Galaxy Size Problem at z=3 Simulated Galaxies Are Too Small

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

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aGalaxySizeProblematz=3:SimulatedGalaxiesAreTooSmallM.RyanJoung1,RenyueCen1,&GregL.Bryan2Received

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

ABSTRACT

Usingstate-of-the-artadaptivemeshre nementcosmologicalhydrodynamic

simulationswithaspatialresolutionof～0.15h 1kpconacosmologicalvolume(20h 1Mpc)3,weinvestigatethesizesofgalaxiesatz=3inthestandardcolddarkmattermodelwherereionizationisassumedtocompleteatzri～6.OursimulatedLymanbreakgalaxies(LBGs)aresmallerthantheobservedonesbyafactorof2.Speci cally,takingintoaccountbothdustextinctionandinstrumen-talresolution,we ndthatthedistributionofhalf-lightradiiofthesimulatedLBGsintheobservedg′-bandpeaksat～1kpc,whereasthedistributionoftheLBGsobservedwiththeAdvancedCameraforSurveysonHSTpeaksat～2kpc.Withoutdustextinctionandwithin niteinstrumentalresolution,boththein-trinsichalf-lightandhalf-stellar-massradiipeakat～0.3kpc.Corroborativeevidenceisprovidedbytherotationcurvesofthesimulatedgalaxieswithtotalmassesof1011-1012M⊙,whichdisplayvalues(300-1000kms 1)atsmallradii(～0.5kpc),largerthanthoseofanyobservedgalaxies.Thesehighrotationve-locitiesarisebecausestellarmassesareconcentratedinsmall(<1kpc)centralregionsofthesimulatedLBGs.Anypotentialsolutiontothisseriousproblemwouldhavetoreducetheamountofstarsthatformearlyandeventuallygetcollectedinthecentraldenseregionsofgalaxiesviadynamicalfriction.Possiblephysicalmechanismsinclude:(1)anearlyreionizationatzri 6tosuppressgascondensationhencestarformation,(2)astrong,internalenergeticfeedbackfromstarsorcentralblackholestoreducetheoverallstarformatione ciency,or(3)asubstantialsmall-scalecuto inthematterpowerspectrum.

Subjectheadings:hydrodynamics—galaxies:formation—galaxies:kinematicsand

dynamics—cosmology:theory—methods:numerical—ultraviolet:galaxies

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

1.INTRODUCTION

Thestandardcosmologicalmodelhasbeenremarkablysuccessfulinaccountingforobservationsonscaleslargerthangalaxysizes(Krauss&Turner1995;Ostriker&Steinhardt1995;Bahcalletal.1999;Tegmarketal.2004;Spergeletal.2007).Weintendtotestthissamemodelwithregardtogalaxyformationandevolution,aregimewhereastrophysicalprocessesareimportantandhenceadetailedtestingofthecosmologicalmodelbecomesmoreintricate.Inthispaper,the rstofaseries,wefocusonthesizesofgalaxiesatredshiftz=3,primarilyLymanbreakgalaxies(LBGs;Steideletal.2003).Previousworksonthissubjectincludethosebasedonsemi-analyticmethods(e.g.,Mao&Mo1999).Here,wetakeabrute-forceapproachusinghigh-resolutionadaptivemeshre nement(AMR)cosmologicalsimulationstominimizethenumberofadjustableastrophysicalparametersandtherebymaximizethepredictabilityofthestandardmodel.

Aphysicalresolutionofoursimulationsof0.15h 1kpcatz=3permits,incosmologicalsimulationsofboxsize20h 1Mpccomoving,anaccuratecharacterizationofthesizesofgalaxiesatz=3.Weshowthattheintrinsichalf-lightradiiofsimulatedgalaxiesintheobservedg′-bandpeakat～0.3kpcatz=3.Takingintoaccountaself-consistenttreatmentofdustextinctionthatattenuatestheobserved uxbyafactorof～15,assuggestedbyobservations(Meureretal.1997;Pettinietal.1998;Sawicki&Yee1998),movesthepeakto～1.0kpc.Includingfurtherthepointspreadfunction(PSF)oftheobservationalinstrument,inparticular,FWHM≈0.05′′fortheAdvancedCameraforSurveys(ACS)onHST,slightlynarrowstheoveralldistributionbutleavesthepeaklocationlittlechangedat～1kpc,smallerthantheobservedsizes(Fergusonetal.2004)byafactorof～2.

Consistentwiththisintriguingresult,therotationcurvesofthesimulatedgalaxieswithtotalmassesof1011-1012M⊙haveunusuallyhighvalues(300-1000kms 1)atsmallradii(～0.5kpc).Suchhighrotationvelocitiesarisebecausestellarmassesarehighly

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

concentratedinsmallcentralregionsofthesimulatedLBGs.Ontheotherhand,thesevelocitieshavenotbeenseeninanyrealgalaxieswithmeasuredrotationcurves.

Thisproblemmightberelatedtodisksizeproblematz=0(e.g,Navarro,Frenk,&White1995;Navarro&Steinmetz1997;Governatoetal.2004).Physicalprocessesathighredshiftthatmayberesponsiblefortheeventualresolutionofthisproblemmaybeless“diluted”atz=3.Therefore,onemaybeabletoobtainimportant“cleaner”cluestothenatureofthedarkmatterand/orimportantastrophysicalprocessesathighredshiftsusingz=3galaxies.Moreover,combiningobservationsatbothz=3andz=0mayprovidestillmorepowerfulconstraints.

2.SIMULATIONANDANALYSISMETHODS

Weperformcosmologicalsimulationswiththeadaptivemeshre nement(AMR)Eulerianhydrocode,Enzo(Bryan1999;Norman&Bryan1999;O’Sheaetal.2004).Firstweranalowresolutionsimulationwithaperiodicboxof20h 1MpconasideinaΛCDMuniversewithcosmologicalparametersconsistentwiththeWMAP3results:( m, Λ, b,h,σ8,ns)=(0.24,0.76,0.042,0.73,0.74,0.95).Weidenti edvirializeddarkmatterhalosinthissimulationatz=3andresimulated11ofthemostmassive20halosinasuiteof vehighresolutionsimulationsembeddedwithinthesame(20h 1Mpc)3boxusingthemultimassinitializationtechnique,whileevolvingtherestoftheboxatlowresolution.The vehighresolutionsimulationshaveavolumerangingfrom～(2.5h 1Mpc)3to～(6.4h 1Mpc)3.Withinresimulatedregions,thecellsizeoftherootgridis39h 1kpcandadditionalgridre nementsareallowedinanadaptivefashiontoreachamaximumleveloflmax=6,resultinginthemaximumspatialresolutionof0.61h 1kpc(comoving)or0.21kpc(proper)atz=3.Thedarkmatterparticlemassis4.6×106M⊙.ThesimulationsincludeametagalacticUVbackground(Haardt&Madau1996),adi use

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

formofphotoelectricandphotoionizationheating(Abbott1982;Joung&MacLow2006),andamodelforshieldingofUVradiationbyneutralhydrogen(Cenetal.2005).Theyalsoincludemetallicity-dependentradiativecooling(Cenetal.1995)includingmolecularhydrogen(Abeletal.1997)andmetalcoolingextendeddownto10K(Dalgarno&McCray1972).StarformationandsupernovaefeedbackaremodeledfollowingCenetal.(2005)witheSN=3×10 6.StarparticlesarecreatedincellsthatsatisfyasetofcriteriaforstarformationproposedbyCen&Ostriker(1992).Eachstarparticleistaggedwithitsinitialmass,creationtime,andmetallicity;starparticlestypicallyhavemassesof～105M⊙.Feedbackenergyandejectedmetalsaredistributedinto27localgascellscenteredatthestarparticleinquestion,weightedbythespeci cvolumeofeachcell.Themetalenrichmentinsidegalaxiesandintheintergalaticmediumisfollowedself-consistentlyinaspatiallyresolvedfashion(Cenetal.2005).

WeidentifyvirializedobjectsinourhighresolutionsimulationsusingtheHOPalgorithm(Eisenstein&Hut1998),whichistestedtoberobust.We nd49haloswithvirialmasses>5×1010M⊙aspotentialLymanbreakgalaxy(LBG)hosts(Somervilleetal.2001)andchoosethemostmassivegalaxieswithinthevirialradiiofthesehalosasLBGcandidates.

ThelightdistributioniscomputedfromthestarparticlesusingtheGISSELstellarsynthesiscode(Bruzual&Charlot2003).WefocusontheluminosityintheSDSSg′-band

[notethattheG lterinSteidel&Hamilton(1993)isnearlyidenticaltotheg′-band],correspondingtorestframeλeff≈1200 A.WeadoptanapproximatemodelfordustextinctionfollowingBinney&Merri eld(1998)butassumethatdustattenuationis

proportionaltothemetalcolumndensityratherthanthetotalhydrogendensityandcorrectfordepletionofrefractoryelements(Zn)ontodustgrainsparametrizedbyfFe,fractionofironindust(Vladilo&Peroux2005):AV=ΣZfFe/(4×1019mpFcm 2)mag,where

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

mpistheprotonmass,ΣZisthemasscolumndensityofmetalsinfrontofagivenstarparticle.Thefactor,F=5,ischosensothattheescapefractionintheUVbandisabout1/15(Meureretal.1997;Pettinietal.1998;Sawicki&Yee1998).Theconversionfrom

′isbasedonthedustextinctionlawproposedbyCalzettietal.(2000).Finally,AVtoAgobs

weapplyaGaussian lterwithFWHM=0.052′′totheprojectedluminositydensitymap(afterdustattenuation)tofacilitatedirectcomparisonbetweenthesimulatedimagesandtheHSTobservationsofhigh-zgalaxiesinFergusonetal.(2004).

3.RESULTS

Figure1showstheprojectedstellarmassdensityofaregionofcomovingsize(1.0h 1Mpc)2withadepthofcomoving2.4h 1Mpcatz=3,cutoutfromourlargesthighresolutionsimulationsub-volumeofsize～(6.4h 1Mpc)3.Theinsetsshowmagni edimagesofthefourmostmassivehalosinthedisplayedregionintheirprojectedluminositydensitydistributions.Foreachgalaxy,theimagesshow,fromlefttoright,intrinsic(beforedustattenuationisapplied),apparent(afterdustattenuation),andsmoothed(afterdustattenuationandPSF ltering)luminositydensities,respectively,allintheobservedg′-band.Ontheonehand,weseethatourhighresolutionpermitsformationofextremelydensestructures.Ontheotherhand,manyrichandsalientfeaturesproducedbycosmologicalprocesses,suchasmergersandtidaltails,paringtheleftmostandmiddlepicturesofeachrowoftheinsetssuggeststhatdustextinctionsigni cantlya ectstheobservedluminositydensitydistributionintheobservedg′-band.ThiscanbeunderstoodsimplyasaconsequenceoftheempiricalSchmidt-Kennicuttrelation(Kennicutt1998):gassurfacedensityincreasesmonotonicallyasstarformationratedensityincreases;andweassumedthatdustextinctionisproportionaltothemetalsurfacedensityhencegassurfacedensity.

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

Fig.1.—Thelargeimagedisplaystheprojectedstellarmassdensityofaregionofcomovingsize(1.0h 1Mpc)2withadepthofcomoving2.4h 1Mpcatz=3,cutoutfromoneofoursimulationvolumes.Theinsetszoominonthefourmostmassivegalaxiesinvolumeregionintermsofvirialmassandshowtheirprojectedluminositydensitydistributions.Foreachgalaxy,theimagesshow,fromlefttoright,intrinsic(beforedustattenuationisapplied),apparent(afterdustattenuation),andsmoothed(afterdustattenuationandPSF ltering)luminositydensities,respectively,allintheobservedg′-band.Thebarsindicatelengthsinproperkpc.

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

Fig.2.—Histogramsofhalf-lightradii(rhl)ofsimulatedgalaxiesatz=3intheobservedg′-band.Ineachpanel,redsolidhistogramrepresentsgalaxieswithhighSFR(>10M⊙yr 1)thatweidentifyasLBGs,whilegreendottedhistogramrepresentsthosewithlowSFR(<10M⊙yr 1),insixorthogonalprojectiondirections.Panels(a),(b),and(c)showhistogramsofhalf-lightradii,respectively,beforedustattenuation,afterdustattenuation,andafterdustattenuationandPSF ltering.(SeetextfordetailsonhowdustattenuationandPSF lteringwereapplied.)In(a),ahistogramofhalf-stellar-massradiiisshowninblackdashedlineforcomparison.Theintrinsicrhlin(a)rangebetween0.2and0.6kpc(proper)butpeakat～1kpcforLBGsafterdustattenuationisapplied.Thethickbluesolidhistogramin(c)istheobservedsizedistributionforthe140galaxiesinthez=3redshiftbinofFergusonetal.(2004),normalizedtothenumberofLBGsinoursimulation.

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

Fig.3.—Rotationvelocitycurvesforthethreegalaxieslabeled“1”,“2”and“3”inFig.1.Thesolidcurvesrepresentrotationvelocitiesduetoallthematterwithinagivengalacto-centricradius,whilethedottedcurvesshowthoseduetostellarmassonly.Thevirialmassesofthethreegalaxiesare8×1011,4×1011and1×1011M⊙,respectively.

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

Figure2showsthehistogramsofhalf-lightradii(rhl)ofsimulatedgalaxiesatz=3intheobservedg′-band.Ineachpanel,redsolidhistogramrepresentsgalaxieswithhighSFR(>10M⊙yr 1)thatweidentifywiththeobservedLBGs,whilegreendottedhistogramrepresentsthosewithlowSFR(<10M⊙yr 1).ThedistributionofthesimulatedLBGs(shadedinred)inpanel(c)ofFigure2di ersfromtheobservedone(bluehistogram).Inparticular,itappearsthatthesimulatedLBGsaresmallerthantheobservedLBGsbyafactorof～2.ThissuggeststhatthecurrentSFactivitiesaswellastheoverallstellarmassdistributionsinthesimulatedgalaxiesatz=3aretooconcentratednearthegalacticcenters.Thisfactcanbeshowninanalternativewayusingrotationcurves.Figure3showsrotationvelocitycurvesforthethreetopgalaxiesinFig.1.Thesecurvesseemtopeakattoohighavalue(300-1000kms 1)atsmallradii(～0.5kpc).

4.DISCUSSIONANDCONCLUSIONS

Thestandardcolddarkmattercosmologicalmodelisingoodagreementwitharichsetofobservationsonlargescales.Ourmainpurposeistosystematicallyexamineit,throughaseriesofpapers,inthecontextofgalaxyformationandevolution,aregimewhere,relativelyspeaking,ithasnotbeenseriouslycontested.Becauseastrophysicalprocessestendtoplayaprogressivelymoreimportantrolewithatsmallerscales,inparticular,ongalacticscalesandsmaller,itisvitaltoemployasfewadjustableastrophysicalparametersaspossible,tohaveatruetestofthecosmologicalmodel.

Inthispaper,the rstofaseries,wefocusonthesizesofgalaxies,primarilyLymanbreakgalaxies(LBGs;Steideletal.2003),atredshiftz=3,usingstate-of-the-artAMRcosmologicalhydrodynamicsimulationswithaspatialresolutionof～0.15h 1kpcinacosmologicalvolume.We ndthat,takingintoaccountbothdustextinctionandinstrumentalresolution,thecomputeddistributionofhalf-lightradiiofLBGsinthe

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

observedg′-bandpeaksat～1kpc,smallerthanthatobservedwithHSTACSthatpeaksat～2kpc.Intheabsenceofdustextinctionandwithin niteinstrumentalresolution,theintrinsichalf-lightradiiaswellasthehalf-stellar-massradiiactuallypeakat～0.3kpc.ConsistentwiththisapparentdiscrepancybetweensimulatedandobservedLBGs,therotationcurvesofthesimulatedgalaxiesoftotalmassesof5×1010-1012M⊙haveunusuallyhighvalues(300-1000kms 1)atsmallradii(～0.5kpc)forgalaxiesoftotalmassof1011-1012M⊙.Suchrotationcurvesarenotseeninlocalgalaxiesforwhichmeasurementsareavailable.

Theoriginofbothoftheseproblemsmaybethatstellarmassesaretoohighlyconcentratedinsmall(<1kpc)centralregionsofthesimulatedLBGs.Thisislikelycausedbyanover-abundanceofsmallergalaxiesthatformedathighredshifts(z>～6)andsubsequentlysanktothecentersoftheLBGsviadynamicalfriction.Thegalaxysizeproblematz=3foundinthepresentworkmayberelatedtoanapparentlargeexcessofpredictedbutunobserveddwarfhalos(Klypinetal.1999;Mooreetal.1999)andanover-concentrationofdarkmatterinsimulateddwarfgalaxiesonthescaleof～1kpc(Moore1994;Flores&Primack1994;Burkert1995;McGaugh&deBlok1998;Kravtsovetal.1998;Mooreetal.1999).

Likely,anypotentialviablesolutiontothisapparentproblemwouldhavetoreducetheamountofstarsthatformearlyandeventuallygetcollectedinthecentraldenseregionsofgalaxies.Possiblephysicalmechanismsinclude:(1)anearlyreionizationwithzri 6tosuppressgascondensationthatwillreduceearlierstarformation(e.g.,Bullock,Kravtsov,&Weinberg2000),(2)astrong,internalenergeticfeedbackfromstarsorcentralblackholestoreducetheoverallstarformatione ciency(e.g.,Sommer-Larsonetal.2003;Governatoetal.2007),or(3)asubstantialsmall-scalecuto inthematterpowerspectrum,forexample,ifthedarkmatterparticlesarewarmratherthancold(e.g.,Hogan&Dalcanton2000;

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

Sommer-Larsen&Dolgov2001;Bode,Ostriker&Turok2001)

Sincetheageoftheuniverseatz=3isonlyabout1/6ofthepresentage,asuccessfulresolutiontothegalaxysizeproblematz～3mayprovideimportant“cleaner”cluestothenatureofthedarkmatterand/orimportantastrophysicalprocessesathighredshifts.Moreover,combiningobservationsatbothz=3andz=0mayprovidestillmorepowerfulconstraints.

WethankDrs.Yen-TingLin,Mordecai-MarkMacLow,andAliceShapleyforhelpfuldiscussions.Wegratefullyacknowledge nancialsupportbygrantsAST-0507521andNNG05GK10G.

Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of 0.15 h-1kpc on a cosmological volume (20 h-1Mpc), we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where re

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