The Effects of Substructure on Galaxy Cluster Mass

arXiv:astro-ph/9503038v29Mar1995TheEffectsofSubstructureonGalaxyClusterMassDeterminationsChristinaM.BirdDepartmentofPhysicsandAstronomy,UniversityofKansas,Lawrence,[e-mail]nintheAstrophysicalJournalLettersReceived;accepted–2–ABSTRACTAlthoughnumerousstudiesofindividualgalaxyclustershavedemonstratedthepresenceofsignificantsubstructure,previousstudiesofthedistributionofmassesofgalaxyclustersdeterminedfromopticalobservationshavefailedtoexplicitlycorrectforsubstructureinthosesystems.InthisLetterIpresentthedistributionsofvelocitydispersion,meanseparation,anddynamicalmassesofclusterswhensubstructureiseliminatedfromtheclusterdatasets.Ialsodiscussthechangesinthesedistributionsbecauseofthesubstructurecorrection.Comparingthemassesofclusterswithcentralgalaxiesbeforeandaftercorrectionforthepresenceofsubstructurerevealsasignificantchange.Thischangeisdrivenbyreductionsinthemeanseparationofgalaxies,notbyadecreaseinthevelocitydispersionsashasgenerallybeenassumed.CorrectionforsubstructurereducesmostsignificantlythemassesofsystemswithcoolX-raytemperatures,suggestingthattheuseofaconstantlinearradius(1.5h−1100Mpcinthisstudy)todetermineclustermembershipisinappropriateforclustersspanningarangeoftemperaturesand/ormorphologies.–3–1.IntroductionStudiesofgalaxyclusterdynamics,simulationsofstructureformationandanalyticalargumentssuggestthatwearelivingintheeraofclusterformation.Forthisreason,theassumptionofdynamicalequilibriummadeinearlyclusterstudiesnolongerseemsvalid.Overthelast15years,thestudyofsubstructureinclustershasbecomevitaltothestudyofclustersingeneral.Fromthecosmologicalpointofview,clustersareusefulfortracingthelarge-scaledistributionofmatterintheUniverse,fordeterminingthevalueoftheHubbleconstantthroughtheSun’yaev-Zel’dovicheffectandothermethods,andformeasuringthevalueofthematterdensityoftheUniverse.Thepresenceofsubstructureimpliesthatnon-equilibriummodelsneedtobeincorporatedintothesestudiestocorrectlyreplicatethebehavioroftheobservedUniverse.Similarly,thedensityofagalaxy’senvironmentappearstohaveprofoundeffectsonthestructureandevolutionofgalaxies.Ahighfrequencyofsubstructureinclustersimpliesthattheenvironmentofanyparticulargalaxyneedstobedeterminedlocally,notglobally(asfirstpointedoutbyDressler,1980).AwidevarietyofobservationsinboththeopticalandX-rayregimesprovideconvincingevidencethatsubstructureinclustersiscommon,ifnotubiquitous.X-rayimagingobservationswiththeEinsteinsatellitefirstrevealedthatcomplexityintheintraclustermedium(ICM)isfrequent(Formanetal.1981;Henryetal.1981),incontrasttothesmoothconfigurationsassumedinearlystudies(cf.Kent&Gunn1982;Kent&Sargent1983).Sincethen,bothoptical(Geller&Beers1982;Baier1983;Beersetal.1991;Bird1993,1994a,b)andX-raystudies(Jones&Forman1992;Davis&Mushotzky1993;Mohr,Fabricant&Geller1993)haverevealedthepresenceofsignificantsubstructureingalaxyclusters.Thephysicalimportanceofsubstructureislessclear.Althoughmostsubstructurediagnosticsaresensitivetodeviationsonsmallmassscales(Escaleraetal.(1994)claimed–4–thatmostofthesubstructuretheydetectisontheorderof10%ofthetotalclustermass),carefulanalysisrevealsthatkinematicalanddynamicalestimatesofclusterpropertiescanbeseverelyaffectedbytheseapparentlylowlevelsofcontamination(cf.Beers,Flynn&Gebhardt1990;Bird1994a).InthispaperIpresentananalysisofthedynamicalmassesofrichgalaxyclustersbasedonthevelocitiesandpositionsofclustergalaxies.Theclusterdatasetconsistsofclusterswithcentraldominantgalaxieswhichhaveatleast50measuredredshifts(theredshiftsaretakenfromtheliterature,listedinTable1ofBird1994a).TheseclustersarelimitedtomorphologicaltypescD(optical)orXD(X-ray);theselectioncriteriaarediscussedinmoredetailinBird1994a.ThelargeobservationaldatabasepermitsuseofanobjectivepartitioningalgorithmcalledKMM(Ashman,Bird&Zepf1994)toidentifyandeliminatesubstructure“contamination”fromtheprimarysubclusters,thosethatcontainthecentralgalaxy.TheopticaldataissupplementedbyX-raytemperaturesfromtheliterature;thesevaluesarepublishedinBird,Mushotzky&Metzler(1995)alongwiththeirsources.Theprimarypurposeofthecurrentworkistoshowthatevenintheseclusters,longbelievedtobethemostdynamically-evolvedsystems,thedistributionofobservedmassesisdramaticallychangedifsubstructureisobjectivelyeliminatedfromtheclusterdatasets.ThisresultisincontrasttothatofBivianoetal.(1993)andEscaleraetal.(1994),whoclaimedthatthepresenceofsubstructuredidnotaffecttheresultsoftheiropticalmassdeterminations.InSection2,Ireviewthedynamicalmassestimatorsandprovidethedistributionsofvelocitydispersion,meangalaxyseparationanddynamicalmassfortheclusterdataset,bothbeforeandaftersubstructurecorrection.InadditionIquantifytheeffectsofsubstructurecorrectiononthesedistributions.IdiscussvariouscausesofthechangeintheclustermassdistributioninSection3.–5–2.DynamicalMassEstimatorsForasystemindynamicalequilibrium,theJeansequationrelatesthekineticenergyofthegalaxiestothebindingmassofthecluster:−GngalMopt(r)r2=d(ngalσ2r)dr+2ngalrσ2r(1−σ2r/σ2t)(1)(Merritt1987),whereMoptistheoptically-determinedbindingmass,ngalis