X-Ray Clusters in a CDM$+Lambda$ Universe A Direct

arXiv:astro-ph/9404012v17Apr1994X-RAYCLUSTERSINACDM+ΛUNIVERSE:ADIRECT,LARGE-SCALE,HIGHRESOLUTION,HYDRODYNAMICSIMULATIONRenyueCenandJeremiahP.OstrikerPrincetonUniversityObservatoryPrinceton,NJ08544USASubmittedtoTheAstrophysicalJournalonSept30,1993Dec22,19931ABSTRACTAnew,three-dimensional,shockcapturing,hydrodynamiccodeisutilizedtodeterminethedistributionofhotgasinaCDM+Λmodeluniverse.Peri-odicboundaryconditionsareassumed:aboxwithsize85h−1Mpc,havingcellsize0.31h−1Mpc,isfollowedinasimulationwith2703=107.3cells.WeadoptΩ=0.45,λ=0.55,h≡H/100km/s/Mpc=0.6,andthen,fromCOBEandlightelementnucleosynthesis,σ8=0.77,Ωb=0.043.WeidentifytheX-rayemit-tingclustersinthesimulationbox,computetheluminosityfunctionatseveralwavelengthbands,thetemperaturefunctionandestimatedsizes,aswellastheevolutionofthesequantitieswithredshift.Thisopenmodelsucceedsinmatch-inglocalobservationsofclustersincontrasttothestandardΩ=1,CDMmodel,whichfails.Itpredictsanorderofmagnitudedeclineinthenumberdensityofbright(hν=2−10keV)clustersfromz=0toz=2incontrasttoaslightincreaseinthenumberdensityforstandardΩ=1,CDMmodel.ThisCOBE-normalizedCDM+ΛmodelproducesapproximatelythesamenumberofX-rayclustershavingLx1043erg/sasobserved.Thebackgroundradiationfieldat1keVduetoclustersisapproximately10%oftheobservedbackgroundwhich,aftercorrectionfornumericaleffects,againindicatesthatthemodelisconsistentwithobservations.Thenumberdensityofbrightclustersincreasestoz∼0.2−0.5anddeclines,buttheluminositypertypicalclusterdecreasesmonotonicallywithredshift,withtheresultthatthenumberdensityofbrightclustersshowsabroadpeaknearz=0.5,andthenarapiddeclineasz→3.Themostinterestingpointwhichwefindisthatthetemperaturesofclustersinthismodelfreezeoutatlatertimes(z≤0.3),whilepreviouslywefoundintheCDMmodelthattherewas2asteepincreaseduringthesameintervalofredshift.Equivalently,wefindthatL∗oftheSchechterfitsofclusterluminosityfunctionspeaksnearz=0.3inthismodel,whileintheCDMmodelitisamonotonicallydecreasingfunctionofredshift.Bothtrendsshouldbedetectableevenwitharelatively“soft”X-rayinstrumentsuchasROSAT,providingapowerfuldiscriminantbetweenΩ=1andΩ1models.DetailedcomputationsoftheluminosityfunctionsintherangeLx=1040−1044erg/sinvariousenergybandsarepresentedforbothclustercores(r≤0.5h−1Mpc)andtotalluminosities(r1h−1Mpc).ThesearetobeusedforcomparisonwithROSATandotherobservationaldatasets.Theyshowtheabovenotednegativeevolutionfortheopenmodel.Wefindlittledependenceofcoreradiusonclusterluminosityandthede-pendenceoftemperatureonluminositylogkTx=A+BlogLx,whichisslightlysteeper(B=0.32±0.01)thanindicatedbyobservations(B=0.265±0.035),butwithinobservationalerrors.Incontrast,thestandardΩ=1modelpredictedtemperatureswhichweresignificantlytoohigh.Themeanluminosity-weightedtemperatureis1.8keV,dramaticallylower(byafactorof3.5)thanthatfoundintheΩ=1model,andtheevolutionfarslower(−30%vs−50%)thanintheΩ=1modeltoredshiftz=0.5.Amodestaveragetemperaturegradientisfoundwithtemperaturesdroppingto90%ofcentralvaluesat0.4h−1Mpcandto60%ofcentralvaluesat0.9h−1Mpc.Examiningtheratioofgas-to-totalmassintheclusters,wefindaslightan-tibias(b=0.9or(ΩgasΩtot)cl=0.083±0.007),whichisconsistentwithobservations[(ΩgasΩtot)obs=0.097±0.019fortheComaclusterforthegivenvalueofh,cf.,White1991].Cosmology:large-scalestructureofUniverse–hydrodynamics–RadiationMech-3anisms:Bremsstrahlung–X-ray:general41.INTRODUCTIONIntheprecedingtwopapersofthisseries(Kangetal.1994=KCORhereafter;Bryanetal.1994),wehaveexaminedthepropertiesofX-rayclus-tersinthestandardCOBE-normalizedCDMuniverseandreachedtwoprimaryconclusions:1)thestandardCDMmodeloverproducesbrightX-rayclusters(Lx1043erg/s)byafactorinexcessoffive;2)observationsoftheratioofgas-to-totalmassingreatclustersofgalaxies,combinedwithoursimulations,impliythatweliveinanopen(Ω=0.2to0.3)universe(withorwithoutacosmologicalconstant).Thereareotherwell-knowndifficultieswiththestan-dardCDMscenario(cf.Ostriker1993forareview),andthereareadvantagestoopenCDMmodels(cf.Efstathiou1992)whicharisefromotherconsiderations,independentofclusterX-rayproperties.Motivatedbythisknowledge,weturninthispapertoexamineanopenCDMmodelwithacosmologicalconstant.Wewishtoinvestigatethedifferenceintheevolutionarybehavioraswellasthez=0propertiesofX-rayclustersinthesetwodifferentmodels.ThereiseveryexpectationthatclusterX-raypropertiesshouldprovideastrongdiscriminantamongcosmictheories.Wewill,throughoutthispaper,makecomparisonswithKCORwhereveritispossible,sincethatcalculationwasmadewithidenticalphysicalassumptionsandwithidenticalnumericalmodelingtechniquesadopted.In§2weoutlinethemethodandinitialconditions,in§3theresults,andin§4weassembleourconclusions.2.METHODANDINITIALCONDITIONS2.1MethodThesuperiorityofthenewTVDcodeoverconventionalhydrodynamiccodes5(e.g.,Cen1992)andvarioustestsofthecodehavebeenpresentedinRyuetal.(1993);essentiallytheshockcapturingtechniqueimprovesresolutionbyapproximatelyafactorof2−3foragivengrid(i.e.,nominalresolution).Thesimulationreportedoninthispaperdidnotincludeanyatomicpro-cesses,i.e.,nocoolingorheatingwasadded,exceptfortheadiabaticcoolingduetoth