2 O 02MNRAS.331. .2 45D 2 1,2 therefore occupylargerorbits. which thelower-massstarswill attainhighervelocitiesand globular clusters(GCs)andrich Large MagellanicCloud(LMC) Dynamical evolutionindensestellarsystems,suchasGalactic obtain arealisticglobalclusterLF. corrections fortheeffectsofmasssegregation,andhence terms ofitsinitialmassfunction(IMF).Withoutreliable luminosity function(LF)atagivenpositionwithinstarclusterin mass ,clearlycomplicatestheinterpretationofanobserved massive starsbeingmorecentrallyconcentratedthanthelower- The effectsofmasssegregationinstarclusters,withthemore Accepted 2001November19.Received16;inoriginalform5 European SouthernObservatory,Casilla19001,Santiago19,Chile Mon. Not.R.Astron.Soc.331,245-258(2002) ^E-mail: [email protected] SEGREGATION R. deGrijs,*G.F.Gilmore,A.JohnsonandD.Mackey Mass segregationinyoungcompactstarclusterstheLargeMagellanic clusters,drivesthesystemstowards energyequipartition,in structure anddynamicalevolutionofthecluster,itisimpossibleto © 2002RAS 1.1 Dynamicalevolutioninstarclustercores 1 PRIMORDIALVERSUSDYNAMICALMASS ^Institute ofAstronomy,UniversityCambridge,MadingleyRoad,CambridgeCB3OHA Cloud -II.Massfunctions © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem respectively, itismostlikelythatsignificantprimordialmasssegregationwaspresentinboth radius, arenotsimplepowerlaws. range usedtofittheslopesormetallicityassumed.ItisclearthatclusterMFs,atany We reviewthecomplicationsinvolvedinconversionofstellarluminositiesintomasses mass segregationisobservedoutto—6/?and—3ÆinNGC18051818, have significantlysteeperslopes. tions oftheyoungLargeMagellanicCloud(LMC)starclustersNGC1805and1818. ABSTRACT clusters. Key words:stars:luminosityfunction,massfunction-MagellanicCloudsgalaxies:star clusters, particularlyinNGC1805. old, thecoreofNGC1805islikelytobe^3-4crossingtimesold.However,sincestrong 20-30 arcsec,formassesinexcessof~1.6-2.5M.Thisresultdoesnotdependonthemass core radiionmassindicateclearsegregationinbothclustersatofr^ and applyarangeofmass-to-luminosityrelationstoourHubbleSpaceTelescopeobserva- slopes inthemassrange(—0.15^logra/M©0.85),andMFsbeyondr30arcsec core 0 We estimatethatwhiletheNGC1818clustercoreisbetween~5and—30crossingtimes The globalandtheannularMFsnearcoreradiiappeartobecharacterizedbysimilar Both theradialdependenceofmassfunction(MF)andcluster 3 Brandi etal.1996),andcanbewritten as(Meylan1987) Lightman &Shapiro1978;Meylan 1987;Malumuth&Heap1994; time, i.e.therelaxationtimeatmeandensityforinnerhalf Davies 1998;Elsonetal.1998).Thecharacteristictime-scaleofa negligible evenattheedgeofcluster(e.g.Chernoff& the bottomofclusterpotential,i.e.centre(cf.Spitzer characteristic fortheclusterasawhole(Spitzer&Hart1971; of theclustermassforstarswithstellarvelocitydispersions cluster maybetakentoitshalf-mass(ormedian)relaxation cluster (Spitzer&Shull1975;InagakiSaslaw1985;Bonnell concentrated high-masscomponentcomparedwiththelower-mass cluster centresinkingthefastest,althoughthisprocessisnot i, =(8.92X10) Weinberg 1990;Hunteretal.1995).Thisleadstoamorecentrally & Hart1971),withthehighest-massstarsandthoseclosestto segregation iscomparabletothedynamicalrelaxationtimeof ,andthustodynamicalmasssegregation. rh The time-scalefortheonsetofsignificantdynamicalmass Consequently, thehigh-massstarswillgraduallysinktowards {m) log(0.4M/(m»' tot 1 U ^ (1) 2 O 02MNRAS.331. .2 45D x between binariesandsinglestarsareveryefficient(e.g.Nemec& presence ofbinarystarsmayacceleratethemasssegregation reached (e.g.Hunteretal.1995:fullglobal,orevenlocal, relaxation timeisshortest,i.e.neartheclustercentre(cf.Fischer higher-mass stars(greater(m))thanfortheirlower-mass immediately thattherelaxationtime-scalewillbeshorterfor masses inM©). Although aclusterwillhavelost all tracesofitsinitialconditions Elson etal.1998).Thisprocesswillactonsimilar(orslightly Harris 1987;DeMarch!&Paresce1996;BonnellDavies1998; Inagaki &Saslaw1985;Elson,Hut1987b).Infact,the frequently andbinaryformationisthoughttobeveryeffective(cf. high-density coresveryrapidly,wherestellarencountersoccur hard todefineproperly.Thisprocesswillbeacceleratedifthereisno higher degreeofequipartition),amongothers. McClure 1986;Sosin1997:flattermassspectrawillspeedupthe Lightman &Shapiro1978;InagakiSaslaw1985;Pryor,Smith fraction oftheclustermass. in theclustercoreoccursonlocal,centralrelaxationtime-scale thermal equilibriuminthecentralparts. velocity scaleand(m)isthemeanmass(inMofallparticlesin the corecanbewrittenas(Meylan1987) this picture(e.g.Aarseth&Heggie1998,seealsoHunteretal. where Ristheclustercoreradius(inpc),v(kms) et al.1998;Hillenbrand&Hartmann1998).Therelaxationtimein dynamical masssegregationwillalsobemostrapidwherethelocal companions; numericalsimulationsofrealisticclustersconfirm dynamical evolutionofaclusteraswhole,significantdifferences cluster massand{m)isthetypicalofastar(both where Æisthehalf-mass(median)radius(inpc),Mtotal dynamical relaxationtime-scaleforaspecificmassivespeciesis cluster centre,theirdynamicalevolutionwillspeedup,andhencethe dynamical evolution,whereassteepmassspectrawilltendtoa equipartition isneverreachedinarealisticstarcluster,noteven with agrainiermassdistribution),thedegreeofequipartition cluster tolosealltracesofitsinitialconditionsalsodependsonthe dynamical evolutionisacontinuingprocess.Thetime-scalefor t^ =(1.55X10') are expectedlocallywithinthecluster.Fromequation(1)itfollows 246 R.deGrijsetal. among themostmassivespecies),andslopeofMF(e.g. and thereforemasssegregationisslowerthaninsmallerclusters a ‘localrelaxationtime’isonlygeneralapproximation,as (comparable tojustafewcrossingtimes,cf.Bonnell&Davies strong functionofpositionwithin a cluster,andvarieswithitsage. (cf. Nemec&Harris1987;BonnellDavies1998;Elsonetal. shorter) time-scalestotheconventionaldynamicalmasssegregation significantly, sincetwo-bodyencountersbetweenbinariesand (full) equipartition(cf.Inagaki&Saslaw1985),thusproducing (Bonnell &Davies1998:largerclustersareinherentlysmoother, smoothness ofitsgravitationalpotential,i.e.thenumberstars 1.2 Primordialmasssegregation 1998). Insummary,thetime-scale fordynamicalrelaxationisa 1998), whereasatime-scaleoctisrequiredtoaffectlarge 1995; Kontizasetal.1998).Fromthisargumentitfollowsthat 0 cores htot 0 r h In addition,asthemoremassivestarsmoveinwardstowards It shouldbeborneinmind,however,thateventheconceptof Thus, significantmasssegregationamongthemostmassivestars Although thehalf-massrelaxationtimecharacterizes © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem (m)log(0.5M/(m)) 0tot vÆ yr, (2) region, wheretheencounterrateishighest(cf.Larson1991; presumably determinedbythepropertiesofinteractionsproto- primordial masssegregation,sincetheouterregionsofthese particular ofthehigh-massstarsincore(riS0.5pc),tohave Bonnell etal.1997,200la,b;Bonnell,Bate&Zinnecker1998; they tendtoformneartheclustercentre,inhighest-density therein), andthereforedissipatemorekineticenergy.Inaddition, more mass(cf.Larson1991;Bonnelletal.2001a,bandreferences massive starsaresubjecttomoremergersandhenceaccreteeven these clumpsexceedstheinitialmassofastartobeformed.More NGC 2157seemtoindicatethepictureinwhichencountersat However, Fischeretal.(1998)concludethattheirobservationsof interactions areunimportantandmasssegregationdoesnotoccur. idea oftheamount‘primordial’masssegregationincluster. process ofmasssegregationinaclusterdetail,wehavetogetan lower-mass stars(cf.Aarseth1999).Inordertounderstandthe formation hastakenplace.Theprocessis,infact,morecompli- to betheresultofdynamicalrelaxationandwaythatstar As partofHubbleSpaceTelescope (HST)programmeGO-7307, 2 THEDATA massive starsinthecoreofONCmostprobablyoriginated therein). Bonnell&Davies(1998)showconvincinglythatthe Bonnell &Davies1998)isprobablytobelargelycausedbymass mass TrapeziumstarsinthecentreofveryyoungOrionNebula Brandi etal.1996).Ontheotherhand,presenceofhigh- taken place(cf.Malumuth&Heap1994;Hunteretal.1995; is sufficientlylongforatleastsomedynamicalmasssegregation,in Malumuth &Heap1994;Brandietal.1996),itsageof—3-4Myr Doradus intheEMC,isprobablyatleastpartiallyprimordial(e.g. in ,thecentralclusterlargestar-formingcomplex30 Bonnell &Davies1998).Thiswillleadtoanobservedposition- caused bythemergingofprotostellarclumpsuntilmass early stagesintheevolutionenhancemassaccretionofcluster classic pictureofstarformation(Shu,Adams&Lizano1987), cated, asthehigh-massstarsevolveonsametime-scale on time-scaleslongerthanitscharacteristicrelaxationtime, data forthetwoyoungestclusters inoursample,NGC1805and Grijs etal.(2001,hereafterPaperI) wepresentedtheobservational compact starclustersintheEMC, covering alargeagerange.Inde we obtaineddeepWFPC2V-and /-bandimagingofsevenrich, old. clusters (andoftheONCaswell)arenotevenonecrossingtime clusters NGC2024andMonocerosR2alsoshowevidencefor within theinner10-20percentofcluster. ance oftheclusterasnon-dynamicallyrelaxed,andreferences Cluster (ONC;^IMyr,equivalentto-3-5crossingtimes; et al.1995;Brandi1996,andreferencestherein). clumps andlower-massstarsformthroughoutthecluster(Hunter consistent withtheideathatmoremassivestarstendtoformin compared withtheMFinclustercentre(althoughlow-mass dependent MFcontainingmorelow-massstarsatlargerradii stellar materialduringthestar-formingepisodeinacluster.In shorter time-scalestheobservedstellardensitydistributionislikely simulations; Hillenbrand&Hartmann1998,basedontheappear- segregation atbirth(Bonnell&Davies1998,basedonnumerical stars arestillpresentatsmallradii).Thisscenarioisfully 1818, anddiscussedthedependence oftheLFsonradiuswithin The natureanddegreeofprimordialmasssegregationis Hillenbrand &Hartmann(1998)arguethattheyoungembedded Although ithasbeenclaimedthattheobservedmasssegregation © 2002RAS,MNRAS 331,245-258 2 O 02MNRAS.331. .2 45D based onindependentdiagnostics.TheagerangeforNGC1805is readily available,butexhibitasignificantrange.Themostrecent presented inthispaper,theuncertaintiesinvolvedtheirmass populating theseareasineachcluster,ishighlymodeldependent et al.1990;Bonatto1995;Santos etal.1995;Cassatella Most estimatesbrackettheagerange betweent~15Myr(Bica indicating aslightlyolderagefor thisclusterthanforNGC1805. Cassatella etal.1996)andlogi(yr)=7.6-7.7(cf.Barbara&Olivi Alloin &Santos1990;BarbaraOlivi1991;etal.1995; which areallroughlyconsistentwitheachother,althoughthey of [Fe/H]=0.0and—0.5forbothclusters. et al.2001). Thévenin 1994;Bonatto,Bica&Alloin1995;seealsoJohnson determinations basedonstellarspectroscopyrangefromroughly determination byJohnsonetal.(2001),basedonHSTCMDfits, certain. oftheyoungLMCpopulationandisthereforeless metallicity estimateavailableforNGC1805,[Fe/H]0.30 near solarmetallicity,fromfitstoHSTCMDs.Theonlyother nations arescarce.Johnsonetal.(2001)obtainedanestimateof cluster massinmoredetail. we needtojustifyourchoicefortheadoptedmetallicity,ageand two youngsampleclusters.Fortheanalysisinthispaper,however, determinations aretoolargeandsystematic(i.e.modeldependent), nation fromisochronefits,forthehandfultofewdozenstars colour-magnitude space,sothatanunambiguousmassdetermi- complex. Stellarpopulationsofdifferentmassesoverlapin Russell (HR)diagramabovethemain-sequenceturn-offisvery CMDs inJohnsonetal.2001forcomparison).Infact,ascanbe from thecolour-magnitudediagrams(CMDs),withcolours MFs; todoso,wewillexcludethefieldLMCredgiantbranchstars include main-sequencestarsbelongingtotheclustersinourfinal the starformationprocess.InSection4wewillderiveMF the outerannularLFs. with respecttothelessluminousstellarpopulationcompared inner annularLFsshowedarelativeoverabundanceofbrightstars within theinner~30arcsecforbothclusters,insensethat each cluster.Wefoundclearevidenceforluminositysegregation logi(yr) =7.0t“ ages. WewillthereforeadoptanageforNGC1805of approximately bracketedbylogf(yr)=6.95-7.00(cf.Bica, and discusstheimplicationsofourresultsintermsIMF similarly suggestsnear-solarabundance,[Fe/H]~0.0.Metallicity (Meliani, Barbuy&Richtler1994)isbasedontheaverage so thatwecannotincludethesestarsinouranalysis. (cf. fig.11inJohnsonetal.2001).Inadifferentialanalysissuchas seen fromtheseCMDs,thetruestructureofHertzsprung- (V —/)>0.67iftheyarebrighterthanV=22mag(seethe (ML) conversionsdiscussedinSection3.Wewilltakecaretoonly slopes forbothclusters,usinganumberofmass-to-luminosity © 2002RAS,MNRAS 331,245-258 [Fe/H] ~—0.8(Melianietal.1994;Will,Romans&deBoer 1996) andt^65Myr(cf.Barbara &Olivi1991),withthemost 1991), withthemostrecentdeterminationsfavouringyounger 1995; Oliva&Origlia1998)to[Fe/H]0.4(Jasniewicz Numerous ageestimatesareavailable forNGC1818,onaverage For thepurposesofpresentpaper,wewillconsidercases Abundance estimatesforNGC1818,ontheotherhand,are Table 1ofPaperIcontainsthefundamentalparametersforour In thispaper,wewillextendouranalysistotheassociatedMFs (ii) Ageestimates.Variousageestimatesexistforbothclusters, (i) Clustermetallicities.ForNGC1805,metallicitydetermi- © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Mass segregationinyoungLMCclusters-II247 4 x3 3 4 respectively. recent estimates,basedonHSTCMDfits,favouringanageof relations arehardtocomeby,and sofarhaveonlybeenobtained by acombinationofthesingle-massisotropicKingclustermodel range derivedbyElson,Fall&Freeman(1987a),i.e.4.1< population models,isclosetotheuppermassallowedbyour1cr log Ly,(L,o)=4.847and5.388forNGC18051818, in theshortCENexposurestherearesomesaturatedstars(cf. number ofsaturatedstarsinthelongCENexposures(i.e. Torrejón 2000).Wewillthereforeadoptanageoft—25Myrfor Hunter etal.1997;vanBever&VanbeverenFabregat for solar-metallicitystars(e.g. Popper 1980;Andersen1991; mass-absolute-magnitude -relation, dm/dMj.EmpiricalML The differentialpresent-daystellarLF,dA7d(/>(A/,),i.e.thenumber NGC 1805and1818inPaperI),agivenpassband/,(M¿),toits The conversionofanobservationalLF(whichwedeterminedfor FUNCTIONS 3 CONVERTINGLUMINOSITYTOMASS used bythemversusourphotometricmassdetermination,anda Hunter etal.(1997)ofM[=3X10M©fallscomfortablywithin log M/M©<5.7,dependingontheMILratio,andestimateof uncertainty. clusters. ThisleadstomassestimatesofM=2.8tog10M© which wecanusetoobtainphotometricmassestimatesforour chip) bycomparisonwiththeshortCENexposures.Althougheven observations wherewelocatedtheclustercentreinWFPC2/PC corrected theseestimatesofL^forthepresencealarge even forthefainterunderlyingstellarcomponent.Wesubsequently exposures, inordertoretainasufficientlyhighsignal-to-noiseratio on fitstothesurfacebrightnessprofilesofourlongestCEN we firstobtainedthetotalV-bandluminosityforeachclusterbased one needstohaveaccurateknowledge oftheappropriateML-or d/V =¿;(m)dm(Kroupa2000),andtherefore corresponding massinterval[m,m+dm],arerelatedthrough differential present-dayMF,d/V/d^ra),i.e.themassin of starsintheabsolute-magnitudeinterval[M^M,+dM],and different treatmentofthebackgroundstellarcontribution. our 1cruncertainty.ThedeterminationbyChrysovergisetal. other availablemass,M=6X10M©(Johnsonetal.2001), & Chariot1996),whicharefairlygoodapproximationsofcoeval Section 3.3inPaperI),theirnumberissmall(12NGC1805and NGC 1818,orlogi(yr)=7.4!“ t —20-30Myr(e.g.Cassatellaetal.1996;Grebel1997; associated MF,£(m),isnotasstraightforwardoftenassumed. although theirmassestimate,basedonearliersimplestellar star clusters,predictmass-to-light(M/L)ratiosasafunctionofage, speculate thatthedifferencebetweenourtwoestimatesiscaused (1989) oflogM/M©=4.69isoutsideour1