X-Ray and Optical Properties of Groups of Galaxies

GROUPSOFGALAXIES1

arXiv:astro-ph/9403003v1 1 Mar 1994IanP.Dell’Antonio,MargaretJ.Geller,DanielG.FabricantHarvard-SmithsonianCenterforAstrophysics,60GardenSt.,

Cambridge,Ma,02138.

ObservationsreportedherewereobtainedattheF.L.WhippleObservatoryandattheMultipleMirrorTelescope,ajointfacilityoftheSmithsonianInstitutionandtheUniversityofArizona.

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ABSTRACT

Wehavemeasured125redshiftsin31groupsofgalaxiesobservedwithEin-stein,andhavecompiledanadditional543redshiftsfromtheliterature.Thereisacorrelationbetweeengalaxysurfacedensityandgroupvelocitydispersion,withµ∝σ1.6±0.6,butthescatteraboutthisrelationislarge.

Weexaminetherelationshipbetweenthegroupx-rayluminosityinthe0.3-3.5keVbandandthemeasuredvelocitydispersion.Richergroupsfollowthesamerelationasrichclusters(cf.Quintana&Melnick1982)withLx∝σ4.0±0.6,buttherelationflattensforlowerluminositysystemswhichhavevelocitydispersionsbelow300kms−1).

WesuggestthattheLx−σrelationarisesfromacombinationofextendedclusteremissionandemissionassociatedwithindividualgalaxies.Thex-rayemissionfortherichergroupsisdominatedbyemissionfromtheintragroupmedium,asforthericherclusters;emissionfromthepoorerclustersisdominatedbylessextendedemissionassociatedwiththeindividualgroupgalaxies.

1.INTRODUCTION

Groupsofgalaxiesareoneofthemostcommonenvironmentsintheuniverse:mostgalaxiesaremembersofgroupsorclusters(Soneira&Peebles,1978,Ramellaetal.1989,hereafterRGH).Groupstracelarge-scalestructure,andaretheprimaryconstituentsoflarge-scalefeaturesliketheGreatWall(GellerandHuchra1989,Ramellaetal1990).Thedistributionofgroupvelocitydispersionsisaconstraintonmodelsfortheformationoflarge-scalestructure(eg.Uedaetal.1993,Mooreetal.1992).

Catalogsofindividualgroupsprovideinformationaboutthemass-to-lightratiosandevolutionofsystemsofgalaxies.Opticaldataalonecanbeusedtotestwhethergroupsofgalaxiesarerelaxedsystems.Forexample,theworkofDiaferioetal.(1993)suggeststhattheyaredynamicallyyoung.X-raydatacanprovideamass-to-lightestimateforgroupsindependentoftheopticaldata(Krissetal.1983,hereafterKCC,Mulchaeyetal.1993),andtherelationbetweenthex-rayandopticalpropertiescanprovidefurthercluestothehistoryofthegroupsandtheirpresentstate.

Althoughtherehavebeenseveralstudiesoftheopticalpropertiesofgroups(RGH,Hicksonetal.1982,Bahcall1980,Beersetal.1984,Huchra&Geller1982,Diaferioetal1993),andsomeanalysesofthex-rayemissionfromgroups(KCC,Priceetal.1991,hereafterPBDN,Mulchaeyetal.1993,Ponman&Bertram1993),therehasbeennoattempttoobtaincompleteopticaldataforalargesetof

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systemsobservedinx-rays.

Herewestudyasampleof31groupsandpoorclustersobservedwiththeEinsteinObservatory.Wehavecollected668redshiftsforgalaxiesinthegroupfields.Weusetheredshift,galaxysurfacenumberdensity,andx-raydatatoin-vestigatethephysicalpropertiesofgroups.Throughoutthepaper,weassumeHo=100kms−1Mpc−1.

Section2.1containsadiscussionoftheobservations.Insection2.2,wediscussthegroupselectioncriteria.Section2.3containstheresultsoftheanalysisoftheopticaldata.Sections3.1-3.5dealwiththex-raydatareduction.Finally,insection4,wecomparetheopticalandx-raydata.

2.OPTICALDATA

2.1GroupSelectionandSpectroscopy

Oursampleincludes31groupsofgalaxiesobservedwiththeEinsteinsatellite.Ofthese,26“groups”arein23fieldsobservedbyPBDN,and5wereobservedbyKCC.Thesampleisnotstatisticallycomplete;thegroupswereoriginallyselectedbecausetheyhadbeenobservedwiththeVLA(Burnsetal.1987),orbecausetheycontainacentrallydominantgalaxy(MKW-AWMgroups).AfewothergroupshavebeenobservedwiththeEinsteinsatellite.Insomecases,wehaveomittedthemfromouranalysisbecausewedonothavecompleteredshiftinformation.WeomitothergroupsbecausetheyaretoonearbytofitwithintheEinsteinfield.Foreachofthesegroups,weobtainedredshiftsforgalaxieswithmB≤15.7within1.5◦ofthex-raypointingcenters,correspondingtoaradiusof∼2.8Mpcattheredshiftofthefarthestgroup(z∼0.04),and∼0.4Mpcforthenearestone(z∼0.005).Inallbutthetwonearestcases,thisradiusislargerthanthetypicalsizeofgroupsobjectivelyselectedfromaredshiftsurvey(rH≃0.6Mpc,cf.RGH).TheangularscaleisalsoslightlylargerthanthefieldofviewoftheEinsteinsatellite.Wechosethisangularscaleratherthanaphysicalscalebecausethegroupswereoriginallyselectedonthebasisoftheirangularextent.Weexaminethegrouppropertieswithinthe1.5◦fieldandwithinafixed0.7Mpccirclearoundthex-raycenters.Table1liststhenewheliocentricradialvelocities(cz).

Wemeasuredredshiftsofthegroupgalaxieswiththephoton-countingReticonsystems(Latham1982)ontheTillinghastReflector(1.5m)attheWhippleObser-vatoryorwiththebluechanneloftheMMTspectrograph.Weobtainheliocentricradialvelocitiesbycross-correlatingobjectspectraagainststellarandgalaxytem-plates(Tonry&Davis1979,Kurtzetal.1992),orbyfittingagaussianfunctiontoemissionlines.Thecross-correlationerrorsareestimatedfromthewidthofthecorrelationpeakanditsheightrelativetothenoise.Ifemissionlinesarepresent,weestimatetheerrorfromthedispersionofvelocitiesdeterminedfromindivid-3

ualemissionlines,weightedbythegoodnessoffit(Tonry&Davis1979,Kurtzetal.1992).Theaveragecalculatedexternalerrorforourvelocitymeasurementsis∼35kms−1;theactualexternalerrorshouldbeonlyslightlylarger(c.f.Lewis1983).Inallcaseswequoteheliocentricvelocitiesintheformv=cz,wherezisthemeasuredspectralredshift.

Foreachgroup,table2liststheposition,meanradialvelocity,andnumberofvelocitiesforgalaxiesbrighterthanmb=15.7inboththe1.5◦and0.7Mpcsamples.Wederivethesequantitiesfromatotalof543redshiftsfromtheliterature(Huchraetal.1992)alongwithour125newmeasurements.Fourofthegroups,N56-388,N56-391,N56-394a,andMKW3,arenotcompletetomB=15.5;weomitthesefromthesurfacenumberdensityanalysis,butweincludetheminourx-rayluminosityandvelocitydispersionstudies.Inseveralcases,therearegalaxiesfainterthanmB=15.7withknownredshiftsinourfields.Weincludethesegalaxiesinourcalculationofthevelocitydispersion.

Column1oftable2liststhenameofthegroup;columns2-4containtherightascensionofthegroupcenters;columns5and6listthegroupcenterdeclination.Column7tabulatesthemeanrecessionvelocityforeachgroupandtheuncertaintyinthemeasurementsderivedfromtheindividualmeasurementuncertaintiesandastatisticaljack-knifeprocedure(DiaconisandEfron1983).Columns8and9andcolumns10and11listthenumberofgroupmembersinthe1.5◦and0.7Mpcsamples,respectively.Ineachcase,thefirstnumberrepresentsthenumberofgroupgalaxiesknown,thesecondisthenumberofgalaxieswithmeasuredredshiftandwithmB≤15.7.Column12givesthecompletenesslimitforeachgroup.

Figures1a-1fshowthespatialdistributionofthegalaxiesonthesky,andthepositionofthe0.7Mpccircleforall31groups.InFigures1a-1f,thefilledcir-clesrepresentgroupmembers;thecrossesandtrianglesrepresentforegroundandbackgroundgalaxies,respectively.

2.2GroupMembership

Oncewehaveselectedthegroupfields,wedefinethegroup“membership”.Objectivegroupselectionalgorithmsextractgroupsfromlarge-scalesurveysbymakingcutsinprojectedseparationandvelocity(RGH).However,onecannot“objectively”selectthegroupsinthiswayaposteriori.

Ourgroupfieldswereselectedbyotherworkersanddonotrepresentacom-pletesample.Ineffect,aselectionbasedonangularsizehasalreadybeenapplied.Wethuslimitourselveswhereverpossibletousingthevelocityseparationsasanadditionalmembershipcriterion.

AllgroupsexceptMKW2,N67-336aandN67-336bcanbedefinedbyavelocitycutalone,aconsequenceoftheeffectivespatialcutmadepreviouslytoselectthegroupfields.Wecalculatethevelocitydispersionofthecentralenvelopeofgalaxies

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(definedasallgalaxiesdifferingbylessthan200kms−1fromanothermember).Iftheseparationbetweenanoutlierandthenearestassignedmemberislessthan1.2σ,weaddthegalaxytothegrouplist.Thisprocedureisinsensitivetotheminimumσcriterion.Werepeattheprocedureforalltheoutliers.Althoughourprocedurediffersfromthe3σclippingprocedure(Yahil&Vidal1977),inpracticethegroupsarewellseparatedinredshiftspace,andthedifferencebetweenourprocedureand3σclippingisgenerallynegligible.Inonlyonecase,S49-147,thevelocitydispersionderivedbyourmethoddiffersfromthe3σclippingvelocitydispersionbymorethantheerrorintheestimate:forS49-147,inclusionoftheoutliersasmandatedby3σclippingyieldsavelocitydispersionσ=422kms−1.Thishighervelocitydispersioniscausedbysymmetricallyplacedoutliersinredshiftspace(seefigure2a).Theseoutliersaresignificantlyseparatedfromthewell-definedcentralpeak;furthermore,alltheoutliersliefarfromthecoreofthegroup(seefigure1a).Thelowerσ=246kms−1probablymakesmoresense.

Evenincaseswheretherearetwogroupssuperimposedonthesky,ourpro-cedureisrobustprovidedthattheredshiftseparationbetweenthegroupsislargeenough(cf.N56-394aandN56-394b.)Forthetwocaseswherethereareoverlappinggroups–MKW2andMKW2s,andN67-336aandN67-336b–weusethegalaxypositionstomakethemembershipassignments(wedonotincludeMKW2Sinourgroupsamplebecausewelackcompleteredshiftdataforit).Becauseitisvirtuallyimpossibletoassignthegalaxiesintheoverlapregion,weconsideronlythecoresofthegroups,definedascirclesof0.45Mpcabouttheopticalcentersofthesubclumps(correspondingtothedensitypeaksandlistedintable3).Althoughthisproceduregreatlyreducesthenumberofredshiftsavailableforanalysis,itreducestheriskofcontaminationfromtheneighboringgroup.

Figures2a-2fshowtheradialvelocitydistributionsforgalaxiesinour1.5◦fields;thegroupmembersappearashatchedhistograms.Table4liststhederivedvelocitydispersions(correctedfor“redshiftinflation”inaccordancewithDaneseetal.1980)ofoursystemsforboththe1.5◦(columns2and3)and0.7Mpcsamples(column4and5).Ineachcase,wecalculatethevelocitydispersionfirstusingalltheavailableredshiftsandthenusingonlythoseofgalaxiesbrighterthanmB=15.7.Column6liststhegroupsurfacenumberdensityparameterµ(seesection2.3).

WiththeexceptionofN45-389,thederivedvelocitydispersionsaregenerallyquitestable,despitethelargevariationsinthenumberofgalaxiesinthedifferentsamplesforaparticulargroup.InthecaseofN45-389,thedifferenceintheve-locitydispersionbetweenthesamplesmightbeattributabletoanouterenvelopeofgalaxiesinfallingontoatightlybound,lowvelocitydispersion,centralcore.Inothercaseswherethevelocitydispersionvariessignificantly–N56-369,N56-394bandMKW6a–thenumberofgalaxiesusedtodeterminethedispersionissmall(3or4galaxies).Inthesecasesthevelocityestimatesintable3areunderestimatesbyasmuchasafactorof2,andthe1-Dvelocitydispersionwecomputeisabiasedes-timatorofthe3-Dvelocitydispersion(Diaferioetal.1993).Fortunately,thisbiasinthecomputedvelocitydispersionsforgroupswithfewredshiftmeasurementsaffectsonlyafewofthegroups,andthusdoesnotaffecttheconclusionsofthis

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study.

2.3CorrelationofVelocityDispersionandSurfaceDensity

Becauseourgroupswereselectedaccordingtotheirangularsize,thephysicalscaleofthegroupsisafunctionofdistance.Theprocedureforgroupselectionmakesitdifficulttodefineagroup“radius”aposteriori.Wedonotyethavesufficientphotometricdatatodetermineluminosityfunctionsforthegroups.Becauseofthedifficultyofuniformlydeterminingaspatialscaleandtheuncertaintyintheopticalluminosityofthegroups,derivedmass-to-lightratiosareindeterminate.Wethereforefocusonthevelocitydispersionandsurfacedensitywhichwecanderivefromourdata.

AlthoughthevalueforNgalintable2isrelatedtothe“richness”ofthegroups,aproperestimateofthesurfacenumberdensityofbrightgalaxiesinthesegroupsrequiresacorrectionfortherangeinthegroupredshifts.Weneedtonormalizeallthegroupstosamedistance.WecountgroupmembersbrighterthanmB=15.7withinthe0.7Mpccircle(smallerthanthe1MpccirclechosenbyZabludoffetal.(1993)).WenormalizetoafixeddistancebyassumingthatallthegroupshavethesameSchechterluminosityfunction.WechooseaSchechterluminosityfunctionwithα=−1.2andM*=−19.15,andnormalizeourdistancesto130Mpc.ThischoiceagreeswiththenormalizationofZabludoffetal.(1993).WherewearenotcompletetomB=15.7,weextrapolatefromthenumberofgalaxiesbrighterthanmB=15.5.TocompareourdatawithZabludoffetal.(1993),wenormalizebythemeanratioofthenumberofgroupmemberswithin1.0Mpcand0.7Mpc,n(1Mpc)/n(0.7Mpc)=r;weusegroupswherewehaveacompletesurveyto1MpcandmB=15.7.Thisratio,r,is1.42.ThenumberdensitiesarenotcorrectedtoaccountforGalacticobscuration.

Figure3showstherelationshipbetweenthenormalizedsurfacedensityandσforourgroupsandfortheclustersofZabludoffetal.(1993).Thevelocitydispersionisderivedusingallgroupgalaxies,includingthosewithmB>15.7(column3,table4).Thecorrelationbetweenthesurfacedensityofgalaxiesandvelocitydispersionextendsacrosstheentireobservedrangeofvelocitydispersions(50kms−1≤σ≤1200kms−1).Thebestfitrelationis

log(µ)=−4.3(±1.6)+1.6(±0.6)log(σ),

(1)

withaQvalue(Pressetal1993)of0.25(HereQistheprobabilitythatthechi-squarevalueofthefitwouldoccurbychance).ThefitisquiteabitmorerobustwhenweexcludethepoorclusterAWM7.AWM7isthegroupmostaffectedbygalacticabsorption,andthereforeweprobablyunderestimatethesurfacedensityofAWM7relativetotheothergroups.Correctingforthiseffectwouldimprovethefit.

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Simplemodelsofgroupscanaccountfortheobservedcorrelation.Foranisothermalsphere,theintegratedsurfacemassdensityinsideafixedradiusfol-lowstherelationµ∝σ2ForaKingmodel,therelationisslightlyflatterbecausethevelocitydispersiondropsoutsidethecoreofthesystem.Areasonableapprox-imationtoaKingmodelgivesµ∝σ1.8−1.9.Foroursampleofpoorclusters,theobservedslope(1.6±0.6)iscertainlyconsistentwiththeseestimatesfromsimplemodels.

3.THEX-RAYDATA3.1Observations

The31“groups”inoursamplewereobservedwiththeEinsteinObservatoryImagingProportionalCounter(IPC).Atotalof32fieldswereobserved,withob-servationtimesvaryingfrom400secondsto23000seconds.Forafewoftheshorterobservations,wederiveonlyupperlimitsfortheluminosity,butmanyofthegroupsaredetected(PBDN,KCC).

Wecalculatethex-rayluminositiesfromtheEinsteinimagesusingthecountsinthe0.3-3.5keVrange,whichcorrespondstoPulseHeightInvariant(PI)bins3-10.Weusetheopticalpositionsofthegroupgalaxiestocheckthatthex-rayemissionisactuallyassociatedwiththegroup.Toprovidethebestpossiblesignal-to-noiseratio,wecomputetheluminositiesonlyintheregionwherethereisadetectableexcessoverbackgrounddeterminedfromtheradialx-raysurfacebrightnessprofile.Wethusobtainisophotalluminositiesforthegroups,ratherthanfixed-apertureluminosities.Thisproceduremightunderestimatethetotalx-rayluminosityofsomeofthegroups,particularlythosewithshortobservationtimes.

Table4liststhex-rayparametersfortheobservedgroups.ThesecondcolumnliststhegalacticHIcolumndensity(incm−2)inthedirectionofthegroups,de-rivedfromtheBurstein&Heiles(1983)maps.Column3givesthearea(insquarearcminutes)usedinthefluxdetermination.Column4givesthemeangroupred-shift.Column5givesthebackground-subtractedcountsmeasuredforeachgroup.Column6liststheeffectiveexposuretimefortheEinsteinobservation.Thederivedtemperatureforeachgroupisincolumn7.Finally,Columns8and9tabulatethex-rayluminositiesforeachgroupinunitsof1042h−1ergss−1fortwoassumedgrouptemperatures,1keVandthetemperaturederivedfromtheLx−Trelation(Edge&Stewart1991),respectively.

42−1−1

Ingeneral,thegroupshavex-rayluminosities<∼10hergss.Thus,withveryfewexceptions,theextractionofthegroupx-rayemissionfromthedataisquitecomplex.Inmanycases,weexpectthex-raymapstobedominatedbyemissionfromtheindividualgalaxies.Atthedistancestypicalofthepoorclustersinthesample(60-90Mpc),almostallthegalaxieshave(optical)angularsizeslessthananarcminute.ThetypicalresolutionfortheEinsteinIPCis∼1.5′.Althoughthe

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largestgalaxiesinthenearergroupswillbeslightlyextendedwhenobservedwiththeEinsteinIPC,mostofthegalaxiesunderconsiderationareconsiderablysmallerthantheIPCresolution;asafirstapproximation,wemodelthemaspointsources.

3.2CreatingaPointResponseFunction

Manygroupsshowx-rayemissionstronglyclumpedatlocationscorrespondingtothepositionsofbrightgalaxies.Anaturalinterpretationforthisphenomenonisthatthex-rayemissionisjusttheintegratedemissionfromindividualsourcesinsidethegalaxiesthemselves,orpossiblyfromhotgasassociatedwiththeinterstellarmediumofthegalaxies(Fabbianoetal.1992).AsafirststepinidentifyingthecontributionofindividualgalaxiestotheX-rayemissionfromthepoorclusters,wemodeltheemissionfromindividualgalaxies.

TheEinsteinIPChasacomplicatedpointresponsefunction,whichdependsonboththephotonenergyandtheinstrumentgain.Tosimulatethesepointsources,wefollowMauche(1983):wemodeltheIPCasaconvolutionofanenergy-dependentmirrorresponsefunctionanda(gaussian)voltagegainsetting-dependentdetectorresponse.ForeachtypicalvalueoftheIPCgainsetting,wethencancreateapointresponsefunctiondependentontheenergyspectrumoftheincomingx-rays.Inordertoestimatetheeffectsofthedetectorresponse,weusetherawpulse-heightchannel(PH)dataratherthanthePIbinning.

Becauseearlyandlatetypegalaxieshavesubstantiallydifferentx-rayspectra,weconstructtworepresentative“pointsources”pergainsetting–oneforaspiralgalaxy,theotherforanelliptical.Weuserepresentativex-rayspectrafromFab-bianoetal.(1992).GiventheenergybandandtheIPCgainsetting,weconvolveagaussianofspecificwidth(Harndenetal.1984)withanEinsteinHRImonochro-matictestexposure.Afterconvolvingthemapsforeachchannel,weconstructaweightedsumoftheresultingmapstoobtainamodelpointresponsefunction.WealsoconstructmodelpointsourcesforAGNwithknownspectra(Wilkes&Elvis1987)inordertotestthevalidityoftheprocedure.Theresultingimagefitsthespatialdistributionofpointsourcesquitewell(figure4).

Thevariationsinthepointspreadfunctionsfordifferentspectraarenotverylarge.Typically,thewidthoftheprofilevariesby<∼5%FWHM.Variationsingainareamoreseriousproblem.Thehighvoltagegainsettinginfluencesthepointspreadfunctionbychangingthecorrespondencebetweenphotonenergiesandpulseheightchannel.Ifweconsiderthesameenergyrangeforallthemaps,thenweneedtoconsiderdifferentpulse-heightchannels.Thisproblemisespeciallyseriousatthelowenergyendofthex-rayspectrum,becausethedifferenceinFWHMbetweenthechannel2andchannel3IPCresponseis∼25%.Figure5showsthedifferenceintheradialprofilesforidenticalpointsourcesobservedwithgainsof12,14,16,18.Weusetheseradialprofilestodeterminewhetherthereisextendedx-rayemissionassociatedwiththegalaxiesinthegroups.

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3.3X-rayImageReduction

Toreducethefullx-rayimages,wefirstsubtractastandardbackgroundfile,scaledaccordingtothecountrateintheimageawayfromstrongsources.Wethenmultiplybyaflatfieldmaptocorrectforthevariationindetectorresponseacrosstheimage.WeconstructanerrorimagefromthedataassumingPoissonnoiseandanuncertaintyof25%inthebackgroundleveldetermination.Finally,toaidintheidentificationoflowsurfacebrightnessfeatures,wesmooththeimage(andtheerrormap)witha1.5′gaussian.Weusetheunsmoothedimagesinalltheanalyses.BecausetheEinsteinIPCfieldsoftencontainsourcesnotassociatedwiththegroups,wecomparethex-raymapwiththeobservedgalaxydistributiontoidentifytheemissionassociatedwiththegroup.Wethendeterminethenumberofcountsassociatedwiththegroupbysummingtheemissionfromtheselectedregionsoftheunsmoothedbackground-subtractedmaps.

3.4GroupProfiles,Poorvs.RichSystems

Itisinterestingtocontrastthemorphologicalappearanceofhighandlowdensityandvelocitydispersiongroups.Forexample,figures6and7comparetheprofilesforahighvelocitydispersion(N67-335==MKW4)andalowvelocitydispersiongroup(MKW10).Inbothcases,thereisasinglebrightsourceassociatedwiththegroup.InMKW10(σ=165kms−1),however,theradialprofileofthesourceisonlyslightlyextended;theexcessoverthepointsourceprofile(thedottedlineinfigure6)accountsforonly∼12%ofthetotalemission.Incontrast,N67-335(σ=476kms−1)isclearlyextended.Heretheexcessoverthepointsourceprofileismorethanafactoroffive.ThesurfacenumberdensityofN67-335(µ=0.748)ismorethantwicethatofMKW10(µ=0.305),asexpectedfromtheµ−σrelation.Thereisaneasilydiscernibletrendinthequalitativenatureofx-raysurfacebrightnessdistributionsforgroups:groupswithahighervelocitydispersion(andahighersurfacedensityofgalaxies)havemoreextendedemission,oftencenteredonthedominantopticalgalaxy.Thesesystemsalsotendtohavesmoother,moreregularx-raysurface-brightnesscontours(AWM4,figure8),thanthelessluminous,lowervelocitydispersionsystems(e.g.S34-111andS49-138,figures9,10).For

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thelowestvelocitydispersionsystems(σ<∼200kms),theemissionappearstobeconcentratedalmostexclusivelyaroundafewbright(mB≤15.7)galaxies;thex-raymorphologyofthesegroupsisinaccordancewithourmodelforthenatureofthegroupemission(seesection3.5).

Thex-rayemissionforlowσgroupsisroughlyconsistentwiththatexpectedfromtheindividualgalaxies.Asacheckonthismodel,weaddedupthebest(highestsignal-to-noise)observationsofgroupsmadewithhighvoltagegainset-tingsof16and18(N79-286,N67-336a,N56-381,S49-138,andMKW1s).Westacktheimagestosuperimposethecenterofemission,or,inthecasewherethereseem

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tobedistinctsources(e.g.S49-138),thecentersofemission.Figure11plotstheradialprofileofthis“summedimage”comparedtothepointsourceprofileforthesamegain.Theprofileisonlyslightlyextended,showinganexcessof∼10%overthepointsource.Someofthisemissioncanbeattributedtothepresenceofotherpointsourcesinthevicinity.Inaddition,uncertaintiesiscentroidingthesuperim-posedimagescouldaccountforsomeoftheexcess.Weestimatethatpositionaluncertaintiescontributeanuncertaintyof∼3%inthepointsourcefit.

3.5X-RayCounts-to-FluxConversionandTemperatures

Becausetheenergybinsareverybroad,thex-raycounts-to-fluxconversionde-pendsontheinputenergyspectrum,andthusonthetemperatureofthegroups.Temperaturesforthepoorclustershavenotbeenwellmeasured,butROSATob-servations(Ramella1993)indicatethatthetemperaturesare∼1KeV.

Wecalculatethecounts-to-fluxconversionintwoways.First,weassumeallthegroupshaveatemperatureof1KeV.Inasecondapproach,weextrapolatetheLx−Trelationforrichclusters(Edge&Stewart,1991)tolowerluminositiesandusetherelationtoderiveatemperatureandaluminosityforeachgroupiteratively.Thissecondprocedureleadstoluminositieswhichareupto40%loweratthelowluminosityendthanthefirstapproach.SomeofthepoorclustersatthehighvelocitydispersionendofoursampledohavepublishedX-raytemperatures(KCC,Schwartzetal.1980).Totreatallourgroupsconsistently,weusethetemperatureestimatesfromtheEdge&Stewartrelationinsteadofthemeasuredtemperatures.Thesetwoapproachesagreeinallcasestowithinthepublishederrorbars(KCC).Forcompleteness,Table5includesfluxesdeterminedfrombothapproaches;columns8and9givethex-rayluminositiesinthe0.3-3.5KeVband:column8tabulatestheluminosityassuminggrouptemperaturesof1KeV,andcolumn9containstheluminositiesassumingthederivedtemperatures(listedincolumn7).Thedifferencebetweenthesetwovaluesisanindicationofthesystematicuncertaintiesinthex-rayluminositymeasurements.

Infigure12,weplotthex-raygroupluminosities(assumingT=1KeV)againstthevelocitydispersions;forcomparison,wealsoincludeluminositiesandvelocitydispersionsforsomerichclusters(Zabludoffetal.1993,Struble&Rood1987).X-rayluminosityandvelocitydispersionareobviouslycorrelated.Wefind

log(Lx)∼31.81(±1.67)+4.0(±0.6)log(σ)

(2)

usingourgroupsalone.Thisresultisconsistentwiththerelationderivedforrichclusters(Quintanaetal.1982).IfweassumethetemperaturesderivedfromtheLx−Trelationforourgroups,wefindLx(Tg)∝σ4.2±0.7,notsignificantlydifferentfrom(2).However,ifweonlyconsiderthegroupswhichshowemissionassociated

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withindividualsources(thosewithLx≤1.5×1042h−1ergs−1),wefindashallowerslope,Lx∝σ2.7±1.3,albeitwithgreaterscatter.ThisflatteningoccursregardlessoftheLx−Trelationassumed.

Becauseweonlycalculateluminositieswithinregionswheretheemissionisstrongerthanthebackground,theluminositieswecalculatearelowerlimits:typ-40−1

icallywewouldnotdetectadiffusecomponentwithLx<∼1−4×10ergss.However,anyadditionalemissiononlyaccentuatesthedeviationofthepoorgroupsfromtheLx−σrelationdefinedbytherichersystems.

4.DISCUSSION

4.1Lx−σ:ObservationandTheoreticalConsiderations

Thestandardexplanationfortheobservedrelationbetweenthex-rayluminosityandthevelocitydispersionofrichsystemsofgalaxiesisthatbothquantitiesdependonthemassofthecluster.Thermalemissionfromtheintraclustergasyieldsanx-rayluminosityproportionaltothesquareofthegasdensity.Foraconstantmass-to-lightratio,thex-rayluminosityisthenproportionaltothesquareofthemassofthecluster.Iftheclusterisarelaxedsystem,thevelocitydispersionisroughlyproportionaltothesquarerootofthemass.Thus,Lx∝σ4,consistentwiththe

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observedslopederivedfromourgroupsample(50kms−1<∼σ<∼800kms)(figure12),andtheslopepreviouslyderivedforclusters.

Figure12showsthatalthoughtherich(highdispersion)groupsfollowtheLx−σrelationdefinedbyclustersquiteclosely,thereappearstobeaflatteningofthe

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relationforvelocitydispersions<∼300kms.Asimplemodelshowsthattheincreasingrelativecontributionoftheintegratedemissionfromindividualgalaxiesshouldcauseashallowerslopefortheselowerσsystems.

Forbothspiralandellipticalgalaxiesthereisacorrelationbetweenthex-rayandopticalluminosity(Fabbianoetal.1992):

.8

Lx(elliptical)=3.16×1021L1B

(3)

and

.0Lx(spiral)=2.00×1029L1B

(4)

whereLxisinergs−1andLBisinsolarluminosities.Thereisalargescatter

(almostanorderofmagnitude!)aroundtheserelations.Ifthegroupluminosity

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functionisaSchechterluminosityfunction,thetotalx-rayluminosityfromthegroupis

Lx(tot)=rµo

󰀃∞

Xmin

x−αe−x(fspLx(spi,x)+(1−fsp)Lx(ell,x))

(5)

wherex=L/L*,risthecorrectionfactorfromsection2.3,andµoisafiducialsurfacenumberdensity.ThelowerlimitofintegrationisXmin=Lmin/L*andLministheminimumgalaxyluminosity(whichwetaketobeMB=−13.)

Ourmeasuredsurfacenumberdensityis

µ=µo

󰀃∞

Xo

x−αe−xdx

(6)

whereXo=Lo/L*andLoistheluminositycorrespondingtoourlimitingmagnitudeofmB=15.7atadistanceof130Mpc(Mo=−20.19).Wecanthenwrite(3)intermsofµ:

󰀁󰀄

Lx(tot)=rµ

x−αe−x(fspLx(spi,x)+(1−fsp)Lx(ell,x))

5.CONCLUSIONS

Wehavecollectedauniformdataset,consistingofvelocitydispersions,surfacenumberdensities,andx-rayluminositiesfor31groupsofgalaxies.Wefindarelationbetweenthesurfacegalaxynumberdensityandvelocitydispersion,µ∝σ1.6±0.6.Forcomparison,foranisothermalspheretherelationisµ∝σ2,andforaKingmodelµ∝σ1.8−1.9.

Thex-rayluminosity-velocitydispersionrelationforrichclusterscontinuesto

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poorersystemsaswell,withLx∝σ4.0±0.6.Forthegroupswithσ<∼300kms,however,thereisasignificantflatteningintherelation:Lx∝σ2.7±0.3.Wesuggestthatthischangeinsloperepresentsthetransitionbetween“ICMdominated”and“galaxy”dominatedsystems.Thismodelisconsistentwiththex-raymorphologyofthegroups;forσ≥300kms−1thegroupshavesmooth,extendedx-raysurfacebrightnessprofiles.Forσ≤300kms−1thegroupemissionisconsistentwithacollectionof“pointsources”associatedwiththeindividualgalaxiesinthegroups.Unfortunately,thex-raydataavailableforthepoorgroupsisnotsufficienttode-terminewhethertheintraclustermediumofthesegroupsislessabundant,orisjusttoocooland/ordiffusetobeseen.Longerobservationswithimagingx-raytelescopessuchasROSATorAXAFshouldallowustoanswerthisquestion.Be-causeweonlycalculateluminositiesinregionswheretheemissionisgreaterthanthebackground,wemightbeunderestimatingtheluminosityofourfaintestgroups.However,thisonlyincreasestheflatteningoftheLx−σrelation,becausetheerrordoesnotdependonthegroupluminosity.

Itwouldbeinterestingtoinvestigatewhetherthereareotherquantitieswhichshowdifferencesbetweenhighvelocitydispersionandlowvelocitydispersionsys-tems.Forexample,studiesofthebaryoncontentoftheComacluster(Whiteetal.1993)suggestthatthebaryonfractioninclustersissubstantiallyhigherthanexpectedfromprimordialnucleosynthesislimits.Blumenthaletal.(1984)havesug-gestedthatricherMKW/AWMgroupsalsohavehigherbaryonfractions.However,Mulchaeyetal.(1993)havefoundamuchlowerbaryonfractionforatleastonepoorergroup.Itwouldbeusefultoextendthiscalculationtosmallersystemsbyacquiringaccuratephotometricdatatoimproveestimatesofmass-to-lightratios.Detailedphotometricstudiesalongwithredshiftsforevenfaintermemberswouldyieldinformationaboutthebaryonfractioningroups,apotentiallyimportantcon-straintonmodelsofgalaxyandstructureformation(Whiteetal.1993).

WethankMassimoRamella,AntonaldoDiaferio,JoeMohrandAnnZabludoffforhelpfulandstimulatingdiscussions.WethankM.Ramellaforprovidinginfor-mationaboutROSATobservationsinadvanceofpublication.WethankS.Tokarzforhelpwiththedatareduction.Wethanktheanonymousrefereeforusefulcrit-cismandsuggestions.ThisresearchfundedinpartbyNASAgrantNAGW-201,andbytheSmithsonianInstitution.

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FigureCaptions

Figures1a-f:Thepositionsofgalaxiesinthe1.5◦fields;groupmembersaredenotedbyfilledcircles,foregroundgalaxiesbycrosses,andbackgroundgalaxiesbyopentriangles.Thelargecirclesindicateregionswithin0.7Mpcofthex-raycenter.

Figures2a-f:Velocityhistogramsforthe1.5◦groupfields.Thehatchedhis-togramrepresentsthegroupmembers,theopenhistogramshowstheinterlopers(or,inthecaseofN67-336a,N67-336bandMKW2,thegalaxiesnotinthecoreofthegroup).

Figure3:Aplotofthesurfacedensityofgalaxies(section2.3)versusvelocitydispersionforthegroupsinoursample(filledcircles)andrichclustersfromtheZabludoffetal.(1993)sample(stars).

Figure4:Acomparisonoftheradialprofileof3C273asobservedbyEinsteinwiththemodelprofileforaAGN-spectrumpointsource.

Figure5:Acomparisonofmodelpoint-sourceprofilesforanellipticalgalaxymeasuredat4differentgainvalues:18(dasheddottedline),16(largedashedline),14(shortdashedline)and12(solidline).Theradiusisinunitsof8-arcsecondpixels.

Figure6:Radialprofileforthex-rayemissionfromthegroupMKW10(squares)andapointsourcemodel(elliptical)normalizedtomatchataradiusof24arcsec-onds.Theerrorbarsare1-σerrors.Theexcessabovethepointsourcemodelatlargerradiiaccountsfor∼12%ofthetotalflux.

Figure7:RadialprofilefortheemissionfromthegroupN67-335(=MKW4)andforapointsourcemodelnormalizedasinfigure6.

Figure8:AcontourplotoftheEinsteinx-raymapforthegroupAWM4.Thecontourlevelsrepresent8,15,30,60,and90percentofthepeakintensity,respectively.ThecrossesrepresenttheopticalpositionsofmB(0)≤15.7galaxiesinthegroupfield;thexmarksthepositionofthecDgalaxy.

Figure9:AcontourplotoftheEinsteinx-raymapforthegroupS34-111.Thecontourlevelsrepresent30,60and90percentofthepeakintensity.Theclumpof

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emissioncenteredaroundpixel(250,100)isassociatedwithabackgroundgalaxy.Figure10:AcontourplotoftheEinsteinx-raymapforthegroupS49-138.Thecontourlevelsrepresent15,30,60and90percentofthepeakintensity.Theemissionappearstobeconcentratedaroundthethreecentralgalaxies.

Figure11:radialprofileofthecombinedx-rayemissionforlowerdispersion

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groups(σ<∼200kms)inourstudy.Figure12:Aplotofthex-rayluminosity(forTg=1Kev)versusvelocitydispersionσforourgroups(filledcircles),richclustersfromfigure3(filledstars)andotherclustersfromRood&Struble(1987)(openstars).Thefive-pointedstarsshowRosatobservationsofgroupsbyMulchaeyetal.(1993)andPonman&Bertram(1993).Thedottedandsolidlinesoutlinetherangeofluminositiesexpectedfromtheintegratedemissionfromindividualgalaxiesassumingµ=3.5×1038σ1.6,andµ=3.6×1034σ1.6,respectively.

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