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
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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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