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

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)