Probing Dark Matter Haloes with Satellite Kinemati

arXiv:astro-ph/0404033v214May2004Mon.Not.R.Astron.Soc.000,000–000(2004)Printed2February2008(MNLATEXstylefilev1.4)ProbingDarkMatterHaloeswithSatelliteKinematicsFrankC.vandenBosch1,PederNorberg1,H.J.Mo2,andXiaohuYang2⋆1DepartmentofPhysics,SwissFederalInstituteofTechnology,ETHH¨onggerberg,CH-8093,Zurich,Switzerland2DepartmentofAstronomy,UniversityofMassachussets,710NorthPleasantStreet,AmherstMA01003-9305,USAABSTRACTUsingdetailedmockgalaxyredshiftsurveysweinvestigatetowhatextentthekine-maticsoflargesamplesofsatellitegalaxiesextractedfromflux-limitedsurveyscanbeusedtoconstrainhalomasses.Unlikepreviousstudies,whichfocussedonlyonsatellitesaroundrelativelyisolatedhostgalaxies,wetrytorecovertheaverageve-locitydispersionofsatellitegalaxiesinallhaloes,asafunctionoftheluminosityofthehostgalaxy.Weshowthatprevioushost-satelliteselectioncriteriayieldrelativelylargefractionsofinterlopersandwithavelocitydistributionthat,contrarytowhathasbeenassumedinthepast,differsstronglyfromuniform.Weshowthatwithaniterative,adaptiveselectioncriteriononecanobtainlargesamplesofhostsandsatel-lites,withstronglyreducedinterloperfractions,thatallowanaccuratemeasurementofσsat(Lhost)overtwoandahalfordersofmagnitudeinhostluminosity.Weusetheconditionalluminosityfunction(CLF)tomakepredictions,andshowthatsatelliteweighting,whichoccursnaturallywhenstackingmanyhost-satellitepairstoincreasesignal-to-noise,introducesabiastowardshigherσsat(Lhost)comparedtothetrue,host-averagedmean.Afurtherbias,inthesamedirection,isintroducedwhenus-ingflux-limited,ratherthanvolume-limitedsurveys.Weapplyouradaptiveselectioncriteriontothe2dFGRSandobtainasampleof12569satellitegalaxiesand8132hostgalaxies.WeshowthatthekinematicsofthesesatellitegalaxiesareinexcellentagreementwiththepredictionsbasedontheCLF,aftertakingaccountofthevariousbiases.Wethusconcludethatthereisindependentdynamicalevidencetosupportthemass-to-lightratiospredictedbytheCLFformalism.Keywords:galaxies:halos—galaxies:kinematicsanddynamics—galaxies:fun-damentalparameters—galaxies:structure—darkmatter—methods:statistical1INTRODUCTIONEversincethe“discovery”ofdarkmatterastronomershaveattemptedtoobtainaccuratemeasurementsofthemassesoftheextendeddarkmatterhaloesinwhichgalaxiesarethoughttoreside.Adetailedknowledgeofhalomassesaroundindividualgalaxiesholdsimportantcluestothephysicsofgalaxyformation,andisanessentialingredientofanysuccessfulmodelthataimsatlinkingtheobservableUniverse(i.e.,galaxies)tothebedrockofourtheoreticalframework(i.e.darkmatter).Themainchallengeinmeasuringtotalhalomassesistofindasuitable,visibletraceratsufficientlylargeradiiinthehalopotentialwell.Traditionally,startingwiththeac-tualdiscoveryofevidencefordarkmatterbyZwicky(1933,1937),astronomershaveusedthekinematicsofsatellitegalaxies.Sincethenumberofdetectablesatellitesinindi-vidualsystemsisgenerallysmall,thistechniqueisbasically⋆E-mail:[e-mail]axies(e.g.,Carlbergetal.1996;Carlberg,Yee&Ellingson1997b)andthelocalgroup(e.g.,Little&Tremaine1987;Lin,Jones&Klemola1995;Evans&Wilkinson2000;Evansetal.2000).However,onecanstackthedataonmanyhost-satellitepairstoobtainstatis-ticalestimatesofhalomasses.Pioneeringeffortsinthisdi-rectionweremadebyErickson,Gottesman&Hunter(1987),Zaritskyetal.(1993,1997),andZaritsky&White(1994).Althoughthesestudiesweretypicallylimitedtosamplesoflessthan100satellites,theyneverthelesssufficedtodemon-stratetheexistenceofextendedmassivedarkhaloesaround(spiral)galaxies.Morerecently,large,homogeneousgalaxysurveys,suchastheSloanDigitalSkySurvey(SDSS;Yorketal.2000)andtheTwoDegreeFieldGalaxyRedshiftSurvey(2dF-GRS;Collessetal.2001)havedramaticallyimprovedboththequantityandqualityofdataon(nearby)galaxies,thusallowingtheconstructionofmuchlargersamplesofhost-satellitepairs(McKayetal.2002;Pradaetal.2003;Brain-erd&Specian2003).Yet,eachofthesestudieshasbeenc2004RAS2vandenBosch,Norberg,Mo&Yangextremelyconservativeintheirselectionof“isolated”hostsand“tracer”satellites.Forexample,McKayetal.(2002),Pradaetal.(2003)andBrainerd&Specian(2003)usedsampleswith1225,2734,and2340satellites,respectively.Forcomparison,theSDSSand2dFGRS,fromwhichthesesampleswereselected,containwellinexcessofonehundredthousandgalaxies.Themainreasonforbeingsoconservativeistopreventtoolargenumbersofinterlopers(i.e.,satellitesthatarenotboundtotheirhostgalaxies,butonlyappearassociatedbecauseofprojectioneffects).Inaddition,these-lectioncriteriaareoptimizedtoonlyselectisolatedgalaxies,withthemotivationthatthedynamicsofbinarysystems,forexample,aremorecomplicated.Inthispaperweuseadifferentapproachandinvesti-gatetowhatextentthekinematicsofsatellitegalaxiesmaybeusedtoestimatethemeanmass-to-lightratio,averagedoverallpossibledarkmatterhaloes.Wemakethesimpleansatzthatsatellitegalaxiesareinvirialequilibriumwithintheirdarkmatterpotentialwell.Thisismotivatedbythefindingthatdarkmattersubhaloes,whicharelikelytobeassociatedwithsatellitegalaxies,haveindeedbeenfoundtobeinasteady-stateequilibrium(Diemand,Moore&Stadel2004).Althoughweacknowledgethatnotallsystemswillbefullyvirialized,wehyp