<<

1992ApJ. . .384. . .50A 3 46 6 7 8 . 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 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 .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 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 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,whereasthose