Dynamical modelling of luminous and dark matter in

arXiv:0709.0691v1[astro-ph]5Sep2007Mon.Not.R.Astron.Soc.000,1–23(2002)Printed1February2008(MNLATEXstylefilev2.2)Dynamicalmodellingofluminousanddarkmatterin17Comaearly-typegalaxiesJ.Thomas1,2⋆,R.P.Saglia2,R.Bender1,2,D.Thomas3,K.Gebhardt4,J.Magorrian5,E.M.Corsini6andG.Wegner71Universit¨atssternwarteM¨unchen,Scheinerstraße1,D-81679M¨unchen,Germany2Max-Planck-Institutf¨urExtraterrestrischePhysik,Giessenbachstraße,D-85748Garching,Germany3InstituteofCosmologyandGravitation,MercantileHouse,UniversityofPortsmouth,Portsmouth,PO12EG,UK4DepartmentofAstronomy,UniversityofTexasatAustin,C1400,Austin,TX78712,USA5TheoreticalPhysics,DepartmentofPhysics,UniversityofOxford,1KebleRoad,OxfordU.K.,OX13NP6DipartimentodiAstronomia,Universit`adiPadova,vicolodell’Osservatorio3,I-35122Padova,Italy7DepartmentofPhysicsandAstronomy,6127WilderLaboratory,DartmouthCollege,Hanover,NH03755-3528,USAAccepted1988December15.Received1988December14;inoriginalform1988October11ABSTRACTDynamicalmodelsfor17early-typegalaxiesintheComaclusterarepresented.Thegalaxysampleconsistsofflattened,rotatingaswellasnon-rotatingearly-typesinclud-ingcDandS0galaxieswithluminositiesbetweenMB=−18.79andMB=−22.56.Kinematicallong-slitobservationscoveratleastthemajorandminoraxisandextendto1−4reff.AxisymmetricSchwarzschildmodelsareusedtoderivestellarmass-to-lightratiosanddarkhaloparameters.Ineverygalaxythebestfitwithdarkmattermatchesthedatabetterthanthebestfitwithout.Thestatisticalsignificanceisover95percentfor8galaxies,around90percentfor5galaxiesandforfourgalaxiesitisnotsignificant.Forthehighlysignificantcasessystematicdeviationsbetweenobservedandmodelledkinematicsareclearlyseen;fortheremaininggalaxiesdifferencesaremorestatisticalinnature.Best-fitmodelscontain10-50percentdarkmatterinsidethehalf-lightradius.Thecentraldarkmatterdensityisatleastoneorderofmagni-tudelowerthantheluminousmassdensity,independentoftheassumeddarkmatterdensityprofile.Thecentralphase-spacedensityofdarkmatterisoftenordersofmag-nitudelowerthanintheluminouscomponent,especiallywhenthehalocoreradiusislarge.Theorbitalsystemofthestarsalongthemajor-axisisslightlydominatedbyradialmotions.Somegalaxiesshowtangentialanisotropyalongtheminor-axis,whichiscorrelatedwiththeminor-axisGauss-HermitecoefficientH4.Changingthebalancebetweendata-fitandregularisationconstraintsdoesnotchangethereconstructedmassstructuresignificantly:modelanisotropiestendtostrengtheniftheweightonregular-isationisreduced,butthegeneralpropertyofagalaxytoberadiallyortangentiallyanisotropic,respectively,doesnotchange.Thispaperisaimedtosetthebasisforasubsequentdetailedanalysisofluminousanddarkmatterscalingrelations,orbitaldynamicsandstellarpopulations.Keywords:stellardynamics–galaxies:ellipticalandlenticular,cD–galaxies:kinematicsanddynamics—galaxies:structure1INTRODUCTIONEllipticalgalaxiesarenumerousamongthebrightestgalax-iesandtheyharbourasignificantfractionofthepresent-daystellarmassintheuniverse(Fukugita,Hogan&Peebles1998;Renzini2006).Keyparametersfortheunderstand-ingofellipticalgalaxyformationandevolutionare,among⋆E-mail:[e-mail],thecentraldarkmatterdensity,thescalingra-diusofdarkmatter,thestellarmass-to-lightratioandthedistributionofstellarorbits.Whiletheconcentrationofthedarkmatterhaloputsconstraintsontheassemblyepoch(Navarro,Frenk&White1996;Jing&Suto2000;Wechsleretal.2002),theorbitalstatecontainsimprintsoftheassemblymechanismofellipticals(e.g.vanAlbada1982;Hernquist1992,1993;Weil&Hernquist1996;Dubinski1998;Naab&Burkert2003;Jesseit,Naab&Burkert2005).2J.Thomasetal.Informationaboutellipticalgalaxymassesareinprincipleofferedthroughvariouschannels.Theanaly-sisofX-rayhalotemperatures,thekinematicsofocca-sionalgasdiscsandgalaxy-galaxylensingprovideev-idenceforextendeddarkmatterhalosaroundearly-typegalaxies(e.g.Bertolaetal.1993;Pizzellaetal.1997;Loewenstein&White1999;Oosterlooetal.2002;Hoekstraetal.2004;Fukazawaetal.2006;Humphreyetal.2006;Kleinheinrichetal.2006;Mandelbaumetal.2006).Thesemethodsdonotconstraintheinnerhalo-profilesstrongly,however.Atnon-localredshiftsstronglensingcon-figurationsallowadetailedreconstructionofthemassen-closedinside,say,reff(e.g.Keeton2001;Koopmansetal.2006).Noneoftheabovementionedobservationalchannelsissensitivetodynamicalgalaxyparameters,suchasthedis-tributionofstellarorbits.Dynamicalmodellingofstellarkinematicshastheuniqueadvantagethatitallowsreconstructionofboththemassstructureandtheorbitalstateofagalaxy.High-qualityobservationsoftheline-of-sightvelocitydistribu-tions(LOSVDs)outtoseveralreffareneededforthispur-pose.Toovercometheproblemsofmeasuringabsorptionlinekinematicsinthefaintoutskirtsofellipticals,discretekinematicaltracerssuchasplanetarynebulaeorglobularclusterscanbeusedtoadditionallyconstrainthemassdis-tribution(e.g.Sagliaetal.2000;Romanowskyetal.2003;Pierceetal.2006).Sincestarsingalaxiesbehavecollisionlesslytofirstor-der,thedistributionofstellarorbitsisnotknownaprioriandverygeneraldynamicalmethodsarerequiredtoprobeallthedegreesoffreedomintheorbitalsystem.Sofaronlyonelargesampleof21round,non-rotatinggiantellipticals