1992ApJ. . .384. . .50A 3 46 6 7 8 protogalaxies. IntheEggen,Lynden-Bell,&Sandage(1962)pictureasmooth,homogeneouscollapseisenvisaged.The Fall&Rees complexes likeOriononlyabout10~oftheoriginalcloud willendupinaboundstarcluster.Theinferenceisthattheprogenitors framework oftheSearle&Zinnmodel,itisplausiblethat thecollisionandcoalescenceofsubunitscouldleadtoconditions model, theprocessoccursoveraperiodoffewbillionyears,severaltimeslongerthaninoriginalEggenetal.model. Withinthe built fromthehierarchicalmergingofsmallersubunits.Asaresultmorechaoticnaturecollapsein Searle-Zinn cooling historyofcloudsimprintsamass-scalecharacteristicglobularclustersontheoriginalspectruminhomogeneities. conditions, theseregions“hang-up”atatemperatureofaround10KandcorrespondingJeansmassM.In thiswaythe (1985) modelforglobularclusterformationfitsnaturallyintothispicture.Inscheme,theprotogalacticgasisrelatively smooth integrated spectraandvelocitydispersionsbetweenthenucleated coresandglobularclusters.Thismayberelatedtotheideaof nucleated dwarfellipticals.Therearevariousobservations thatprovidetentativesupportforthisview,suchassimilaritiesin mass ~5x10M- and atthevirialtemperatureofgalactichalo.Smalloverdensitiescondenseoutgasviathermalinstability. Under certain clusters. Mostofthemass thedwarfgalaxies,whichoriginallyresidesinlesstightly boundregions,isassumedtoformthe this viewofayoungglobularcluster.Inparticular,hecites a “superstarcluster”inNGC1705withanageexcessof10yrand of globularclustersmusthavehadmassesinexcess10 M. Suchobjectsmaybeidentifiedwiththeprotogalacticlumpsof of protogalaxiespromotestheconsiderationotherideas about globularclusterformation. appropriate fortheFall-Reesmodelglobularclusterformation (cf.Kangetal.1990).However,anemphasisonthelumpynature outer regionsofthedwarfsare easilyremoved,andFreemansuggeststhattheremaining densecoresarenowobservedasglobular are surroundedbymanysuch nucleateddwarfellipticalswhichsubsequentlygetdisrupted bysomedynamicalprocess.Thetenuous Larson (1986)discussedabove, sinceNGC1705appearstobecurrentlynucleating.Freeman (1990)suggeststhatglaxiesoriginally Searle-Zinn picture.Larson(1986)alsopointsoutthatsome starburstgalaxieshaveregionswhichmaysimilarpropertiesto well ascorrelationsbetweenclustermetallicityandpositionwithintheGalaxy,stronglysuggesttheseglobularclusters formedas the Galaxycollapsed(e.g.,Fall&Rees1988;Zinn1988). process ofgalaxyformation.WithintheMilkyWay,similaritiesbetweenglobularclustersystemandspheroid stars,as are judged.Becauseoftheirgreatages,spatialdistribution,kinematics,andmetallicity,theystandoutasobservableproducts ofthe 0 0 0 The AstrophysicalJournal,384:50-61,1992January1 © 1992.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. 1 AlsoSpaceTelescope ScienceInstitute. Zinnecker etal.(1988)andFreeman(1990)havesuggested thattheprecursorstoglobularclustersmaybecoresof Searle &Zinn(1978)proposedanalternativeviewofgalaxyformationinwhichprotogalaxiesareverylumpyand galaxies are Larson (1986)hasnotedthatinobservedstar-formingregions thefractionofparentcloudthatendsupinstarsissmall.In Models oftheformationglobularclustersduringprotogalacticcollapsearesomewhatdependentonassumed natureof In manywaysglobularclustersarethephilosopher’sstoneagainstwhichtheoriesofformationandearlyevolution ofgalaxies tests includedirectobservationsofnewlyformedglobularclustersinongoingmergersandpredictionsabout hypothesis isconsistentwithanumberofcurrentobservationsanddescribepossibleteststhemodel.These the numberandmetallicityofclustersasafunctionradiusinellipticalgalaxies. allows ustoestimatethenumberofclustersformedingalaxyinteractionsandmergers.Weshowthatour trum ofdensityfluctuations,thenumberglobularclustersthatformasafunctiongalacticmass.Italso large globularclustersystemsaroundsomegalaxiesinthecenterofgalaxyclusters.Weshowthatifallproto- Clouds, theexcessofclustersaroundellipticalsrelativetospiralssameluminosityandanomalously around spiralswillbeconstant.Extendingtheargumentallowsustopredict,foragivencosmologicalspec- spirals containsubgalacticcloudswithasimilarmassspectrum,thespecificfrequencyofglobularclusters Such eventscouldexplainthediskpopulationofclustersinGalaxy,youngglobularsMagellanic Subject headings:galaxies:ellipticalandlenticular,cD—formationinteractions THE FORMATIONOFGLOBULARCLUSTERSINMERGINGANDINTERACTINGGALAXIES © American Astronomical Society • Provided by the NASA Astrophysics Data System We suggestthatatleastsomeglobularclustersareformedduringtheinteractionormergerofgalaxies. galaxies: MagellanicClouds—globularclusters:general Space TelescopeScienceInstitute,3700SanMartinDrive,Baltimore,MD21218 Johns HopkinsUniversity,HomewoodCampus,Baltimore,MD21218 Received 1991April19;acceptedJuly3 1 Keith M.Ashman 1. INTRODUCTION Stephen E.Zepf ABSTRACT AND 50 1992ApJ. . .384. . .50A 4 46 fundamentally differentfromtheoldones.Moreover,forreasonablemass-to-lightratiosmassofGalacticglobulars hasquitea young clusters,whereaslatertype galaxiestendtocontainsuchobjects. conclusions fromsuchasmall andnonuniformsample.However,theydonotethatthe two massivespiralsarenotablydeficientin NGC 1569,1705,and NGC 5253,allofwhichseemtocontainyoungclusters.As KCpointout,itisdifficulttodrawfirm whereas IC1613appearstohave neitheryoungnoroldglobularclusters.Theremaining galaxiesconsideredbyKCareM33,M82, whereas youngclustersinthe SMCareclosetotheadoptedluminositythreshold.NGC 6822issimilartotheSMCinthisregard, globulars isnegligible(zerointheMilkyWay;afewmarginal candidatesinM31).TheLMChasalargenumberofyoungglobulars, with B—V<0.5andamassexceeding10M.Forthe twomassivespiralgalaxiesintheLocalGroup,numberofyoung possible associationwithgiantHncomplexesinnearbygalaxies. Theseauthorssummarizeresultsforasampleofnearbygalaxies that itmorecloselyresemblestheluminosityfunctionofMilky Wayglobulars. clusters oftheGalaxy,althougholdestLMChavemassescomparabletothosehaloclusters.Whilethis maysuggest that youngglobular clustersformpreferentially ininteractinggalaxies.Ofthe 14galaxiesdescribedabove, sixshowgoodevidencefor and attempttoidentifygalaxiesinwhichthenumberofyoung clustersrelativetooldislarge.Thisasomewhatqualitative disruption byvariousevolutionaryprocesses(Chernoff&Weinberg 1989).ThiswillmodifytheLMCclusterluminosityfunctionso two systemsisthepresenceofmassiveclustersinLMC whichhavenocounterpartsinthediskofMilkyWay.These suggested bysimilaritiesintheclusterluminosityfunctions (Elson&Fall1987).However,themostapparentdifferencebetween broad rangefromlessthan10Mtoover(Ashman1989).ManyoftheyoungLMCclustersfallcomfortably inthisrange. approach sincethedefinitionofayoungglobularclusteris necessarilyratherarbitrary.KCdefineayoungglobularasanyobject LMC containsyoungclusterswithmassescharacteristic of globulars.Wenotethatlessmassiveclustersaremoresusceptibleto observations areconsistentwiththeideathatbothGalactic diskandtheLMCarecurrentlyformingstarclusters,butonly some alterationintheconditionsofclusterformationoverpastseveralGyr,itneednotimplythatyoung clustersare older counterparts.Forinstance,Larson(1988)hasnotedthattheyoungLMCclustersaregenerallylessmassive than thehalo Magellanic Clouds.However,therehasbeensomedebateastowhethertheseveryyoungclustersaretrulyanalogous totheirmuch frequency ofglobularclustersaroundspiralgalaxies.Wealsoestimatethenumberthatform ingalaxy discuss otherimplicationsofourmodelin§6andpresentconclusions. interactions asafunctionoftheavailablegasmass.In§4wecompareourtheoreticalpredictionstoobservedglobular cluster interacting withlargergalaxies.Wealsodescribeindirectevidencethatsomeoftheglobularclustersinmassivegalaxies formedas increase inthenumberofclustersaroundellipticalsprovided,ashasbeensuggestedfromindependentconsiderations, suchgalaxies (1981) havequantifiedthiseffectbydefiningthespecificfrequencyofclustersS,whichisnumberperunit(M= systems andfindreasonableagreement.Theseconsiderationsleadtoobservationaltestsofthemodelwhichwedescribe in§5.We the resultofmergerorinteraction.In§3wedevelopourtheoryandpresentanargumenttoexplainconstancy ofthespecific nearby galaxies.Wesuggestthatgalaxiesinwhichglobularclusterformationiscurrentlyoccurringareusuallysystems whichare galaxies whichshowsignsofinteraction. have arelativelyhighfrequencyofmergersandinteractions.Perhapsmostimportantly,youngglobularclustersaremostly foundin are mergerproducts.TheenvironmentaldependenceofSarisesnaturallyinthisscheme,providedregionshigh galaxy density constancy ofthenumberclustersperunitgalaxyluminosityaroundgalaxiessamemorphologicaltype(Harris&Racine globular clustersformduringgalaxymergersandinteractions.AsSchweizer(1986)pointsout,thishypothesiscan explainthe that thenumberofglobularclustersaroundellipticalsexceedsspiralssameluminosity.Harris&vandenBergh these andsimilargalaxiesare“true”globularclusters.Theseconddifferencerelatestoclustersystemstheobservation terminated atanearlyepoch,therearesomegalaxieswhereglobularclustersstillforming.Thebest-studiedexamplesthe systems. this paperthatthereareimportantcluestotheformationofglobularclustersbefoundindifferencesbetweencluster galaxies withthelumpswithinprotogalaxy. visible spheroidofspiralgalaxies.InthecontextSearle-Zinnpicturegalaxyformationonecouldidentifythesedwarf sense thatgalaxiesofthesamemorphologicaltypegenerallyhavehighervaluesSinclustersthanfield(Bridges&Hanes Magellanic Clouds(e.g.,Westerlund1990,andreferencestherein),althoughthereisstillsomedebatewhethertheyoungglobularsin similarities includetheindependenceofcharacteristicmassclustersfromhostgalaxy(Harris1987),aswell 0 0 1990 andreferencestherein). 1979; Harris1988).AnequallystrikingandperhapsrelatedobservationisacorrelationbetweenSgalaxyenvironment,inthe 1979). Whilethesimilaritiesinglobularclusterpropertiesundoubtedlyprovideinsightsintoformationprocess,wesuggest v —15) galaxyluminosity.FornormalellipticalsthetypicalvalueofSisaboutafactor2higherthaninspirals(Harris&Racine There isnodoubtthatobjectssimilartotheoldglobularclustersofGalactichaloarecurrentlyformingingalaxies suchasthe Despite thelimitationsimposed bythecurrentobservations,wesuggestthatabove results areconsistentwiththehypothesis Kennicutt &Chu(1988;hereafterKC)haverecentlyreviewed thequestionofformationyoungglobularclustersandtheir A greaterconcernisthattheyoungobjectsinLMCaremorecloselyanalogoustoopenclustersofMilky Way,as The planofthispaperisasfollows.In§2wereviewobservationsyoungclustersintheMagellanicCloudsand someother In thispaperweattempttoexplainthesetwosetsofobservationsbyacommonmechanism.Wesuggestthatatleastsome These differencesfallundertwomaincategories.First,itisapparentthat,whileglobularclusterformationinmanygalaxies All oftheseschemesforglobularclusterformationmustexplainthesimilarityclustersinmanydifferentenvironments.These © American Astronomical Society • Provided by the NASA Astrophysics Data System 2. OBSERVATIONALCLUESTOGLOBULARCLUSTERFORMATION 2.1. GlobularClusterFormationatthePresentEpoch FORMATION OFGLOBULARCLUSTERS51 1992ApJ. . .384. . .50A merger productrelativetotheprogenitorspiralgalaxies. by normalellipticals.IthasbeenfoundthatthespecificfrequencyofglobularclustersSaroundellipticalsissignificantly greater from thesitesdiscussedin§2.1abovethatwearenowconcernedwithmucholderobjects.Thefirstpieceofevidence isprovided interacting galaxies.However,thereisotherevidencetosupportthisview.Further,asweillustrateinand in subsequent whether theseobjectsarecompactenoughtobeyoungglobulars,buttheobservationishighlysuggestive. present contextisthatNGC3077connectedtoM81byanHibridge,indicatingthesetwogalaxiesareinteracting.Inthis produce aglobularcluster,buttheresultsofKCsuggestthatconditionsaresuitableforthistooccur.Ofimportancein is moremassivethansimilarregionsinthediskofMilkyWay.Itobviouslyunclearwhetherthiscomplexwilleventually formation inmergersifonebelievesthatellipticalsformbymerger!However,weshow§5.1thespatialand metallicity envisage aninitialpopulationofglobularclustersformedduringprotospiralcollapse,withadditional forming when presence ofanumberbluestarclusters.Lutz(1991)notesthattheresolution100pcmakesitdifficulttoestablish categorically Vaucouleurs surfacebrightnessprofile,butthesignsofrecentmergerarestillapparent.Ofgreatinterestforthispaperis sections, thehypothesiscanexplaincertainpeculiaritiesofglobularclustersystems. These authorssuggestthattheclustermayhaveformedoutofPerseuscoolingflowwhichiscenteredonNGC1275,butthey globular clusters. Nulsen, &Cañizares1984;Ashman1990a)andcluster swapping(Muzzio1986).Mergersandinteractionsprovideanother values ofSinclustersthanthefield(Bridges&Hanes1990andreferencestherein).Thisispotentiallyveryinteresting sinceitmay distributions ofglobularclustersaroundellipticalsaddstrongsupporttoourhypothesis. galaxies mergeorinteractwitheachother.Ofcourse,thehigherSvaluesinellipticalsonlyprovideevidenceforglobular cluster the mergersofspiralsandthatglobularclustersareformedduringmergerevent(seeSchweizer1986).Morespecifically, we against amergingoriginforellipticals,sinceonewouldexpectStobethesame,orpossiblyless(dueclusterdisruption), inthe than thataroundspirals.TypicallySisafactorof2higherellipticals(Harris1988).Thishasbeenusedas anargument also notethatcollisionwithaforegroundgalaxymaybetriggeringthestarformation. and otherproperties,NGC3077isverysimilartoM82,whichasnotedaboveshowsevidencebothforinteractionyoung galaxies inwhichyoungglobularclustersareobservedoflatetype,themajorityclearlyinteracting. hypothesis. epochs areexpectedtocondenseoutofhighermetallicity gas. Thereisalreadyevidenceofahighermeanmetallicityintheclusters would expectdifferentepochsofclusterformationandthus aspreadinclusterages.Furthermore,globularclustersformingatlater possibility. Thepositionofcentralclustergalaxiesmakes themlikelysitesforaccretionofsmallergalaxies,soinourpicturewe galaxies inhigherdensityenvironmentsundergoearlier,moregaseousmergingevents,asmightbesupposed. propitious forformingellipticalsalsoleadtotheefficientformationofglobularclusters.ThistrendinScouldbe explainedif be relatedtotheincreaseoffractionellipticalsrelativespiralsinclusters.Inotherwords,maybeconditions thatare around M87(Strometal.1981)andNGC1399(Geisler& Forte1990)relativetoGalacticglobularswhichisconsistentwithour the originofthisanomaly(White1987),includingtidalstripping (Merrit1984),condensationoutofclustercoolingflows(Fabian, of NGC3077byBecker,Schilke,&Henkel(1989).Theseauthorsfindagiantmolecularcomplexinthisdwarfirregulargalaxythat satellite ofM31(Binney&Tremaine1987),althoughitisnotusuallyregardedasinteractingwithitslargerneighbor.Thustheonly gas-rich dwarfleadingdirectlytotheformationoftheseclusters isapossibility.Thereareargumentssuggestingthatgalaxylike kinematic, andmetallicitycharacteristicsofathickdisk (Zinn 1985).Inthecontextofpresentscenario,accretiona motivated bytheobservation thatthereisanapparentgroupofhaloclusterswithanarrow rangeinmetallicity,allofwhichappear counterparts (Tripicco1989). Asimilarscenarioforallglobularclustershasbeen proposed byRogers&Paltoglou(1984), consistent withthisidea.M31 alsohasadiskpopulationofmetal-richglobularswhich appearstobeyoungerthantheirhalo evidence thatthediskpopulation ofglobularsmaybesomewhatyoungerthanthe haloclusters(Sarajedini&King1989)is the MilkyWayislikelytohaveaccretedanappreciablemass fractionthroughsuchevents(e.g.,Bahcall&Tremaine1988).Recent accreted dwarf galaxies.Onepieceofevidence againstthisisthefactthat LMCglobularclustersshow moreflatteningthanMilky to haveretrogradeorbits. modulus makeitdifficulttoestablishifthisgalaxyisincloseproximityothers.Finally,M33anScwhichmaybeabound dynamically. Oftheremainingtwogalaxieswithyoungclusters,NGC1569isclassifiedasIrr,butuncertaintiesinitsdistance a classcharacterizedbybeingsatellitegalaxiesthatareusuallyinteractingwithlargergalaxy(Sandage&Brucato1979).The a substantialpopulationofyoungclusters(eightifoneincludestheSMCandNGC6822).Threethesegalaxiesareclassifiedas10, LMC isclearlyinteractingwiththeMilkyWay,bothhalogas(asevidencedbyMagellanicStream)aswell 52 ASHMAN&ZEPFVol.384 There areatleastthreedistinctsiteswherethereisindirectevidencethatglobularclustershaveformedinmergers. These differ Another objectofinterestistheyoungstarclusterfoundbyShields&Filippenko(1990)infilamentsaroundNGC1275. Galaxy environmentisalsoimportantindeterminingSsince,onaverage,galaxiesofthesamemorphologicaltype have higher One obviouswayofexplainingthehighervaluesSinellipticalsrelativetospiralsissupposethatareproduced by On theabovegroundsaloneitwouldbesomewhatspeculativetosuggestthatglobularclustersareformedin merging or Perhaps themostintriguingsystemofallismerginggalaxyNGC3597(Lutz1991).Thisobjectcanbefittedbyade Further evidenceforacorrelationbetweengalaxyinteractionsandtheformationofglobularclustersisprovidedbyobservations It ispossiblethattheseobservations canbeexplainedbyaccretionofglobularclusters thathadalreadyformedaroundthe Some largegalaxiesinclustershaveextremelypopulousglobular clustersystems.Therehavebeenvarioussuggestionsregarding One ofthemostinterestingaspectsglobularclusters is theidentificationofapopulationinGalaxywithspatial, © American Astronomical Society • Provided by the NASA Astrophysics Data System 2.2. IndirectEvidenceforClusterFormationinInteractionsandMergers 1992ApJ. . .384. . .50A important hinttotheformationprocess.Wewilladoptviewthathalopopulationofclustersaroundspiralgalaxiesforms in §2. number ofglobularclustersthatarelikelytobeformedinmergersandcomparethiswiththeexcessvarioussitesdescribed during protogalacticcollapse.Thediskglobularclustersinspirals,aswellthe“excess”aroundellipticalsrelativetoare mena, theideaisalreadyestablishedinadifferentcontext.Themassofglobularclusterssuggeststhattheycanformonlyfairly around spirals.Theideaisextendedtoexplaintherelativemassesofvisiblehaloanddiskspiralgalaxies.Wethenestimate assumed toformduringaccretionormergerevents.InthissectionwefirstpresentanargumentexplaintheconstancyofS explanations forthehighstarformationratesinthesegalaxiesisthattheyareinteractingormergingsystems(e.g.,Kennicutt1990). therefore favorascenarioinwhichglobularsformduringoraftertheaccretionevent. Way clusters(Freeman1990).AnysatelliteaccretedbytheGalaxywillpresumablybesimilartoMagellanicClouds.We No. 1,1992FORMATIONOFGLOBULARCLUSTERS53 We returntothispointin§6. It isthereforefairlynaturaltosupposethatgalaxiesinwhichglobularclustersarepresentlyformingundergoingsimilarevents. globular clusters.However,notonlydoesoursuggestionaffordacertaineconomyinexplainingtheseapparentlydiversepheno- where AandxareconstantsNisthenumberofcloudsmassM.Thisspectrummayeitherreflectcosmological fluctuations or spectrum oftheform active star-formingregions.Starburstgalaxiesareperhapsthebestexampleofsuchstarformation.Onemostpopular where Mistheminimummassofclouds.Itfollowsthat where Misthemaximumcloudmass.canbeevaluatedforagivenmassspectrumindexxandprotogalaxy mass (Ashman globular clustersthatformis exceed somecriticalmassMinorderforglobularstobeproduced.Fromequation(3.1)itfollowsthatthetotal numberof the totalmassincloudsis a subsequentspectrumimprintedbyprocessessuchasthermalinstabilityandcloudcoalescence.Weassumethatthese cloudsmust formation, butinallcasesunder considerationitissimple.InmodelsbasedontheSearle &Zinn(1978)picture,M=where density fluctuations.IfwefurtherassumethatM> >Mwecanapproximateequation(3.5)by The relationshipbetweenthetotalmassincloudsand gasmassoftheprotogalaxydependsonmodelforglobularcluster clouds. Toafirstapproximation Fisexpectedtobeindependentofgalaxymass.Ingeneral then,wecansetM=FM,where Such aspectrumisrequiredbyFall-Reestypemodelsand willprobablyariseinotherpicturesasareflectionofthecosmological From equations(3.2)and(3.4)weobtain F <1,theprecisevaluedepending onthemodelforclusterformation. M isthegasmassofprotogalaxy. InFall-Reestypemodels,M=FMwhereFis thefractionofprotogalacticgasincool 1989), butprovidedM>itsvalueisunimportantforthefollowingdiscussion.TheconstantAevaluated by notingthat min max crit totG maxcrit min totG g totG maxcrit We willrefertotheprecursorsofglobularclusterswithinprotogalaxyas“clouds”andassumethattheysatisfy amass The factthatthespecificfrequencyofglobularclustersaroundgalaxiessamemorphologicaltypeisconstantprovidesan Many oftheaboveobservationshavealternativeexplanationsthatdonotrequiregalaxymergersandinteractionstoform It seemslikelythatthemassspectrumisadecreasingfunction ofmass;thatis,manylow-masscloudswithfewerhigh-massones. If variationsofmass-to-lightratios withgalaxymassareignored,thenSocN/M,sothat equation(3.6)implies tG © American Astronomical Society • Provided by the NASA Astrophysics Data System 3. THESPECIFICFREQUENCYOFGLOBULARCLUSTERS Mmx1 M =Ai“dM(M*:,-M*t),(3.3) tot N = t 3.1. OriginoftheConstancyS N', »/Mmin ^ t :)C J'-ATmax ^ S oc Merit ( £M) =—=AM*-\(3.1) A = x +1\M(M*-MJ) totaxrit x1 M~ dM=—(M^M£),(3.2) x -f-1\M/ x +1 axrit totcrit * JM\, min Ml (x +l)M dN t< Ml M • min Ml (3.7) (3.6) (3.4) (3.5) 1992ApJ. . .384. . .50A 6 2 2 10 7 10 model, forexample,aisactuallyfunctionofmass,but forscalesofrelevancehere(i.e.,subgalacticmassscales),aæ0.More (cf. Gott&Turner1977).Fromequation(3.1)itfollowsthat theslopeofcloudmassspectrumwithinprotogalaxiesisrelatedto probably setbytheminimummassoffluctuationsproduced inahierarchicalclusteringmodel,whichisroughlytheJeansmassat the cosmologicalfluctuationspectrumby fragment andformstarsinthe halo. relative massesofthevisible halo anddiskonthebasisofasimplecloudmassspectrum inwhichonlythemostmassiveclouds recombination. Thisdependssomewhatonthetotalandbaryonic densitiesoftheuniversebutis~10M(Peebles&Dicke1968). that equation(3.12)impliesxliesbetween—1.5and —2.0. Finally,weneedavaluefortheminimummassofclouds.Thisis general considerationsoflarge-scalestructuresuggestthat a<^(Press&Schechter1974),andmustbepositivebydefinition,so galaxy ofagivenmass.Forx = —2,equation(3.6)gives For massscalesofinterest,thisimpliesaspectrumtheform pictures densityperturbationscanbedescribedbyapower-lawspectrumsuchthat quantities toreflectthecosmologicalspectrumoffluctuations.Wemakeusualassumptionthatinhierarchical clustering We nowneedvaluesfortheminimumcloudmassandslopeofspectrum.InSearle-Zinnpicturewe expectboth whereas thetotalmassinclouds,M,isgivenbyequation(3.3)above.Theratioofthesequantitiescanbesimplified byagain fraction ofthatspheroidnowinglobularclusters.FortheMilkyWay,aboveresultsimply/^8x10“and/ %1x10“. our model,asconstrainedby cosmological considerations,brackettheobservationalvalue. Inotherwords,wecanunderstandthe Mtot/Msph =üpí,theresultssummarizedabovegiveanobserved valueforthisratioof~12.Thustherangevaluespredictedby noting thatM!>>toobtain From theseideasandthecloudmassspectruminequation(3.1),itfollowsthatspheroidis current diskmassaboveM.Wethereforeassumethatæ6x10,equaltothemass,butnote thatthereis some uncertaintyinthisnumber. gas mayformbaryonicdarkmatter(Ashman1990a,b).Ontheotherhand,accretionofsatellitegalaxieswould increasethe the observeddiskmass,sincesupernovawindsmaydrivesomegasfromprotogalaxy(seeDekel&Silk1986),orafractionof containing cloudswiththesamemassspectrum.Inotherwords,providedslopeofspectrumandminimumcloud We thereforeseethattheobservationSisconstantforspiralscanbeunderstoodsimplyasaconsequenceofallprotospirals whereas thetotalmassinhaloclustersisaround5x10M(obtainedfromdataofZinn1985).Thecurrentdiskabout the halo(since,accordingtoourpicture,itcorrespondsmassincloudslessmassivethanM).Thismaysomewhatexceed 6 x10M(Binney&Tremaine1987).However,weareinterestedinthetotalgasmasswhichavoidsformingvisiblestars the disk.) this case,theprotogalacticcloudswithM>formvisiblespheroid,whereasthoseaccretion ofasatellitegalaxy,theaccretedgalaxyprobablyhaspropertiessimilartoMagellanicClouds.Thepresent Himassin required gasmasstoformthispopulationisMä5x10(€/10).If,assuggestedabove,theseclustersare formed bythe their lowGalacticlatitudes,sowewillassumethatthereareatotalof~25theseclusters.Equation(3.14)thenimplies thatthe has sofarbeenoflittleimportancewouldthereforehavealargerspecificnumberglobularsthantheMilkyWay. this case,theuppervalueofeisappropriateinevaluatinginitialnumberglobularclusters.Youngsystemswhich disruption regions ofinitiallyverymassiveclusters.Insteadtheyaremorenaturallyviewedasbeingcompletelydisruptedglobular clusters.In This isalmostcertainlythecaseinFall-Rees-typemodels,sincespheroidstarscannotbeoriginallyassociatedwithouter globular clusters. It canbeseenthattheproductofthesetwoquantitiesrelatestoefficiencyglobularclusterformation,whichwedenotebye,in estimating themassofgasinMagellanicCloudsatany particularepoch.IntheLMC,KCidentify20youngclusterssatisfying form. Again, thissuggeststhattheaccretionofoneormoresatellite galaxiescanprovideasufficientgasmassforthediskglobularsto accreted. Forinstance,itcomparestomassfractionsinH ialoneof~33%intheSMCand8%LMC(Westerlund1990). the gasfractioninaccretedgalaxiesneedstobe~25%. Thisisnotunreasonableforthesortofgalaxiesweanticipatebeing a totalmassduetoaccretedgalaxiesofabout2x10M - Ifagasmassof5x10Misrequiredtoformthediskglobulars,then are moregas-richatearlyepochs,inwhichcasealowervalue of€wouldbesufficient. where Misthecharacteristicmassofglobularclustersandavailablegasmass. the sensethatifvisiblespheroidformedindependentlyfromglobularclusters,e«8x10,whereasstars suggested byequation(3.7). suggests that€^6x10is sufficient toproducethisnumberofclusters,wellwithinthe expectedrange. their colorandluminositycriteria. UsingWesterlund’s(1990)valueof5x10M©for theHimassofLMC,equation(3.14) globular cluster,andpartlybecauseofthelargenumbers candidateobjectsinthesesystems.Thereistheaddedcomplicationof clusters, denotedbye,tothisvalueof10“.Fromtheabovediscussion,itfollowsthatnumbernewclusters formduringa efficiency ingiantmolecularclouds.ItisalsoconsistentwiththeideasofFreeman(1990)thatnucleuscomprises about10~ and whichshould notbecountedwhenwecompare observationswiththe predictionsofourmodel.If weassumethatthegasmass refer totheclusterswithages between 1and7GyrdescribedbyWesterlund(1990).Itis estimated thatintheLMCthereare~4000 galaxy mergerorinteractionATis above rangebracketstheconversionefficiencyof10“suggestedbyLarson(1986),whobasesthisnumberon star-forming above, itispossiblethatmany oftheseobjectsaremorecloselyanalogoustoopenclusters whichwearenotattemptingtoexplain, of themassanucleateddwarfgalaxy.Infollowingcalculation,wenormalizeefficiencygasconversion intoglobular of theseclusters(Hodge1988). Itisdifficulttoexplainalltheseclustersonthebasisofour model.However,aswementionedin§2.1 gctot gc 0 0 gas0 0 0 clusgas new We nowapplyequation(3.14)tothepossiblesitesofrelativelyrecentglobularclusterformationidentifiedabove. Thedisk The importantpointhereisthatitpossibletheGalaxyoriginallycontainedfarmoreglobularclustersthandoesnow. To constrainthevalueofconstantproportionalityinequation(3.7),weuseobservedvaluesof/and/foundabove. In principle,onecoulduseequation(3.13)topredictthenumberofglobularsformedingalaxymergers,onassumptionthat Another approachtothisproblemisadoptthearguments ofBahcall&Tremaine(1988)whosuggestthattypicalbright It isobviouslyunfortunatethattheresuchalargeuncertaintyinthisformationefficiency.Oneencouragingaspect isthatthe The MagellanicCloudsareamoredifficultproblem,partly becauseofthequestiondefiningexactlywhatconstitutesayoung A biggerproblemarisesifone wishestoexplainthe“intermediate-age”clustersinMagellanic Cloudsinourmodel.Herewe sphgc © American Astronomical Society • Provided by the NASA Astrophysics Data System 3.3. TheNumberofClustersFormedinGalaxyMergersandInteractions N new ^ 4. COMPARISONTOOBSERVATION 4.2. TheMagellanicClouds 4.1. TheGalaxy 5 ‘^chis\ 2 x10MJ 10 ( Mgns\ \io Mj’ (3.14) 1992ApJ. . .384. . .50A 10 13 12 5 8 forms fromtwosuchspirals.)SinceS«2SweexpectAS1,butleavethisasafreeparameterinorder tomakethe merger, thiscouldallbeconvertedintostarsandglobular clustersinthesameratioasspiralgalaxyspheroids,required first case,onewouldrequireafractionofatleast/AS theoriginalmassofprotogalaxytostillbegaseous.If,during following calculationsmoregeneral. where Sandarethecharacteristicspecificfrequenciesaroundellipticalsspirals,respectively.(Onecanthink ofSasthe ellipticals relativetospirals,thenumberofclustersformedinmergeritselfmustbecomparable originally (l-2/ AS)oftheoriginalgasmass,mustformbulk thestarsofellipticalgalaxy.Itmustnot,however,formmanymore clusters andstarsinananalogousfashiontothespheroid formationduringprotospiralcollapse.Theremaininggas,constituting number ofglobularclusterswouldbeformed.Inthesecond case,onerequiresaround/ASofthegasindisktoformglobular can beformedduringamerger.However,thereisanaddedcomplicationintheformationofellipticalswhichwe havesofar Way representsasmalladditiontothetotalclusterpopulation.However,becauseSisroughlyfactorof2higher innormal formation occursinsmallerregionswhicheventuallydisperse toformtheobservedfieldstars.However,inourmodelyoung the problemofexplainingwhymostgasinaforming ellipticalundergoesadifferentmodeoffragmentationinwhichonlyfield globular clusterssincetheresultingvaluesofSforellipticals wouldbelargerthanobserved. all ofthegasinprotospiraldisksformsstarsbeforemerger,ordiskremainscompletelygaseousuntil merger. Inthe specific frequencythataprotospiralwouldhaveattainedhaditnotmerged,andSastheofan ellipticalthat formed. Inadditiontotheoldandnewglobularclusterswehaveconsiderfieldstarsthatareformedinmerger, aswell of globularclustersthatformisproportionaltotheavailable gasmass,asisexpectedfromequation(3.7).However,weareleftwith the starsthatwereoriginallyassociatedwithprogenitorspirals.IfMilkyWayistypical,andglobular clustersinthe anticipate nearlyalloftheclustersbeingformedthroughaccretionormerger,whereasdiskpopulationglobulars intheMilky elliptical clearlydoeshavemassivegasclouds,sincethatit how wesupposethenewglobularclustersform. stars areformed.Inthecaseofspiralgalaxies,results of KCsuggestthatmassivegascloudssimplydonotform,sostar time ofmergingiscrucialindeterminingthenaturemergerremnant. avoided. Thisstemsfromthefactthatnotonlyareglobularclustersbeingformedinsuchamerger,butnewgalaxy isalsobeing associated withtheprogenitorspirals. constitute mostofthemass,must thenformthefieldstarsofelliptical. case, onecanthinkofthemerger asrepopulatingthepartofmassspectrumabove M.Thesmallclouds,whichagain low-mass cloudsatthisstage, thenmerge.Wehavearguedthatmergingleadstotheformation ofmassiveclouds.Inthepresent spectrum ofcloudmasses,and thatonlythosecloudsaboveamassMformglobularclusters. Asnotedin§3.2,itisplausiblethat spheroid ofaspiralconstituteonly~8%thegalaxymass.Itisthereforeapparentthatstateremaining material atthe smaller cloudsavoidfragmentation andinsteadcollapsetothedisk.Thegas-richdisksof twospirals,whichcontainpredominantly which isestimatedtohaveanexcessof~10,000clusters.Thetotalgasmassthatmustbeenaccretedbetween3x10M fewer clusters.ThusifwecanexplainthenumberofclustersinLMCalsoformenoughSMC.Itmaybe although itshouldberememberedthatthetotalmassinluminouscomponentofM87is~10M©.Thus,ifmostof and 3x10Maccordingtoequation(3.14)theexpectedrangeinparameter€.Thisisaprodigiousamountofmaterial, clusters isgreaterinthegalaxywithhigherluminosity.Itmayalsoindicatevariationstimeofgasfraction Way (orSMC)islikelyoveritslifetime(Murai&Fujimoto1980;Murai1984). normalized valueoftheclustermass2x10M.However,meanLMCintermediate-ageclustersisprobablyless M87 wasacquiredthroughcannibalismoraccretion,therequiredgasmassisreasonable. In thiscase,thenumberofclustersformedinanyoneburstisrelativelylow,sothatrequiredavailablegasmassreasonable. total numberofclusterswerereducedsomewhat,itmaybenecessarytoformtheintermediate-ageglobularsinmorethanoneburst. Magellanic-type galaxies,aswouldbeexpectedifoccasionalinteractionsandcollisionsleadtoburstsofglobularclusterformation. significant thatthestellarmassofSMCissmallerthanLMC,soasfoundinnormalspirals,numberglobular Such episodicglobularformationisattractiveanywayinourpicture,sincemorethanoneinteractionbetweentheLMCandMilky than thisvalue,atleastifoneisconsideringallthe4000candidateobjectsidentifiedbyHodge(1988).Evenmeanmassand of theLMCis5x10Matallepochs,maximumnumberclustersthatcanform~200fromequation(3.14),assuming ellspi sph ellspi spi sph sph ell crit crit 0 0 0 56 ASHMAN&ZEPFVol.384 0 We favorthesecondoptioninwhichprogenitorspirals arepredominantlygaseous.Thishastheadvantagethatnumber There aretwoextremesituationswhichusefulinconstrainingwhatmayhappenwhenanellipticalgalaxyforms.Either nearly Normal ellipticalsrepresentthemostinterestinglaboratoriesfortestingourhypothesis.Ingiantglobularcluster systemswe We defineaquantityAS,whichmeasurestheincreaseinspecificfrequencyduetomerger,by We canverifyfromequation(3.14)thatprovidedtheprogenitorspiralsarereasonablygas-richrequirednumber ofclusters To resolvethisproblemweenvisage thefollowingscenario.Wehavealreadysuggested thatwithintheprotospiralgasonehasa In §2.2wenotedthatsomecentralclustergalaxieshavehugepopulationsofglobularclusters.Asanexample,considerM87, One mightworry whythesmallcloudsdidnot formstarsintheprotospiral andwhycloudcoalescence doesnotkeepproducing We haveconcentratedtheabovediscussiononLMCforsimplereasonthatSMChasasmuchgas,butsomewhat © American Astronomical Society • Provided by the NASA Astrophysics Data System 4.4. NormalEllipticalGalaxies 4.3. CentralClusterGalaxies Sm AS =~^(4.1) Sspi 1992ApJ. . .384. . .50A 4 massive cloudsoutofsmalleronesintheyoungelliptical.Onepossibilityisbasedonfactthatmetallicitygasincreases inhibited. However,asthemetallicityinmergerproductincreases,coolingandfragmentationareenhanced.Itislikelythatsome as moreglobularclustersform.Thelowmetallicityoftheprotospiralgasimpliesinefficientcoolingsothatfragmentationis the galaxydensity.Thepropertiesofellipticalcoresalsoargueforpresencegasduringmerger(Lauer1988; reasonably gas-richmergersisprovidedbythesimpleobservationthatellipticalstendtobedenserthanspirals.Theeasiestway described above. star formationoccursinthedisksbeforemerger,sorealsituationisprobablysomewherebetweentwoextremes ellipticals relativetospiralsonthebasisofourmergerhypothesis.Moreimportantly,thereareotherconsequencesmodelthat Kormendy 1989). account forthisistosupposethatasignificantmassfractionoftheprogenitorspiralsgaseous,soitcandissipateandincrease No. 1,1992FORMATIONOFGLOBULARCLUSTERS57 metallicity ofthenewclustersandfieldstarswillexceedthatoldsincegasoutwhichthey form willhave particular, thenewglobularsareexpectedtoroughlyfollowdensitydistributionofellipticalgalaxyfield stars.The resulting ellipticalisthisoldglobularclusterpopulation,sinceallothercomponentshaveexperiencedsubsequent dissipation. In to formaretheoldglobularsaroundprotospirals.Itisclearfromdiscussionin§4.4thatmostdiffusecomponentof are independentofthecomplicationsdiscussedaboveandwhichformbasisobservationaltests.Inourmodel,firstobjects will bemoreextendedthanthegalaxyitself,asisfoundobservationally(Harris1986).Further,atagivenradius, theglobular been pollutedbytheinitialphaseofstarformationinspirals. clusters willhavelowermetallicitiesthanthestars.Thisisalsoobservedinellipticalgalaxies(e.g.,Harris1988).Wecan demonstrate clusters tobemorespatiallyextended.Hereriandaretheeffectiveradiiofoldnewcluster distributions, This canbewrittenas observed toprovideagoodfitspheroidalsystems,soitisnaturalusethisformdescribetheshapeofcluster distributions. this quantitativelyifweassumeaspecificformforthespatialdistributionofclusterpopulations.ThedeVaucouleur’s Alawis manipulate theequationtogetitintermsoftotalnumberclustersN(i.e.,JVandfortwopopulations). Ingeneral, respectively. We assumethatboththenewandoldclusterdistributionsfollowthisrelationship,butwithr>,sincewe expect theold we canwrite and itiswell-known(e.g.,Mihalas&Binney1981)thatthedeVaucouleur’slawgives From equations(5.1)and(5.3)weobtain This appliestoboththenewandoldclusterpopulationsifwe substituteNandJVforr,respectively. 0dnewe number formedinthemergerlVarerelatedby equation (4.1),itfollowsthatthenumberofglobularclusters originallyassociatedwiththeprogenitorspiralgalaxiesNand totoldnew oldnew From equations(5.4)and(5.5)weobtain difference increases inverselywithAS.This is tobeexpected,sinceifthere arenonewclusters,thedifference betweentheglobular difference betweenthedensity fall-offoftheglobularclustersandthatgalaxy. Itcanbeseenthatthemagnitudeofthis denominator has,byassumption, thesamesurfacedensityprofileasunderlying galaxy. Thusequation(5.6)representsthe nevioldtotnewe new old It isclearthedefinitiveanswerstothesequestionsawaitmorecompletemodelsofstarformation.However,somesupportfor Whatever thedetailsofmerger,abovediscussionillustratesthatwecanexplainspecificfrequencyglobularsin The obviousconsequenceofthisisthattheglobularclustersystemanellipticalgalaxy,comprisingoldandnew clusters, In ordertouseequation(5.1)weneedknowthefactorNthatscalesnumberofclusters.Itismoreilluminating to We areinterestedinthetotalnumberofclustersrelativeto thenewclustersasafunctionofradius.FromdefinitionASin e The numeratorontheleft-hand sideofthisexpressionisjustthetotalnumberclusters asafunctionofradius,whilethe © American Astronomical Society • Provided by the NASA Astrophysics Data System ^new(r) +NqJT) lV(r) new 5. PREDICTIONSANDOBSERVATIONALTESTS fwî767,4l '-ïèî“'{•[fâ N(r) =Nexp e 5.1. NormalEllipticals N =J2nrN(r)dr,(5.3) tot 2 N =7.22nr.(5.3) lote JV =ASN. (5.5) newold (5.1) (5.6) 1992ApJ. . .384. . .50A metallicity gradientswithrineitherclusterpopulation(onecaneasilygeneralizethediscussionforsuchgradients,but theprincipal values ofASandr/rarerepresentedbybrokenlines.Theprofiletheglobularsisclearlyflatterthanthatgalaxy. (Z —Z).Thisgivesameasure ofthedifferenceinmetallicityclustersrelativeto theellipticalgalaxyasfunctionofgalactic galaxy metallicityinellipticals isreproduced,atleastqualitatively. Thus atsmallr,equation(5.9)impliesthatAZ»0,whereas forverylargerweobtain,AZæ(Z—Z),reflectingthefactthat The behaviorofthisexpressionistransparentifonerealizes thatN(r)/N(r)isamonotonicallydecreasingfunctionofradius. The lasttwoequationsthengive roughly thesameanddenotedbyZ,whereasoldclustershavealowermetallicity.Themeanin allclustersat clusters givingtheoverallclusterpopulationalowermetallicitythangalaxyatgivenradius.Letusassumethat thereareno radius. Fromequations(5.4)and (5.9)weobtain the majorityofclustersatlargerareoldpopulation. Thustheobserveddifferencebetweenglobularclustermetallicityand result derivedbelowisunaffectedbythiscomplication).Themetallicityoftheellipticalgalaxyandnewclusters assumed tobe reproduced byourmodel.Indeed,theoreticalplotsaresimilartotheempiricalonesofTonry(1990). tendency fortheglobularclustersaroundellipticalgalaxiestohaveflattersurfacedensityprofilesthan themselvesis cluster distributionandellipticalgalaxyisgreatest.Thedifferencealsoincreasesasr/rincreases,atleastfor > r.Thisis a radiusrinthegalaxyisthen because increasingtherelativespatialextentofoldclustersmeansthattheymakemoreacontributionatlarger. of ASandr/r.Thebehaviordeducedfrominspectionequation(5.6)isclearlyapparent.Aswehavealready noted,the oldnew newold newold ncwold newold 58 oldnew new oldnew 1/4 Fig. 1.—Acomparisonofthesurfacedensityglobularclusterswithunderlyingellipticalgalaxy.Thegalaxyisrepresentedbysoldline,whereas different To investigatethisquestion further, itisinstructivetoconsidertheradialdependence ofthedimensionlessquantityAZ(r)/ We canalsoinvestigatethedifferencesinmetallicitybetweenglobularclustersandellipticalgalaxy,arisingfrom theold At agivenradius,thedifferenceinmetallicitybetweenglobular clustersandthestarsofellipticalis In Figure1weplotthetotalnumberofclustersgivenbyequation(3.7)andcompareprofilewithanrlawforvarious values © American Astronomical Society • Provided by the NASA Astrophysics Data System Zew nold AZ(r) exp {-7.67[(r/r n AZ(r) =Z„ 2» = 4 O-newA-oidriVAS) exp{-7.67[(r/r A -1]} old — Zoldj^ p/4 _ AZ(r) =Z n ASHMAN &ZEPF VoidW^oid +NJr)Z aen 21 4 1]} +(r„ewA-oid) (l/AS) exp{-7.67[(r/r) / -1]}' 1 old _j_ -*new' W(r) +NJr) oldne N , V(r) old (^) Znew ZJr) Zold ]/[ 1 j -*new' N(r). oid N , (r) Vol. 384 (5.10) (5.9) (5.8) (5.7) 1992ApJ. . .384. . .50A were muchmore gas-richthantheyarenow (Ostriker 1990). disks suggestthatiftheaccretion ofsmallgalaxiesisfairlycommon,thenmostaccretion musthaveoccurredatepochswhenspirals currently forming.Ideally,one wouldliketocatchsuchaneventasithappened.However, thesmallvelocitydispersionsofspiral major mergersthemselves.However,wehavealreadymentioned theargumentsthatspiralshaveaccretedsomemasssincetheir that showthesortofstarformation activityexhibitedbythelate-typegalaxiesdescribed byKCinwhichyoungglobularsare galaxy isbeingaccreted,orpossibly whenthediskissufficientlydisturbedbyaninteraction. Thereshouldthereforebesomespirals globular clustersinourownGalaxy andinM31.Indeed,ourviewspiraldiskscanonly produceglobularclusterswhenasmaller time offormation.Further,we havesuggestedthattheacccretionofasatellitegalaxy was responsibleforthediskpopulationof below, intheseobjectsweshouldfindyoungglobularclusters formedduringthemerger. believed fromindependentconsiderations(e.g.,Toomre1977). However,afewmergersareoccurringnow,andaswediscussin§5.3 firmed, theaboveexpressionswouldallowaquantitativecomparison.Weshouldalsoemphasizethat explain increasingly atlargeradii.ThistrendisapparentintheplotsofFigure2.Again,iftwopopulationsclusters within agiven provides oneofthemostdefinitivetestsourmodelandcanbereadilyunderstood.Wepredictthatdifference between bimodal distributioninmetallicityandspatialextentforclustersaroundnormalellipticals.Ifthisqualitativeprediction iscon- However, thesimpleobservationthatAZincreaseswithrwould clearlyprovidecompellingevidenceinsupportofourtheory.Ifthe galaxy canbeidentifiedandtheirmeanmetallicitiesspatial distributionsdetermined,wehavedetailedquantitativepredictions. known propertiesofellipticals. determined forspecificgalaxies.Indeed,wewouldliketostressthatanobservationalprogramcoulddeterminewhether thereisa a givenradius. We plotthisfunctioninFigure2fordifferentvaluesofASandr/r.ThefactthatthenormalizedvalueAZisgreater thanzero equations couldbemodifiedtotakethisintoaccount. predictions fornormalellipticalsshouldpertain,except that theremaybemanypopulationsofdifferentclusters.Theabove massive ellipticalgalaxieswithanomalouslylargeclusterpopulations forminasimilarmannerthroughmergerandaccretion,the globular clusterandfieldstarmetallicityshouldincreasewithgalactocentricradius,sincethemetal-poorclusters dominate above, itmaybepossibletodistinguishthetwopopulationsusingmetallicityidentifyoldandnewclusters.Thesecond prediction alternative models.Itissimplythattheglobularclustersaroundellipticalsaresumoftwoseparatepopulations. Aswenoted at allradiiconfirmsthatourmodelexplainstheobserveddifferencebetweenglobularclustersandunderlyingelliptical galaxyat are aconsequenceofourmodel.Thefirstisfairlyobvious,butneverthelessimportantsinceitdifficulttoseehow couldarisein globular clustersaremetal-poorcomparedtothegalaxyatagivenradius,andthatthismetallicitydifferenceincreaseswithradius. oldnew No. 1,1992 1/4 If wearetosupposethatellipticalgalaxiesformedbygalaxy mergers,itfollowsthatpresent-dayspiralscannothavesuffered We havetacitlyassumedinthisdiscussionthatmostofthe mergerswhichformellipticalsoccuratearlyepochs,ashaslongbeen While thesequantitativepredictionsprovidetestsofourmodelinthemselves,theabovecalculationrevealsadditional effectsthat At present,thisdiscussionofmetallicityprofilesisincomplete,sincetherelevantparametersareunknown,butthey couldbe Fig. 2.—ThedimensionlessquantityAZ/(Z—Z)plottedagainstrforthesamevaluesofASand/rusedin1.Forallvalues,we predict thatthe newold © American Astronomical Society • Provided by the NASA Astrophysics Data System FORMATION OFGLOBULARCLUSTERS 5.2. Spirals 59 1992ApJ. . .384. . .50A 6 89 8 6 metallicity ofthediskclustersprobablyreflectsfactthatgasinaccretedsatellitegalaxyexceeds thatofthe metal-rich thanthehaloclusters,sincestarformationincanpollutegasthateventuallyfallstodisk. However,the clear signatureofglobularclustersformedfromanaccretedsatellitewouldbeaclusterpopulationwithagesignificantlylessthan the satellitemergeswithprogradegasalreadyinspiraldisk.However,itseemslikelythatafewcasesretrogradedisk retrograde ones,sothatmoreprogradesatellitesshouldbeaccreted.Further,itisnotclearwhathappenswhengasfrom unfortunately berelativelyrare.Thisispartlybecauseprogradeorbitsaremoresusceptibletodynamicalfrictionthan could notaccountforsuchanobservation.Inouraccretionschemeaphenomenonisexpectedoccasionally,butmay population. Whilemostaccretionshouldoccuratearlyepochs,afewspiralshaveswallowedsatellitefairlyrecently.Thus Way diskglobulars,characteristicofathickdisk,alsoindicateanintermediateformationepochbetweenhaloandassuming have formedtowardtheendofcollapsephaseprotogalaxy.Inthiscase,evidencefromMilkyWaysuggeststhat 60 ASHMAN&ZEPFVol.384 mergers. Thefirstisthattheuncertaintyaboutwhetherdensestar-formationregionwillformaboundclusterremoved. Thisis problem withdetectingyoungglobularsinongoingmergersisthattheyarelocatedregionsofrecentstarformation which central regionsoftheseprotoglobularsarereallysodensethattheywouldbeexpectedtoformatrueglobularcluster. Anadditional resolution images,likethosethatmightbepossiblewithacorrectedHubbleSpaceTelescope,arenecessarytodetermine ifthe clusters insystemswhichareknowntobecurrentlymerging.TheworkthisdirectionbyKCpointsthepotential ofthis metallicity. be ararephenomenonsincemetallicityincreaseswithgalaxyluminosity,sothatgenerallyspiralwillaccrete oflower collapse picturewherethediskglobularsarenaturallyviewedasformingbeforemajorityofstars.Again, this islikelyto disk, sothatthediskglobularshavehighermetallicitiesthanstars.Itisdifficulttoseehowthiscouldoccur inthesimple protogalactic halogas.(Thelattermaybevirtuallypristine,withtheobservedmetallicityofglobularclusters beingdueto disk globularsarelikelytobemetal-poorcomparedtheyoungerstars,asisobserved.Inouraccretionpicture, thehigher globular clusterscouldbeproduced. the stellardisk.Thiscouldnotariseinonlyobviousalternativepicturedescribedabove. satellite galaxy,sothatifsuchaneventisresponsibleforthediskglobularclusterswewouldexpectmostspiralstohavea a diskpopulationofglobulars.TheresultsBahcall&Tremaine(1988)indicatethatmostspiralshaveaccretedatleastone they formaspartoftheprotogalacticcollapse. disk globularsformed~10Gyrago,roughlywhenthefirststarsformed.ThespatialdistributionandkinematicsofMilky globulars. Irrespectiveofthedetailsothermodels,itseemsinevitablethat,withoutaccretionmaterial,diskglobularsmust will haveanapparentmagnitudeofm=22atadistance 20Mpc,sosuchobjectsmightbedetectableintheappropriatesystems. find thata10Mglobularclusterwillhave=—12at 10yrandwillfadetoM=—9.5atyr.Anobjectof cluster appearsboundatthisstageitwillprobablyremainsounlessdisruptedbyexternaltidalforces.Thesecond advantageof because anyclustersformedwhenthemergerbegan(~5x10yr)aremucholderthantheircrossingtime 10 yr),soifa approach aswellitsproblems.Whenclustersareyoung,theyverybrightandeasilydetected.However,in their brightest self-enrichment.) However,occasionallyitispossiblethatthemetallicityofgasinaccretedgalaxymayexceed inthespiral mergers somehowdrivethecoalescence oftheselumps,therebyallowingglobularclusters toform.Onespecificpossibilityisthatthe This islinkedtothequestionofwhyglobularclustersdonot forminthedisksofspiralgalaxies,despitesignificantamounts A similaranalysishasbeencarriedoutbyLutz(1991)forthe specificcaseofthemerginggalaxyNGC3597. However, itwillnothavefadedhopelessly.BasedontheChariot &Bruzual(1990)modelsoftheevolutionstellarpopulations,we optical morphologicalidentifications.Theobviousdisadvantage isthattheyoungglobularclusterwillbesignificantlylessbright. using somwhatoldermergersisthatthegalaxyhasamore relaxedappearancewithoutasmuchdustconfusinginterpretationof tail signaturesofaformermerger(e.g.,NGC7252).Thisapproachhastwoadvantagesoverlookingforclusters in veryyoung typically havechaoticdistributionsofdustandgenerallyheavyextinction. stages theyareyoungenoughthatitisnotyetclearwillformdynamicallyboundclusters.AsKCpoint out, veryhigh considerations leadustosuggest thatthemassofgascloudsinspiraldisksislimited some way,butthatgalaxyinteractionsand active starformationisdrivenbygalaxyinteractions.Afeature ofsucheventsseemstobethebuild-uplargegascomplexes.These these appeartobetheprogenitorsofobservedyoungglobular clusters.Aswenotedin§2.2,thisissimilartotheideathatvery star formationobservedinthesesystems.Fromtheresults of§2,itseemsthatwerequiremassivegascloudstobeproduced,since the orderedrotationofagasdisk, therebyallowingverymassivecloudstoform. across asizablegascloudin rotatingdiskleadstoitsbreak-up.Perhapsonlyinsystems withoutordereddifferentialrotationcan differential rotationcharacteristic ofdisksdisruptscloudsaboveacertainradiusandmass (Larson1986).Inotherwords,theshear sufficiently massivecloudsform andeventuallyfragmenttoproduceglobularclusters.In thiscase,galaxyinteractionsmaydisrupt B 0B B The sparseinformationonglobularclustersystemsaroundspiralgalaxiesmakesitimpossibletojudgethefractionofspiralswith An alternativeapproachistostudyslightlyoldersystemswithamorerelaxedmorphologyinthecenter,butstill thetidal An equallyclearsignaturewouldbetofindadiskpopulationofglobularswithretrogradeorbits.Again,simplecollapsepicture In ordertodeviseadditionaltestsofourhypothesis,itisinstructiveconsideralternativeschemesfortheformationdisk In thissectionweturnourattentiontopossiblephysicalprocesses thatleadtoglobularclusterformationingalaxyinteractions. Perhaps themostdirecttestofourhypothesisthatglobularclustersformduringgalaxymergersisasurveyforyoung globular Metallicity toomaybeusedasaprobetotestourtheory.Inthecollapsepicture,itisexpectedthatdiskclustersaremore This discussion isobviouslyspeculativeand islikelytoberefinedonly whenobservationsgiveabetter understandingofthe © American Astronomical Society • Provided by the NASA Astrophysics Data System 5.3. CurrentMergers 6. DISCUSSION 1992ApJ. . .384. . .50A .1988,inIAUSymposium126,TheHarlow-Shapley on .1987,ASP,99,1031 Kormendy, J.1989,ApJ,342,L63 .1988,inIAUSymposium126,TheHarlow-Shapleyon Larson, R.B.1986,inNearlyNormal Galaxies,ed.S.Faber(NY:Springer), Kennicutt, R.C,Jr.,&Chu,Y.-H.1988, AJ,95,720(KC) Kennicutt, R.C,Jr.1990,inIAUColloquium124,PairedandInteracting Kang, H.,Shapiro,P.R.,Fall,S.M.,&Rees,M.J.1990,ApJ,363,488 Hodge, P.1988,PASP,100,1051 Harris, W.E.,&vandenBergh,S.1981,AJ,86,1627 Gott, J.R.,&Turner,E.L.1977,ApJ,216,357 Geisler, D.,&Forte,J.C.1990,ApJ,350,L5 Harris, W.E.,&Racine,R.1979,ARA&A,17,241 Harris, W.E.1986,AJ,91,822 .1990b,ApJ,359,15 Fujimoto, M.,&Murai,T.1984,inIAUSymposium108,Structureand Evo- Freeman, K.C.1990,inDynamicsandInteractionsofGalaxies,ed.R.Widen Dekel, A.,&Silk,J.1986,ApJ,303,39 .1990a,MNRAS,247,662 Fall, S.M.,&Rees,M.J.1985,ApJ,298,18 Fabian, A.C,Nulsen,P.E.J.,&Cañizares,CR.1984,Nature,310,733 Elson, R.A.W.,&Fall,S.M.1987,ApJ,323,54 Eggen, O.J.,Lynden-Bell,D.,&Sandage,A.R.1962,ApJ,136,748 Chemoff, D.F,&Weinberg,M.1990,ApJ,351,121 Chariot, S.,&Bruzual,G.1991,ApJ,367,126 Cayrel, R.1986,A&A,168,81 Bridges, T.J.,&Hanes,D.A.1990,AJ,99,1100 Ashman, K.M.1989,Ph.D.thesis,UniversityofLondon Binney, J.,&Tremaine,S.1987,inGalacticDynamics(Princeton:Princeton Becker, R.,Schilke,P.,&Henkel,C.1989,A&A,211,L19 Bahcall, S.R.,&Tremaine,1988,ApJ,326,LI clusters inobviousmergerremnantsorgalaxieswhicharestillmerging. retrograde, ofhighermetallicitythanthestellardisk,ormuchyoungerdisk;(d)presenceyoung globular cosmological fluctuationspectrum. distributions maybemultimodal);(c)mostspiralgalaxiesshouldhavediskpopulationsofglobulars,occasional being bimodal ageandmetallicitydistributionfortheglobularsinellipticals(ingalaxieswithanomalouslylargepopulations the an increaseinthemetallicitydifferencebetweenellipticalfieldstarsandglobularswithincreasinggalactocentric distance; (b)a constancy ofthisspecificfrequencyforspiralgalaxiescanalsobeexplainedinscenarioasaconsequencethesamespectrum clusters comparedtostars;and(e)thedependenceofspecificfrequencyglobularsongalaxyenvironment.Theapproximate lower metallicityofclustersrelativetofieldstarsatthesameradiuswithinellipticalsandmorediffusespatialdistribution No. 1,1992FORMATIONOFGLOBULARCLUSTERS61 of densityfluctuationsoccurringwithinallspirals.Theabsolutenumberglobularclustersaroundspiralsisthenaresultthe higher specificfrequenciesofglobularclustersaroundellipticalsrelativetospirals;(b)thelargenumberglobularsassociatedwith that thissinglehypothesiscanaccountforanumberofpropertiesglobularclustersystems.Inparticular,itexplain(a)the globular clusters. interpret theSearle-Zinnmodelasamergingscenario,withlumpysubunitsofprotogalaxyeventuallycoalescingtoform some massivegalaxiesinthecentersofgalaxyclusters;(c)presencediskpopulationclustersMilkyWay;(d) single entity.Thisagainillustratestheeconomyofourhypothesisthatmergersandinteractionareresponsibleforformation highly analogoustothesortofconditionsthatonemightexpectinmergingandinteractinggalaxies.Indeed,couldeven collapsing gasofprotospirals.Thechaoticconditionsatthisepochcollidingclouds,asadvocatedbySearle&Zinn(1978),are since, asweexplainedintheIntroduction,thereisconsiderableobservationalevidencethatglobularclustersformedoutof that thisthemeiscentraltoouranalogybetweengasinprotospiralsandmerginggalaxies.Thisofparticularimportance student fellowship. K. M.A.issupportedbypostdoctoralfellowshipsfromESAandSERC/NATOS.E.Z.anSTScI graduate somehow allowtheformationofverymassivegascloudswhicharenecessarytoformglobularclusters.Itshouldbeemphasized origin ofstar-formingcomplexesandgasclouds.Whateverthedetails,commonthemeinourviewisthatgalaxyinteractions p. 26 p. 269 (Dordrecht :Kluwer)p.237 Galaxies, ed.J.W.Sulentic,C.Keel, &C.M.Telesco(NASACP-3098), Globular ClusterSystemsinGalaxies,edsJ.Grindlay&A.G.C.Philip (Dordrecht: Reidel,p.115 (Berlin :Springer),p.36 lution oftheMagellanicClouds,ed.S.vandenBergh&K.deBoer (Dordrecht :Kluwer),p.232 Globular ClusterSystemsinGalaxies,ed.J.Grindlay&A.G.C.Philip Univ. Press) There arevariouspredictionsarisingfromourmodelwhichcanbeusedtoprovidestringenttestsitsvalidity.Theseinclude(a) In summary,wehavepresentedamodelinwhichglobularclustersareformedgalaxymergersandinteractions.Weshown This workbenefitedfromhelpfulconversationswithKenFreeman,GeorgeLake,GeorgesMeylanandFrançois Schweizer. © American Astronomical Society • Provided by the NASA Astrophysics Data System REFERENCES .1988,inIAUSymposium126,TheHarlow-Shapley on Zinnecker, H.,Keable,C.J.,Dunlop, J.S.,Cannon,R.D.,&Griffiths,W.K. Zinn, R.1985,ApJ,293,424 White, R.E.,III.1987,MNRAS,227,185 Westerlund, B.E.1990,AstronApRev.,2,29 Tripicco, M.J.1989,AJ,97,735 Toomre, A.1977,inTheEvolutionofGalaxiesandStellarPopulations, ed. Tonry, J.L.1990,inDynamicsandInteractionsofGalaxies,ed.R.Widen, Strom, S.E.,Forte,J.C,Harris,W.K.M,Wells,D.&Smith, Shields, J.C,&Filippenko,A.V.1990,ApJ,353,L7 Searle, L.,&Zinn,R.1978,ApJ,225,357 Schweizer, F.1986,inNearlyNormalGalaxies,ed.S.Faber(NewYork: Sarajedini, A.,&King,C.R.1989,AJ,98,1624 Sandage, A.,&Brucato,R.1979,AJ,84,472 Rogers, A.W.,&Paltoglou,G.1984,ApJ,283,L5 Press, W.H.,&Schechter,P.1974,ApJ,187,425 Peebles, P.J.E.,&Dicke,R.H.1968,ApJ,154,891 Ostriker, J.P.1990,inEvolutionoftheUniverseGalaxies,ed.R.G.Kron Muzzio, J.C.1986,ApJ,301,23 Murai, T.,&Fujimoto,M.1980,PASJ,32,581 Mihalas, D.,&Binney,J.1981,inGalacticAstronomySanFrancisco: Merrit, D.1984,ApJ,276,26 Lutz, D.1991,A&A,inpress Lauer, T.R.1988,inCoolingFlowsClustersandGalaxies,ed.A.C.Fabian Larson, R.B.1988,inIAUSymposium126,TheHarlow-Shapley (Dordrecht :Kluwer),p.603 (Dordrecht :Kluwer)p.37 lar ClusterSystemsinGalaxies, ed. J.Grindlay&A.G.C.Philip Globular ClusterSystemsinGalaxies,ed.J.Grindlay&A.G.C.Philip p. 420 (Berlin :Springer),p.275 B. M.Tinsley&R.Larson(NewHaven:YaleUniversityObservatory), (Conf. Proc,Vol.10),ASP,p.25 M.G. 1981,ApJ,245,416 Springer) p.18 (Dordrecht: Kluwer)p.215 (Dordrecht: Kluwer),p.311 1988, inIAUSymposium126,TheHarlow-Shapley SymposiumonGlobu- Freeman) on GlobularClusterSystemsinGalaxies,ed.J.Grindlay&A.G.C.Philip