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galaxy formation from cosmological simulations …...sfr(t)=a t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ b + t τ...

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  • Galaxy Formation From Cosmological Simulations …...SFR(t)=A t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ B + t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ −C ⎣ ⎢ ⎤ ⎦ ⎥ −1 Fig. 3 demonstrates correlation
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Galaxy Formation From Cosmological Simulations And Observations Rachel Losacco 1, 2 ; Camilla Pacifici 1; Jonathan Gardner 1 ; Michaela Hirschmann 3 1 National Aeronautics and Space Administration, Goddard Space Flight Center, Code 665 2 Stony Brook University, College of Arts and Sciences 3 Institute d’Astrophysique de Paris, Paris, France We thank Stephane Charlot, Jacopo Chevallard, and Emma Curtis Lake for useful discussions. RL would like to thank the Universities Space Research Association for funding this opportunity and the Office of Education at GSFC, specifically Melissa Cannon and Mableiene Burrell, for all of their support. CP acknowledges support by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center, administered by USRA through a contract with NASA. Acknowledgments Behroozi, P. H., Wechsler, R. H., & Conroy, C. 2013, ApJ, 770, 57 Noeske, K., Weiner, B. J., et al. 2007, ApJL, 660, 43 Hirschmann, M., De Lucia, G., & Fabio, F. 2016, MNRAS, 461, 1760 References One of the big unknowns in galaxy evolution is the timescale on which galaxies grow by forming stars and die by quenching the star formation. When interpreting observations and deriving a galaxy’s physical properties, we must assume a possible formation history, therefore guessing this timescale. For this project, we study a model of galaxy formation to find the most realistic and physically motivated functional form to describe a galaxy’s star formation history. To do this, I fit several functional forms with varying degrees of freedom onto stochastic star formation histories derived from a semi-analytical model of galaxy formation. The parameters of the best fit are examined for correlation with observable physical properties of the galaxies, such as their stellar mass and star formation rate. Identifying this functional form and correlations of its parameters to observable features will allow us to gain insight into the star formation histories of real observed galaxies. Abstract Introduction Galaxies are composed of stars, gas, dust, and dark matter which play a role in their structure and formation. For this project, we follow their stochastic star formation histories from a semi-analytical model (SAM) of galaxy formation in order to characterize their general formation history. The process of estimating a galaxy’s star formation history (SFH) based on observations is challenging. Computer simulations and SAMs allow us to follow the histories of simulated galaxies forming as they might have in real life. We can then look at such simulated SFHs, find an analytic function to described the overall shape (Fig. 1a), and relate that to observable features. This can help identify the observations needed to best derive the star formation histories of real galaxies. We consider as observable properties their final star formation rate (SFR) and total stellar mass, which are empirically correlated. This correlation is called star-formation galactic main sequence (Noeske et al. 2007). An example of this relation is shown in Fig. 1b. Data points on this plot are entire galaxies, and the main sequence is a positive slope describing star forming galaxies. Galaxies which fall under the main sequence are becoming quiescent. A correlation between the fitted parameters of a given functional form and the position of a galaxy on the main sequence can help estimate the general star formation history of real galaxies. In order to consider galaxies that are reliable according to the SAM, I select those with a stellar mass larger than 10 9 M⦿. The SFHs of these remaining galaxies are fitted with an exponentially declining function, a delayed tau function with two parameters and with three parameters, and a double power law using python’s lmfit. Behroozi et al. 2013 argues that an accurate representation of the general trend of a galaxy’s SFR is given by a double power law: where A is proportional to the amplitude, B is the rate of decrease, C is the rate of increase, and τ is proportional to the time of peak SFR (shown in Fig. 1a). To know which functional form is best to describe the SFHs of the SAM we explore, I calculate the goodness of fit as the average residual, or difference between the data and the fit, divided by the average SFR to normalize it. Comparing the goodness of fits of the four functional forms, shown in Fig. 2, the double power law was determined to be the best function to describe the SFR. We consider the galaxies with a double power law fit with goodness of fit below 0.5 from which to draw results. Method SFR( t ) = A t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ B + t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −C ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ −1 Fig. 3 demonstrates correlation between each of the four parameters that describe the double power law and the star formation main sequence. As parameter A increases, the SFR also increases and the final stellar mass of the galaxy grows. The rate of decrease (parameter B) is nearly 0 for star forming galaxies because at the time of observation the SFR is still rising, whereas Results There is a slight correlation between parameter C and stellar mass such that galaxies on the main sequence tend to have shallower rising slopes with lower stellar mass. Finally, the τ parameter, proportional to the peak time of star formation, is very high for star forming galaxies that may not have reached a peak yet. For galaxies below the main sequence, there is a trend Results (cont.) By fitting the model SFHs with analytic functions, we find correlations between the characteristics of the SFHs and physical properties, specifically their SFR and stellar mass. The double power law function provides a good fit for the galaxies from this SAM as it shows the most galaxies with a goodness of fit below the applied threshold. We could use these correlations to derive the star formation histories of real galaxies based on the observed SFR and stellar mass. Future work includes combining the model SFHs with simple stellar population spectra, derive spectral energy distributions of galaxies, and compare these to real observations. Conclusion Figure 1: (a) A double power law fit (red) of a single galaxy’s star formation history (black) derived from the SAM; (b) Galaxy main sequence with star forming galaxies Double Power Law Fit of Single Galaxy Star Formation Main Sequence Figure 2: Goodness of fit for four different functional forms, fitted on the star formation histories. The double power law (red) had the most galaxies below the Figure 3: Star formation main sequence, color coded by each parameter, of galaxies with goodness of fit below 0.5. log 10 C B Hig Lo Stee Shallo Stee Shallo Youn Ol (τ) τ (Gyr)

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Page 1: Galaxy Formation From Cosmological Simulations …...SFR(t)=A t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ B + t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ −C ⎣ ⎢ ⎤ ⎦ ⎥ −1 Fig. 3 demonstrates correlation

GalaxyFormationFromCosmologicalSimulationsAndObservationsRachelLosacco1,2;CamillaPacifici1;JonathanGardner1;MichaelaHirschmann3

1NationalAeronauticsandSpaceAdministration,GoddardSpaceFlightCenter,Code665

2StonyBrookUniversity,CollegeofArtsandSciences3Instituted’AstrophysiquedeParis,Paris,France

WethankStephaneCharlot,JacopoChevallard,andEmmaCurtisLakeforusefuldiscussions.RLwouldliketothanktheUniversitiesSpaceResearchAssociationforfundingthisopportunityandtheOfficeofEducationatGSFC,specificallyMelissaCannonandMableieneBurrell,foralloftheirsupport.CPacknowledgessupportbyanappointmenttotheNASAPostdoctoralProgramattheGoddardSpaceFlightCenter,administeredbyUSRAthroughacontractwithNASA.

AcknowledgmentsBehroozi,P.H.,Wechsler,R.H.,&Conroy,C.2013,ApJ,770,57Noeske,K.,Weiner,B.J.,etal.2007,ApJL,660,43Hirschmann,M.,DeLucia,G.,&Fabio,F.2016,MNRAS,461,1760

References

Oneofthebigunknownsingalaxyevolutionisthetimescaleonwhichgalaxiesgrowbyformingstarsanddiebyquenchingthestarformation.Wheninterpretingobservationsandderivingagalaxy’sphysicalproperties,wemustassumeapossibleformationhistory,thereforeguessingthistimescale.Forthisproject,westudyamodelofgalaxyformationtofindthemostrealisticandphysicallymotivatedfunctionalformtodescribeagalaxy’sstarformationhistory.Todothis,Ifitseveralfunctionalformswithvaryingdegreesoffreedomontostochasticstarformationhistoriesderivedfromasemi-analyticalmodelofgalaxyformation.Theparametersofthebestfitareexaminedforcorrelationwithobservablephysicalpropertiesofthegalaxies,suchastheirstellarmassandstarformationrate.Identifyingthisfunctionalformandcorrelationsofitsparameterstoobservablefeatureswillallowustogaininsightintothestarformationhistoriesofrealobservedgalaxies.

Abstract

IntroductionGalaxiesarecomposedofstars,gas,dust,anddarkmatterwhichplayaroleintheirstructureandformation.Forthisproject,wefollowtheirstochasticstarformationhistoriesfromasemi-analyticalmodel(SAM)ofgalaxyformationinordertocharacterizetheirgeneralformationhistory.Theprocessofestimatingagalaxy’sstarformationhistory(SFH)basedonobservationsischallenging.ComputersimulationsandSAMsallowustofollowthehistoriesofsimulatedgalaxiesformingastheymighthaveinreallife.WecanthenlookatsuchsimulatedSFHs,findananalyticfunctiontodescribedtheoverallshape(Fig.1a),andrelatethattoobservablefeatures.Thiscanhelpidentifytheobservationsneededtobestderivethestarformationhistoriesofrealgalaxies.Weconsiderasobservablepropertiestheirfinalstarformationrate(SFR)andtotalstellarmass,whichareempiricallycorrelated.Thiscorrelationiscalledstar-formationgalacticmainsequence(Noeskeetal.2007).AnexampleofthisrelationisshowninFig.1b.Datapointsonthisplotareentiregalaxies,andthemainsequenceisapositiveslopedescribingstarforminggalaxies.Galaxieswhichfallunderthemainsequencearebecomingquiescent.Acorrelationbetweenthefittedparametersofagivenfunctionalformandthepositionofagalaxyonthemainsequencecanhelpestimatethegeneralstarformationhistoryofrealgalaxies.

InordertoconsidergalaxiesthatarereliableaccordingtotheSAM,Iselectthosewithastellarmasslargerthan109M⦿.TheSFHsoftheseremaining

galaxiesarefittedwithanexponentiallydecliningfunction,adelayedtaufunctionwithtwoparametersandwiththreeparameters,andadoublepowerlawusingpython’slmfit.Behroozietal.2013arguesthatanaccuraterepresentationofthegeneraltrendofagalaxy’sSFRisgivenbyadoublepowerlaw:

whereAisproportionaltotheamplitude,Bistherateofdecrease,Cistherateofincrease,andτisproportionaltothetimeofpeakSFR(showninFig.1a). ToknowwhichfunctionalformisbesttodescribetheSFHsoftheSAMweexplore,Icalculatethegoodnessoffitastheaverageresidual,ordifferencebetweenthedataandthefit,dividedbytheaverageSFRtonormalizeit.Comparingthegoodnessoffitsofthefourfunctionalforms,showninFig.2,thedoublepowerlawwasdeterminedtobethebestfunctiontodescribetheSFR.Weconsiderthegalaxieswithadoublepowerlawfitwithgoodnessoffitbelow0.5fromwhichtodrawresults.

Method

€

SFR(t) = A tτ

⎛

⎝ ⎜ ⎞

⎠ ⎟ B

+tτ

⎛

⎝ ⎜ ⎞

⎠ ⎟ −C⎡

⎣ ⎢

⎤

⎦ ⎥

−1

Fig.3demonstratescorrelationbetweeneachofthefourparametersthatdescribethedoublepowerlawandthestarformationmainsequence.AsparameterAincreases,theSFRalsoincreasesandthefinalstellarmassofthegalaxygrows.Therateofdecrease(parameterB)isnearly0forstarforminggalaxiesbecauseatthetimeofobservationtheSFRisstillrising,whereas

Results

ThereisaslightcorrelationbetweenparameterCandstellarmasssuchthatgalaxiesonthemainsequencetendtohaveshallowerrisingslopeswithlowerstellarmass.Finally,theτparameter,proportionaltothepeaktimeofstarformation,isveryhighforstarforminggalaxiesthatmaynothavereachedapeakyet.Forgalaxiesbelowthemainsequence,thereisatrend

Results(cont.)

ByfittingthemodelSFHswithanalyticfunctions,wefindcorrelationsbetweenthecharacteristicsoftheSFHsandphysicalproperties,specificallytheirSFRandstellarmass.ThedoublepowerlawfunctionprovidesagoodfitforthegalaxiesfromthisSAMasitshowsthemostgalaxieswithagoodnessoffitbelowtheappliedthreshold.WecouldusethesecorrelationstoderivethestarformationhistoriesofrealgalaxiesbasedontheobservedSFRandstellarmass.FutureworkincludescombiningthemodelSFHswithsimplestellarpopulationspectra,derivespectralenergydistributionsofgalaxies,andcomparethesetorealobservations.

Conclusion

Figure1:(a)Adoublepowerlawfit(red)ofasinglegalaxy’sstarformationhistory(black)derivedfromtheSAM;(b)Galaxymainsequencewithstarforminggalaxies

DoublePowerLawFitofSingleGalaxy StarFormationMainSequence

Figure2:Goodnessoffitforfourdifferentfunctionalforms,fittedonthestarformationhistories.Thedoublepowerlaw(red)hadthemostgalaxiesbelowthe

Figure3:Starformationmainsequence,colorcodedbyeachparameter,ofgalaxieswithgoodnessoffitbelow0.5.

log 1

0C

B

Hig

Lo

Stee

Shallo

Stee

Shallo

Youn

Ol

(τ)

τ(Gyr)

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