2006
ApJ 637 1094Fischer D A Vogt S S Marcy G W et al 2007
ApJ 669 1336Gandolfi D Barragan O Hatzes A P et al 2017
AJ 154 123Gray D F 1984a ApJ 277 640
1984b ApJ 281 719Gray R O amp Corbally C J 1994 AJ 107 742Grevesse N Asplund M Sauval A J amp Scott P
2010 ApampSS 328 179Han E Wang S X Wright J T et al 2014 PASP
126 827
Hellier C Anderson D R Collier Cameron A et al2015 AJ 150 18
Hempelmann A Mittag M Gonzalez-Perez J N et al2016 AampA 586 14
Henry G W Marcy G W Butler R P amp Vogt SS 2000 ApJ 529 41
Herbst W Eisloeffel J Mundt R amp Scholz A 2007in Protostars and Planets V ed V B Reipurth DJewitt amp K Keil (Tuczon AZ UAP) 927
Hestroffer D amp Magnan C 1998 AampA 333 338Hinkel N R Timmes F X Young P A et al 2014
AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
ApJS 226 4Howard A W Johnson J A Marcy G W et al
2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
Planetary Systems and Host Stars PhD Thesis Col-lege of Science at Florida Institute of Technology
Jofre P Heiter U Soubiran C et al 2014 AampA 564133
Johns-Krull C M McCullough P R Burke C J etal 2008 ApJ 677 657
Johnson J A Marcy G W Fischer D A et al 2006ApJ 647 600
Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
Joshi Y C Pollacco D Collier Cameron A et al2009 MNRAS 392 1532
Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
H C amp Weiss W W 1999 AampAS 138 119Kupka F amp Dubernet M-L 2011 BaltA 20 503Kurucz R L 2005 MSAIS 8 14Kuzuhara M Tamura M Kudo T et al 2013 ApJ
774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
1996 Natur 380 606Luhman K L Patten B M Marengo M et al 2007
ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
536 43Marcy G W Butler R P Fischer D A et al 2002
ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
2015 ApJ 810 105Marzari F amp Weidenschilling S J 2002 Icar 156 570Mayor M amp Queloz D 1995 Natur 378 355McBride N amp Gilmour I 2004 An Introduction to the
Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
copy C
op
yri
gh
t 2
02
1 In
stitu
to d
e A
stro
no
miacutea
U
niv
ers
ida
d N
ac
ion
al A
utoacute
no
ma
de
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xic
oD
OI h
ttp
s
do
iorg
10
22
20
1i
a0
18
51
10
1p
20
21
57
01
15
216 FLOR-TORRES ET AL
Mittag M Schroder K-P Hempelmann A Gonzalez-Perez J N amp Schmitt J H M M 2016 AampA 59189
Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
673 79Moutou C Mayor M Bouchy F et al 2005 AampA
439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
S Blanco-Cuaresma Harvard-Smithsonian Center for Astrophysics Cambridge MA USAR Coziol L M Flor-Torres D Jack and K-P Schroder Departamento de Astronomıa Universidad de
Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
AampA 502 391Skumanich A 1972 ApJ 171 565Smalley B Anderson D R Collier Cameron A et al
2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
2008 AampA 620 58Stauffer J R amp Hartman L W 1986 PASP 98 1233Tassoul J-L 2000 Stellar Rotation (New York NY
CUP) doi101017CBO9780511546044Torres G Bakos G A Hartman J et al 2010 ApJ
715 458Tsantaki M Sousa S G Santos N C et al 2014
AampA 570 80Udry S Mayor M Naef D et al 2000 AampA 356
590Udry S amp Santos N C 2007 ARAampA 45 397Uzdensky D A Konigl A amp Litwin C 2002 ApJ
565 1191Valencia D OrsquoConnell R J amp Sasselov D 2006 Icar
181 545Valenti J A amp Debra A 2005 ApJS 159 141van der Marel N Williams J P amp Bruderer S 2018
ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
D P amp Mandell A M 2011 Natur 475 206Wang J amp Zhong Z 2018 AampA 619 1Weidenschilling S J amp Marzari F 1996 Natur 384
619West R G Hellier C Almenara J-M et al 2016
AampA 585 126Wilson O C 1963 ApJ 138 832Wolff S amp Simon T 1997 PASP 109 759
copy C
op
yri
gh
t 2
02
1 In
stitu
to d
e A
stro
no
miacutea
U
niv
ers
ida
d N
ac
ion
al A
utoacute
no
ma
de
Meacute
xic
oD
OI h
ttp
s
do
iorg
10
22
20
1i
a0
18
51
10
1p
20
21
57
01
15
SPECTROSCOPIC CHARACTERIZATION OF HOST STARS WITH TIGRE 215
Beatty T G Pepper J Siverd R J et al 2012 ApJ756 39
Beauge C amp Nesvorny D 2012 ApJ 751 119Berget D J amp Durrance S T 2010 Journal of the
Southeastern Association for Research in Astronomy3 32
Bieryla A Collins K Beatty T G et al 2015 AJ150 12
Blanco-Cuaresma S Soubiran C Heiter U amp JofreP 2014 AampA 569 111
Blanco-Cuaresma S 2019 MNRAS 486 2075Bland A P amp Schwenzer S P 2004 in An Introduction
to the Solar System ed D A Rothery N McBrideand I Gilmour (New York NY CUP) 129
Borucki W J Koch D G Basri G et al 2011 ApJ736 19
Boss A P 1997 Sci 276 1836Bouchy F Udry S Mayor M et al 2005 AampA 444
15Bruntt H Bedding T R Quirion P-O et al 2010
MNRAS 405 1907Butler R P Vogt S S Marcy G W et al 2000 ApJ
545 504Chabrier G Baraffe I Leconte J Gallardo J amp Bar-
man T 2009 AIPC 1094 Cool Stars Stellar Systemsand the Sun 1094 12
Charbonneau D B Brown T M Latham D W andMayor M 2000 ApJ 529 45
Chatterjee S Ford E B Matsumura S amp Rasio AF 2008 ApJ 686 580
Chiang E amp Laughlin G 2013 MNRAS 431 3444da Silva R Udry S Bouchy F et al 2006 AampA 446
717Dalgaard P 2008 Introductory statistics with R (New
York NY Springer) doi101007978-0-387-79054-1Damasso M Esposito M Nascimbeni V et al 2015
AampA 581 6Dawson R I amp Johnson J A 2018 ARAampA 56 175Doyle A P Davies G R Smalley B Chaplin W J
amp Elsworth Y 2014 MNRAS 444 3592Eisner N L Barragan O Aigrain S et al 2020
MNRAS 494 750Fischer D A Laughlin G Butler P et al 2005 ApJ
620 481Fischer D A amp Valenti J 2005 ApJ 622 1102Fischer D A Laughlin G Marcy G W et al 2006
ApJ 637 1094Fischer D A Vogt S S Marcy G W et al 2007
ApJ 669 1336Gandolfi D Barragan O Hatzes A P et al 2017
AJ 154 123Gray D F 1984a ApJ 277 640
1984b ApJ 281 719Gray R O amp Corbally C J 1994 AJ 107 742Grevesse N Asplund M Sauval A J amp Scott P
2010 ApampSS 328 179Han E Wang S X Wright J T et al 2014 PASP
126 827
Hellier C Anderson D R Collier Cameron A et al2015 AJ 150 18
Hempelmann A Mittag M Gonzalez-Perez J N et al2016 AampA 586 14
Henry G W Marcy G W Butler R P amp Vogt SS 2000 ApJ 529 41
Herbst W Eisloeffel J Mundt R amp Scholz A 2007in Protostars and Planets V ed V B Reipurth DJewitt amp K Keil (Tuczon AZ UAP) 927
Hestroffer D amp Magnan C 1998 AampA 333 338Hinkel N R Timmes F X Young P A et al 2014
AJ 148 54Hinkel N R Young P A Pagano M D et al 2016
ApJS 226 4Howard A W Johnson J A Marcy G W et al
2011 ApJ 730 10Irwin S A 2015 Analysis of Angular Momentum in
Planetary Systems and Host Stars PhD Thesis Col-lege of Science at Florida Institute of Technology
Jofre P Heiter U Soubiran C et al 2014 AampA 564133
Johns-Krull C M McCullough P R Burke C J etal 2008 ApJ 677 657
Johnson J A Marcy G W Fischer D A et al 2006ApJ 647 600
Johnson J A Winn J N Bakos G A et al 2011ApJ 735 24
Joshi Y C Pollacco D Collier Cameron A et al2009 MNRAS 392 1532
Kraft R P 1967 ApJ 150 551Kupka F Piskunov N Ryabchikova T A Stempels
H C amp Weiss W W 1999 AampAS 138 119Kupka F amp Dubernet M-L 2011 BaltA 20 503Kurucz R L 2005 MSAIS 8 14Kuzuhara M Tamura M Kudo T et al 2013 ApJ
774 11Latham D W Bakos G A Torres G et al 2009
ApJ 704 1107Leconte J Baraffe I Chabrier G Barman T S amp
Levrard B 2009 AampA 506 385Lee E J amp Chiang E 2017 ApJ 842 40Lin D N C Bodenheimer P amp Richardson D C
1996 Natur 380 606Luhman K L Patten B M Marengo M et al 2007
ApJ 654 570Marcy G W Butler R P amp Vogt S S 2000 ApJ
536 43Marcy G W Butler R P Fischer D A et al 2002
ApJ 581 1375Martin R G amp Livio M 2012 MNRAS 425 6
2015 ApJ 810 105Marzari F amp Weidenschilling S J 2002 Icar 156 570Mayor M amp Queloz D 1995 Natur 378 355McBride N amp Gilmour I 2004 An Introduction to the
Solar System ed N McBride and I Gilmour (Cam-bridge UK CUP)
McKee C F amp Ostriker E C 2007 ARAampA 45 565McNally D 1965 Obs 85 166
copy C
op
yri
gh
t 2
02
1 In
stitu
to d
e A
stro
no
miacutea
U
niv
ers
ida
d N
ac
ion
al A
utoacute
no
ma
de
Meacute
xic
oD
OI h
ttp
s
do
iorg
10
22
20
1i
a0
18
51
10
1p
20
21
57
01
15
216 FLOR-TORRES ET AL
Mittag M Schroder K-P Hempelmann A Gonzalez-Perez J N amp Schmitt J H M M 2016 AampA 59189
Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
ApJ 819 7Noyes R W Bakos G A Torres G et al 2008 ApJ
673 79Moutou C Mayor M Bouchy F et al 2005 AampA
439 367Pal A Bakos G A Torres G et al 2008 ApJ 680
1450Pepper J Siverd R J Beatty T G et al 2013 ApJ
773 64Perez S Casassus S Baruteau C et al 2019 AJ
158 15Piskunov N amp Valenti J A 2017 AampA 597 16Plummer C C Carlson D H amp Hammersley L 2015
Physical Geology (New York NY McGraw-Hill Ed-ucation)
Queloz D Anderson D R Collier Cameron A et al2010 AampA 517 1
Radick R R Thompson D T Lockwood G W Dun-can D K amp Baggett W E 1987 ApJ 321 459
Rasio F A amp Ford E B 1996 Sci 274 954Raymond S N Barnes R amp Mandell A M 2008
MNRAS 384 663Raymond S N amp Morbidelli A 2020 arXiv e-prints
arXiv200205756Sato B Fischer D A Henry G W et al 2005 ApJ
633 465Schmitt J H M M Schroder K-P Rauw G et al
2014 AN 335 787
S Blanco-Cuaresma Harvard-Smithsonian Center for Astrophysics Cambridge MA USAR Coziol L M Flor-Torres D Jack and K-P Schroder Departamento de Astronomıa Universidad de
Guanajuato Guanajuato Gto MexicoJ H M M Schmitt Hamburger Sternwarte Universitat Hamburg Hamburg Germany
Schneider J Dedieu C Le Sidaner P Savalle R ampZolotukhin I 2011 AampA 532 79
Seager S 2010 Exoplanets (Tucson AZ UAP)Skillen I Pollacco D Collier Cameron A et al 2009
AampA 502 391Skumanich A 1972 ApJ 171 565Smalley B Anderson D R Collier Cameron A et al
2011 AampA 526 130Smette A Sana H Noll S et al 2015 AampA 576 77Sousa S G Adibekian V Delgado-Mena E et al
2008 AampA 620 58Stauffer J R amp Hartman L W 1986 PASP 98 1233Tassoul J-L 2000 Stellar Rotation (New York NY
CUP) doi101017CBO9780511546044Torres G Bakos G A Hartman J et al 2010 ApJ
715 458Tsantaki M Sousa S G Santos N C et al 2014
AampA 570 80Udry S Mayor M Naef D et al 2000 AampA 356
590Udry S amp Santos N C 2007 ARAampA 45 397Uzdensky D A Konigl A amp Litwin C 2002 ApJ
565 1191Valencia D OrsquoConnell R J amp Sasselov D 2006 Icar
181 545Valenti J A amp Debra A 2005 ApJS 159 141van der Marel N Williams J P amp Bruderer S 2018
ApJL 867 14Walsh K J Morbidelli A Raymond S N OrsquoBrien
D P amp Mandell A M 2011 Natur 475 206Wang J amp Zhong Z 2018 AampA 619 1Weidenschilling S J amp Marzari F 1996 Natur 384
619West R G Hellier C Almenara J-M et al 2016
AampA 585 126Wilson O C 1963 ApJ 138 832Wolff S amp Simon T 1997 PASP 109 759
copy C
op
yri
gh
t 2
02
1 In
stitu
to d
e A
stro
no
miacutea
U
niv
ers
ida
d N
ac
ion
al A
utoacute
no
ma
de
Meacute
xic
oD
OI h
ttp
s
do
iorg
10
22
20
1i
a0
18
51
10
1p
20
21
57
01
15
216 FLOR-TORRES ET AL
Mittag M Schroder K-P Hempelmann A Gonzalez-Perez J N amp Schmitt J H M M 2016 AampA 59189
Motalebi F Udry S Gillon M et al 2015 AampA 58472
Nagasawa M Ida S amp Bessho T 2008 ApJ 678 498Neveu-VanMalle M Queloz D Anderson D R et al
2014 AampA 572 49Nomura H Tsukagoshi T Kawabe R et al 2016
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