Environmental Dependence of Cold Dark Matter Halo

arXiv:astro-ph/0608690v221Nov2006Mon.Not.R.Astron.Soc.000,000–000(2006)Printed5February2008(MNLATEXstylefilev2.2)EnvironmentalDependenceofColdDarkMatterHaloFormationH.Y.Wang1,3,4⋆,H.J.Mo2,3,Y.P.Jing3,41CenterforAstrophysics,UniversityofScienceandTechnologyofChina,Hefei,Anhui,China2DepartmentofAstronomy,UniversityofMassachusetts,AmherstMA01003-9305,USA3ShanghaiAstronomicalObservatory;thePartnerGroupofMPA,NandanRoad80,Shanghai200030,China4JointInstituteforGalaxyandCosmology(JOINGC)ofSHAOandUSTCAccepted........Received.......;inoriginalform......ABSTRACTWeuseahigh-resolutionN-bodysimulationtostudyhowtheformationofcolddarkmatter(CDM)halosisaffectedbytheirenvironments,andhowsuchenvironmentaleffectsproducetheage-dependenceofhaloclusteringobservedinrecentN-bodysimulations.Weestimate,foreachhaloselectedatredshiftz=0,an‘initial’massMidefinedtobethemassenclosedbythelargestspherewhichcontainstheinitialbarycenterofthehaloparticlesandwithinwhichthemeanlineardensityisequaltothecriticalvalueforsphericalcollapseatz=0.Forhalosofagivenfinalmass,Mh,theratioMi/Mhhaslargescatter,andthescatterislargerforhalosoflowerfinalmasses.HalosthatformearlieronaveragehavelargerMi/Mh,andsocorrespondtohigherpeaksintheinitialdensityfieldthantheirfinalmassesimply.Oldhalosaremorestronglyclusteredthanyoungeronesofthesamemassbecausetheirinitialmassesarelarger.Theage-dependenceofclusteringforlow-masshalosisentirelyduetothedifferenceintheinitial/finalmassratio.Low-massoldhalosarealmostalwayslocatedinthevicinityofbigstructures,andtheiroldagesarelargelyduetothefactthattheirmassaccretionsaresuppressedbythehotenvironmentsproducedbythetidalfieldsofthelargerstructure.Theage-dependenceofclusteringisweakerformoremassivehalosbecausetheheatingbylarge-scaletidalfieldsislessimportant.Keywords:darkmatter-large-scalestructureoftheuniverse-galaxies:haloes-methods:statistical2H.Wangetal.1INTRODUCTIONInthestandardcolddarkmatter(CDM)paradigmofstructureformation,virializedCDMhalosareboththebuildingblocksofthelarge-scalestructureoftheUniverseandthehostswithinwhichgalaxiesaresupposedtoform.Duringthelastdecade,thepropertiesofCDMhalos,suchastheirinternalstructure,formationhistoriesandclusteringproperties,havebeenstudiedingreatdetailusingbothN-bodynumericalsimulationsandanalyticalmodels.Thesestudieshaveshownthatthehalobiasdependsstronglyonhalomass,inthesensethatmoremassivehalosaremorestronglyclustered(e.g.,Mo&White1996;Jing1998;Seljak&Warren2004).Thismassdependenceofthehalobiashasplayedacrucialroleinunderstandingthecorrelationfunctionofbothdarkmatterandgalaxies,viathehalomodel(e.g.,Mo,Jing&B¨orner1997;Ma&Fry2000;Seljak2000),thehalooccupationmodels(e.g.,Jing,Mo&B¨orner1998;Peacock&Smith2000;Zhengetal.2005),andtheconditionalluminosityfunction(e.g.,Yang,Mo&vandenBosch2003).RecentlyGaoetal(2005),usingaverylargeN-bodysimulationofaΛCDMcosmology,reexaminedthedependenceofhalobiasonthepropertiesofdarkmatterhalos.Theyfoundthat,forlow-masshalosatredshiftz=0withMh≪M⋆1,thebiasdependsnotonlyonthemassbutalsoontheformationtimeofdarkmatterhalos.Foragivenmass,halosthathaveearlierformationtimesareonaveragemorestronglyclusteredinspace.Thisage-dependenceofhaloclusteringhasbeenconfirmedbyanumberofindependentstudies(e.g.Zhuetal.2006;Harkeretal.2006).Sincehaloformationtimeisknowntobecorrelatedwithhaloconcentration(e.g.Navarro,Frenk&White1997;Jing2000;Wechsleretal2002;Zhaoetal.2003a,b;Luetal.2006),theagedependenceofhaloclusteringalsoshowsupasahalo-concentrationdependenceofhaloclustering(Wechsleretal.2005).FormassivehaloswithMh≫M⋆,theage-dependencemaybereversed,asshowninWechsleretal.(2005)andWetzeletal.(2006).Althoughthemass-dependenceofhaloclusteringiswellunderstoodintheexcursion-setmodelbasedonsphericalcollapseinGaussianinitialdensityfield(Mo&White1996),theformation-timedependence(orage-dependence)isnot.Inthesimplestexcursion-setmodelfromwhichthePress-Schechterformulaisderived(Bondetal.1991),theformationhistoryofahaloisentirelydeterminedbythelocaldensityfield,independentofthemass⋆E-mail:[e-mail]1M⋆isthecharacteristicmassscaleatwhichtheRMSofthelineardensityfieldisequalto1.686atthepresenttime.ForthepresentsimulationM⋆≈1.0×1013h−1M⊙.EnvironmentalDependenceofColdDarkMatterHaloFormation3distributiononlargerscales.Therefore,thelarge-scaleclusteringofhalosisindependentofformationtimeinthismodel.Anage-dependenceofhaloclusteringisexpectedintheexcursion-setmodelbasedonellipsoidalcollapse(Sheth,Mo&Tormen2001),becauseherethecollapseofahalodependsnotonlyonthelocaldensityfieldbutalsoonthetidalfieldgeneratedbyitslarge-scaleenvironment.Unfortunately,thisaspectofthemodelwasnotexploredinanydetailinShethetal.(2001).Instead,theseauthorsusedameanrelationbetweenhalomassandtheshapeparameterofthelarge-scaletidalfieldtoderiveanaveragecriticalcollapseoverdensitythatdependsonlyonhalomass.Sincethepropertiesofgalaxiesthatforminahaloareexpectedtodependontheforma-tionhistoryofthehalo,understandingtheoriginoftheage-dependenceofhaloclusteringiscrucialforabetterunderstandingabouthowgalaxiesarerelatedtotheirlarge-scaleenviron-ments.I