Global Probes of the Impact of Baryons on Dark Mat

arXiv:astro-ph/0102334v120Feb2001GlobalProbesoftheImpactofBaryonsonDarkMatterHalosC.S.KochanekandMartinWhiteHarvard-SmithsonianCenterforAstrophysics,60GardenSt.,Cambridge,MA02138email:ckochanek,[e-mail]nction,dn/dM,predictedbyhierarchicalclusteringmodelscanbemeasuredindirectlyusingdynamicalprobeslikethedistributionofgravitationallensimageseparations,dn/dΔθ,orhalocircularvelocities,dn/dvc.Thesedynamicalvariablesdependonthehalostructureaswellasthehalomass.Sincebaryonicphysics,particularlycooling,significantlymodifiesthecentraldensitystructureofdarkmatterhalos,bothobservationaldistributionsshowafeaturecorrespondingtothemassscalebelowwhichthebaryonsinthehalocancool(i.e.galaxiesversusclusters).Weusesimplifiedbutself-consistentmodelstoshowthatthestructuralchangestothehalosproducedbythecoolingbaryonsexplainbothdistributions.Givenafixedhalomassfunction,matchingtheobservedimageseparationdistributionorlocalvelocityfunctiondependslargelyonΩbthroughitseffectsonthecoolingtimescales.Thesebaryoniceffectsonthehalostructurealsoaffecttheevolutionofthevelocityfunctionofgalaxieswithredshift.Subjectheadings:cosmology:theory–galaxies:formation–gravitationallensing–large-scalestructureofuniverse–darkmatter1.IntroductionThenumberdensity,spatialdistributionandpropertiesofdarkmatterhalosarenowwellunderstoodinmodelsbasedonhierarchicalclustering(e.g.Jenkinsetal.2000;Sheth&Tormen1999;Navarro,Frenk&White1996;Mooreetal.1998),thanksinlargeparttonumericalexperimentsinvolvinghighresolutionN-bodysimulations.However,therelationshipbetweenthesedarkmatterhalosandastrophysicalobjectscanbecomplicatedbythemodificationstothehalosproducedbybaryonicphysicsandthedependenceofoursearchandmeasurementmethodsontheirbaryonicproperties.Thedominantdivideintheobservedpropertiesofhalosisbetweengalaxiesandgroupsorclustersofgalaxies.Physicallythisdivisionisbetweenhalosinwhichthebaryonshavecooledandformedstarsascomparedtohaloswhichhavenot(Silk1977;Rees&Ostriker1977;White&Rees1978;Blumenthaletal.1984).Inthispaperweexplorehowthehalomassfunction,dn/dM,isgloballyrelatedtothemassesorinternalvelocitiesoftheobjectsweobserve.Byusingdynamicalprobesofthehalos–2–ratherthanluminositieswecantrytoavoidtwoproblems.First,dynamicalprobescanprovideacommonmeasurementscaleforbothgalaxiesandclusters,allowingustoexplorethelocationandpropertiesoftheboundarybetweenthetwotypesofastronomicalobjects.Second,byfocusingondynamicalpropertiesofthehalosratherthanluminosities,wepartlyavoidtheissuesrelatedtostarformationandfeedbackwhicharecentraltoanyrelationshipbetweenthehalomassfunctionandtheluminosityfunction,dn/dL.Wecannot,however,simplyignoretheeffectsofthebaryons,becausethebaryonssignificantlymodifythehalostructurewhentheycool(e.gBlumenthaletal.1986;Mo,Mao&White1998;Coleetal.2000;Gonzalezetal.2000).Bothmassivegalaxiesandsmallgroupsofgalaxiescanhaveinternalvelocitydispersions∼200kms−1,butitisdifficulttoinferfromthatfactthetotal,andpresumablydifferent,massesofthetwosystems.Thus,anyglobalrelationshipbetweenthehalomassfunction,dn/dM,andtheobservedpropertiesofgalaxies,groupsandclustersshouldshowafeatureatthecoolingmassscaleMcdividingcooledanduncooledhalos.InthispaperwequantitativelydevelopthisthemebycombiningPress-Schechter(1974)basedestimatesofthemassfunctionwithadiabaticcompressionmodels(e.g.Blumenthaletal.1986)toestimatetheeffectsofthecoolingbaryonsonthestructureofthehalo.Thisallowsustomakerelativelyself-consistentestimatesfortheeffectsofthebaryonsindistortingtheinitialhalomassfunctionintowhatourobservationalprobescanmeasure.Manyoftheissueswewillexplorehavebeentreatedinearlierstudies.Thatdifferencesincoolingtimescalescreatethedivisionbetweengalaxiesandclustersiswellknown,andmostoftheeffectswediscussareexplicitlyincludedinsemi-analyticmodels1ofgalaxyformation(e.g.Lacey&Silk1991;White&Frenk1991;Coleetal.1994;Baugh,Cole&Frenk1996;Kauffman,White&Guiderdoni1993;Kauffmanetal.1999;Somerville&Primack1999;Bensonetal.2000;Coleetal.2000).Howeverourfocushereissomewhatdifferentandwehighlighttwoissueswhichhavenotpreviouslybeenemphasized.First,wefocusonglobalprobesofthemassfunctiononbothgalaxyandclusterscalesandtheroleofcoolinginproducingameasurablefeatureintheseobservationaldistributions.Second,weemphasizetheimportanceofstructuralchangesinthemassdistributionofthedarkmatterhaloratherthantheeffectsofcoolingonthestarformationrateandluminosity/colorsofgalaxieswhichareamajorfocusofsemi-analyticwork.Theoutlineofthepaperisasfollows.In§2wereviewthemodifiedPress-Schechterformalismwhichweusefordeterminingthemassfunctionofhalos,adiabaticcompressionmodelsfortheeffectsofthecoolingbaryonsonthestructureofthehalos,andsimplecoolingmodelsforthedeterminingthecoolingmassscale.In§3weusethesemodelstoexplorethedistributionofimageseparationsingravitationallenses,andin§4weillustratetheeffectsofthecoolingbaryonsonthedistributionofhalosindynamicalvelocities.In§5wesummarizeourresults.1Sincethecoolingmodelsadoptedinthecurrentgenerationofsemi-analyticmodelsareverysimilar,wewillcollectivelyrefertothemas“SA”hereafter–3–2.TheProp