2 0 0 3MNRAS.338. . .85M 6 10 Institute ofAstronomy,UniversityCambridge,MadingleyRoad,CambridgeCB3OHA *E-mail: [email protected] prising then,thatwhilecataloguesofhigh-resolutionsurfacebright- ness profilesandstructuralparametersexistforGalacticglobular that shedlightontheevolutionhistoryofentireLMC.Itissur- namics, toluminosityandmassfunctionstudies,investigations fore offersaseeminglyperfectopportunityforstudiesofallaspects The starclustersystemoftheLargeMagellanicCloud(LMC)is Accepted 2002August28.Received27;inoriginalform2001December7 Mon. Not.R.Astron.Soc.338,85-119(2003) © 2003RAS catalogue existsforalargesample oftherichLMCclusters. clusters (e.g.Träger,King&Djorgovski 1995),nosuchuniform of starclusterastronomy,fromformation,evolutionanddy- Galactic globularclusters,butcoveringawideagerange(10- unique incontainingrichstarclustersofmassescomparableto A. D.Mackey*andG.F.Gilmore clusters intheLargeMagellanicCloud 1 INTRODUCTION Surface brightnessprofilesandstructuralparametersfor53richstellar 10 yr)andbeingcloseenoughfordetailedobservation.Itthere- © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 610 profiles ofyoungclusters(suchasbumps,dipsandsharpshoulders),evidenceforboth results presentedheretoformthebasisforseveralfurtherprojects,wedescribeindetail present surfacebrightnessprofilesfortheentiresample,andderivestructuralparameters We havecompiledapseudo-snapshotdatasetoftwo-colourobservationsfromtheHubble ABSTRACT clusters. Key words:stars:statistics-globularclusters:generalMagellanicCloudsgalaxies:star characteristic orphysicalprocess. expansion owingtomassloss,andotherslarge-scalesomeunidentified for theGalacticglobularclustersystem.Inaddition,weexamineprofileofR136indetail in theinnerregionsofseveralcandidatePCCclusters,withslopesapproximately—0.7,but double clustersandpost-core-collapse(PCC)clusters.Inparticular,wefindpower-lawprofiles with thoseofpreviousground-basedstudies. data reductionandsurfacebrightnessprofileconstructionprocesses,compareourresults each cluster,includingcoreradii,andluminositymassestimates.Becauseweexpectthe Space Telescopearchiveforasampleof53richLMCclusterswithages10-10yr.We and appearstoshowabifurcationatseveralhundredMyr.Wearguethatthisobservedrelation- and showthatitisprobablynotaPCCcluster. of theLargeMagellanicCloud(LMC)hasenteredPCCevolution,asimilarfractiontothat ship reflectstruephysicalevolutioninLMCclusters,withsomeexperiencingsmall-scalecore several previouspublicationsbydifferentauthors.Ourdiagramhasbetterresolution,however, showing considerablevariation.Weestimatethat20=b7percentoftheoldclusterpopulation We alsoobserveatrendincoreradiuswithagethathasbeendiscoveredanddiscussed The surfacebrightnessprofilesshowalargeamountofdetail,includingirregularitiesinthe the coreradius,ratheruncertain.In addition,eachsetofauthorsuses ters. This,inturn,rendersthederivation ofkeyparameters,suchas Freeman &Lauer1989;Elson1991,hereafterE91;1992); In particular,significantnumbersofsurfacebrightnessand/orden- which limittheirresolution,particularly intheinnerregionsofclus- tributions -intheLMCdisc(Kontizas,Chrysovergis&Kontizas clusters (Elson,Fall&Freeman1987,hereafterEFF87;Elson, and collaboratorsconstructV-band surfacebrightnessprofiles; a differentdatasetandmakes measurements(e.g.Elson Kontizas 1988).Thesestudiesareallground-basedandtherefore old clusters(Mateo1987);andwithdifferentspatialdis- suffer fromproblems-primarilycrowdingandseeingrelated (Kontizas, Hadjidimitriou&Kontizas1987b;Metaxa, (Chrysovergis, Kontizas&1989);andintheLMChalo sity profileshavebeenpublishedforyoungandintermediateage 1987a); intheLMCdiscandwithin5kpcofrotationcentre There has,however,beensomeconsiderableactivityinthisfield. 2 0 0 3MNRAS.338. . .85M balance ultimateaccuracy(maximum data)foranygivenclusterin ranges describedabove,eventhoughformanyoftheclustersfrom possible, weattemptedtomimicthesnapshotdatabyusingonlytwo between 1994January27andDecember25,butmostlybeforethe range 20-300sinF555Wand40-600F450W,dependenton project 5475).ThisdatasetconsistsoftwoWideFieldPlanetary brightness profiles(Fig.6)areavailableon-lineathttp://www.ast. between coreradiusandagefortheLMCclustersystem.Thisrela- processes (Sections3and4,respectively).InSection5wepresent possible, forthepurposesofdifferentialcomparison.Tothisend, providing anatlasofsurfacebrightnessprofilesfromthisdata,the to bereducedwithinareasonable time frame.Therefore,wehadto match theleastobservedclusters. This fittedwithourprimaryaim targets’, itwasnecessarytolimit the useoftheseextraframesto these sixstudies,anabundanceofarchivalframesisavailable.To frames percluster,withexposuretimesasclosepossibletothe located afurthersixsuitablestudies(HSTprojects5114,5897,5904, to obtainobservationsofasmanyadditionalclusterspossible.We nor asvarieddesired,andconsequentlywereturnedtothearchive WFPC2 cool-downon1994April23. the ageofclusterunderobservation.Thedatawereacquired F555W filters,respectively,andwithexposuretimescoveringthe The observationalbasisofthisprojectisthepresenceinHST 2.1 Observations 2 THECLUSTERSAMPLE into thisproblem. tionship hasbeenstudiedpreviously(Elsonetal.1989;E91;Elson ters. Finally,inSection6weobserveanddiscusstherelationship in thesample-suchasbinaryclustersandpost-core-collapseclus- mentioned, andexaminesomeoftheinterestingsubgroupspresent ments, comparetheseresultswiththoseoftheauthorspreviously the surfacebrightnessprofilesandstructuralparametermeasure- its selection(Section2)andthereductionprofileconstruction the problemsthatbesetground-basedstudies.Ratherthansimply number densityprofiles),somostoftheimportantderivedvalues Mateo uses5-bandprofiles;andKontizascollaboratorsuse we requireddataforaslargeasample ofclustersaspossible,but of investigatingtheLMCclustersystem asawhole.Forthispurpose avoid biasessuchasthatowingtoobserverselectionof‘interesting clusters each.Tomaintaintheuniformityofourselectionasfar 5916,7307 and8134),consistingofdetailedobservationsseveral Camera 2(WFPC2)exposurespercluster,throughtheF450Wand archive ofasnapshotsurveyLMC(andSMC)clusters(HST cam.ac.uk/STELLARPOPS/LMC_clusters/. additional projects,inthispaperwediscussatlengththedatasetand and becauseweexpectourmeasurementstoformthebasisofseveral available observations.Becausetheseproceduresareratherdetailed, therefore appliedauniformselectionandreductionprocesstothe we requireasampleasfreefrombiaspossible,andhave aim ofthepresentstudyistoobtainastatisticallyhomogeneous observations ofrichLMCclustersintheHubbleSpaceTelescope are notstrictlycomparablebetweenstudies. set ofprofilesandkeystructuralparametersforasmanyclusters {HST) archivetocompileahigh-resolutiondataset,unaffectedby 86 A.D.MackeyandG.EGilmore 1992); however,ourmeasurementsareabletoprovidenewinsight Upon retrieval,wediscoveredthatthesamplewasneitheraslarge The datapresentedinTables1,2,4and6,thesurface We havetakenadvantageofthepresencealargenumber © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem hms ; hms0/ profile constructionprocess,thechoiceofsecondcolouris been included.Nonetheless,wewerecarefulnottounnecessarily base, wehavenotcompiledallsuchidentifiersforoursample,rather purport tobeacompletesurveyoftheavailableliterature;ratheritis position, ageandmetallicitydatafromtheliteratureforcomplete 2.2 Literaturedata little consequence. their secondfilter.Wenote,however,thatforoursurfacebrightness the F450Wfilter,withremaining22clustershavingF814Was high-resolution dataset;31oftheclustersarealsoobservedthrough in Table1togetherwiththeobservationaldetails.Thesamplecon- the extrasixstudiesbeingF555WandF814W.Fornineclusters tional datawouldhavecompromisedourresults(e.g.inextremely to provideanatlasofsurfacebrightnessprofiles,orstudyone the sampleagainstoverallreductiontime.Hadouraimbeensimply tre ata=052639,5-69° 1536"(J2000.0)(Rohlfsetal. a =052056,á-69284 F' (J2000.0)(Bicaetal.1996), projected angulardistanceRtotheopticalcentreofLMCat logue ofBicaetal.(1999).Usingthesepositionswecalculatethe J2000.0 positionsforLMCobjectsareingeneralfromthecata- logues asfollows:Hodge(Hodge1960);SL(Shapley&Lindsay NGC number,withtheotheridentifiersandcorrespondingcata- We havetakenpositionandnomenclatureinformationfromthe 2.2.1 Clusternamesandpositions for useinthisandsubsequentprojects. intended toprovideaconsistentsetofageandmetallicityestimates For severalclusters,scarcityofinformationhasnecessitatedthe for thisandfuturepublications,wehavecompilednomenclature, As asupplementtotheabovedataset,andasreferencepoint der toovercomedatadegradationowingseverecrowdingand/or we retrievedbothlong(~500s)andshort(~10exposuresinor- crowded clusters)weincludedminimalnumbersofextraframesin degrade thequalityofourdata.Incaseswhereneglectaddi- each cluster;however,theliterature valueslistedhereareneversub- values thatrepresentapproximatelytheconvergenceofdata. data setconstruction,theemphasisisonobtainingashomogeneous cluster sample.ThisinformationisdisplayedinTable2.Aswiththe was notpossible,withtheonlyuniformchoiceoffiltersbetween order toproceed. or twoclustersingreatdetail,theextradatawouldcertainlyhave and theprojectedangulardistance 5t totheHirotationcurvecen- only themostcommon.Ingeneral,principaldesignationisan almost allrecognizedidentifiersforaclusterareincludedinthisdata Simbad AstronomicalDatabase(http://simbad.u-strasbg.fr/).While of high-qualityobservationswherenecessary.Inthecases accuracy ofthedata.Thismeansusingresultslargesurveysor a compilationaspossible,whilestillmaintainingtheintegrityand sample isobservedthroughtheF555Wfilter,providingaunique sists of53LMCclustersspanningthefullagerange.Theentire saturation (asmentionedabove).Thefinalclustersampleislisted stantially differentfromourcalculated positions. selection ofolderorlower-qualitydata.Thiscompilationdoesnot several suchhigh-qualitystudiesareavailable,wehavechosenthe studies forthemostpart,andsupplementingthesewithresults 1984; Westerlund1990).Laterwe derive moreaccuratecentresfor 1963); LW(Lyngâ&Westerlund1963).IntheSimbaddatabase, op{ ro In theend,completereproductionoforiginalsnapshotdata © 2003RAS,MNRAS 338,85-119 2 0 0 3MNRAS.338. . .85M /7 0 "The archivedimagesofthiscluster areincorrectlylabelledasNGC2156.Thearchivedimagesofthiscluster areincorrectlylabelledasSL633. R136 HODGE 14 HODGE 11 HODGE4 NGC 2257 NGC 2249 NGC 2231 NGC 2214 NGC 2213 NGC 2210 NGC 2209 NGC 2193 NGC 2173 NGC 2172 NGC 2164 NGC 2162 NGC 2159 NGC 2157 NGC 2156 NGC 2155 NGC2153 NGC 2136 NGC 2121 NGC 2100 NGC 2031 NGC 2019 NGC 2011 NGC 2005 NGC 2004 NGC 1984 NGC 1916 NGC 1898 NGC 1868 NGC 1866 NGC 1860 NGC 1856 NGC 1850 NGC 1847 NGC 1841 NGC 1835 NGC 1831 NGC 1818 NGC 1805 NGC 1786 NGC 1777 NGC 1754 NGC 1718 NGC 1711 NGC 1651 NGC 1466 name © 2003RAS,MNRAS 338,85-119 SL855 SL842 Cluster Table 1.Clusterlistandobservationdetails. © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Program 5475 5904 5916 5916 5475 5916 5916 5475 5475 5475 5475 5475 5897 5916 5475 7307 5897 5475 5916 5475 5904 5475 5897 5114 5475 5475 5475 5475 5475 5475 5475 5475 5475 5475 5475 5897 5475 5475 5475 5475 5475 5475 5475 5475 5475 7307 8134 8134 8134 8134 8134 8134 8134 ID F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W F555W Filter u2hk0302t u2hk0304t u26m0n02t u26m0f02t u26m0o02t u26m0q02t u26m0h02t u26m0102t u26m0d02t u26m0y02t u26m0s02t u26ml802t u2xj0403t u26m0w02t u26m0p02t u26m0m02t u5ay0502r u5ay0101r u26m0t02t u5ay0401r u26ml902t u5ay0303r u5ay0301r u26m0k02t u26ml502t u26ml702t u26m0x02t u26mlc02n u2y80301t u2xq0601t u2xq0603t u5ay0803r u5ay0801r u2xq0501t u2xq0503t u26mld02t u5ay0901r u2xq0401t u2xq0403t u2xq0304t u26m0z02t u5ay0601r u26ml202t u26ml302t u26mle02t u26mlb02p u2xj0708t u2xq0201t u2xq0203t u26ml002t u4ax3005r u4ax0206r u2xj0203t u26m0u02t u2xq0101t u2xq0103t u26m0j02t u2y80502r u26m0r02t u2xj0103t u26m0v02t u5ay0903r Data setDate Principal frame 21/08/1999 07/02/1994 06/02/1994 27/01/1994 25/09/1998 25/07/1998 23/11/1994 21/10/1995 21/10/1995 06/02/1994 01/02/1994 22/10/1995 25/09/1994 25/09/1994 01/02/1994 01/02/1994 01/02/1994 01/02/1994 01/02/1994 05/02/1994 06/02/1994 25/12/1994 01/02/1994 02/02/1994 24/09/1999 23/08/1994 26/03/1994 22/08/1999 22/08/1999 01/02/1994 02/02/1994 21/04/1994 20/10/1995 21/04/1994 09/07/2000 08/07/2000 30/01/1994 10/12/1995 10/12/1995 10/04/1994 15/05/1994 10/04/1994 14/11/1995 18/10/1995 18/10/1995 19/10/1995 18/10/1997 18/09/1994 11/08/1994 16/02/1994 13/12/1995 14/10/1999 16/10/1999 19/04/1994 11/02/1994 18/10/1995 18/10/1995 19/08/1999 19/08/1999 19/10/1995 19/10/1995 10/12/1995 Time (s) 500 500 500 260 500 260 260 500 500 350 300 300 300 350 350 350 350 300 350 350 800 100 140 140 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 40 40 20 20 20 20 23 20 20 20 20 20 30 30 30 30 30 10 10 10 3 F814W F814W F450W F814W F450W F450W F450W F450W F814W F814W F450W F814W F814W F814W F450W F814W F450W F814W F450W F814W F450W F450W F450W F450W F450W F450W F450W F450W F450W F450W F814W F450W F450W F450W F814W F814W F450W F814W F450W F814W F450W F450W F450W F450W F814W F814W F814W F814W F450W F814W F814W F814W F814W F814W F450W F814W F450W F814W F814W F814W F814W F814W Structure ofrichLMCclusters87 Filter u2xq0409t u2xq0309t u26m0z01t u5ay0604r u26ml201t u26ml301t u26mle01t u26mlb01p u2xj0707t u2xq0206t u2xq0209t u26ml001t u4ax300cr u4ax020br u2xj0201t u26m0u01t u2xq0106t u2xq0109t u26m0j01t u2y80504r u26m0r01t u2xj0101t u2hk030qt u2hk030rt u26m0n01t u26m0f01t u26m0o01t u26m0q01t u26m0h01t u26m0101t u26m0d01t u26m0y01t u26m0s01t u26ml801t u2xj0401t u26m0w01t u26m0p01t u26m0m01t u5ay0504r u5ay0105r u26m0t01t u5ay0404r u26ml901t u5ay0306r u5ay0304r u26m0k01t u26ml501t u26ml701t u26m0x01t u26mlc01t u2y80304p u2xq0606t u2xq0609t u5ay0806r u5ay0804r u2xq0506t u2xq0509t u26mld01t u5ay0904r u2xq0406t u26m0v01t u5ay0906r Data setDate Secondary frame 22/08/1999 07/02/1994 06/02/1994 27/01/1994 25/09/1998 25/07/1998 23/11/1994 21/10/1995 21/10/1995 06/02/1994 01/02/1994 22/10/1995 25/09/1994 25/09/1994 01/02/1994 01/02/1994 01/02/1994 01/02/1994 01/02/1994 05/02/1994 06/02/1994 25/12/1994 01/02/1994 02/02/1994 24/09/1999 23/08/1994 26/03/1994 22/08/1999 22/08/1999 01/02/1994 02/02/1994 21/04/1994 20/10/1995 20/08/1999 20/08/1999 21/04/1994 09/07/2000 09/07/2000 30/01/1994 10/12/1995 10/12/1995 10/04/1994 15/05/1994 10/04/1994 14/11/1995 18/10/1995 18/10/1995 19/10/1995 18/10/1997 18/09/1994 11/08/1994 16/02/1994 13/12/1995 14/10/1999 16/10/1999 19/04/1994 11/02/1994 18/10/1995 18/10/1995 19/10/1995 19/10/1995 10/12/1995 Time (s) 230 230 600 230 230 230 230 600 230 230 230 260 230 230 230 230 230 600 600 600 600 200 600 260 230 600 230 230 260 350 350 350 350 300 350 350 350 300 300 300 800 40 40 40 40 40 60 60 60 60 60 20 20 20 20 20 80 80 10 10 10 5 2 0 0 3MNRAS.338. . .85M hms ; hms / Notes. ^Calculatedmetallicity(orage forNGC1916),asdescribedinthetext.«Relativetoopticalcentre oftheEMCbar,ata—052056, et al.(1991);(13)Rich(2001);(14) Siriannietal.(2000);(15)Suntzeff(1992). Reference list:(1)deGrijsetal.(2002b); (2)Dirschetal.(2000);(3)Elson(1991);(4)&Fall(1988);(5) Geisler etal.(1997);(6)Hill(2000); R136 HODGE 14 HODGE 11 HODGE4 NGC 2257 NGC 2249 NGC 2231 NGC 2214 NGC 2213 NGC 2210 NGC 2209 NGC 2193 NGC 2173 NGC 2172 NGC 2164 NGC 2162 NGC 2159 NGC 2157 NGC 2156 NGC 2155 NGC 2153 NGC 2136 NGC 2121 NGC 2100 NGC 2031 NGC 2019 NGC 2011 NGC 2005 NGC 2004 NGC 1984 NGC 1916 NGC 1898 NGC 1868 NGC 1866 NGC 1860 NGC 1856 NGC 1850 NGC 1847 NGC 1841 NGC 1835 NGC 1831 NGC 1818 NGC 1805 NGC 1786 NGC 1777 NGC 1754 NGC 1718 NGC 1711 NGC 1651 NGC 1466 name Principal 5 =-69°2841"(J2000.0)(Ricaetal. 1996).^RelativetotheHirotationcentreofEMC,ata=052639 , 8=-69°1536"(J2000.0)(Rohlfsetal. (7) Hunteretal.(1995);(8)Jasniewicz &Thévenin(1994);(9)Johnsonetal.(2001);(10)OlivaOriglia(1998); (11)Olsenetal.(1998);(12)Olszewski SL855 SL842 SL663 Table 2.Literaturenomenclature,position,ageandmetallicitydatafortheclustersample. 88 A.D.MackeyandG.EGilmore 1984; Westerlund1990). © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem NGC 2070,30Dor LW420 LW399 LW273 SL796 SL803, LW347 SL792, LW341 SL762 SL725, LW303 SL662 SL577 SL554 SL559 SL518 SL523 SL488 SL361 SL350 SL330, LW169 SL319, LW163 SL284 SL271 SL261 SL240 SL215 SL227, LW133 SL201 SL186 SEI 49 SL121, LW96 SL91 SL65 SL55 SL7, LW12 SEI, LW1 SL506, LW220 SL868, LW437 SL556, LW237 SL895, LW481 SL893, LW479 SL884, LW466 SL860, LW426 SL857, LW419 SL858, LW423 SL849, LW408 SL839, LW387 SL807, LW348 SL812 SL808 SL814, LW351 SL799 SL794 Alternative names hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hir h111 hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms hms 06 1257 06 1042 06 ll31 06 0834 06 17 05 5758 06 0005 05 5854 06 0031 05 57 05 5734 05 5745 05 5833 05 5751 05 5317 05 4812 05 4208 05 3341 0531 05 32 05 3009 05 3040 05 2740 05 1839 05 1642 05 1436 05 1339 05 1039 05 0929 05 0844 05 0708 04 4523 05 05 0616 05 0414 05 0221 0459 06 04 5548 04 5417 0452 25 04 5037 04 3732 03 4433 05 3843 05 2839 06 1422 053154 06 1053 06 0815 05 4229 06 3012 06 2549 06 2044 1s 1s 56 19 / / r / / / / /// -69° 06'03" -13° 31'48" -69° 50'54" -64° 42'00" -65° 02'36" -62° 59'18" -65° 2L48" -64° 19'36" -68° 55'12" -67°3106" -68° 15'36" -71° 31/42" -69° 0718" -73° 5O'30" -65° 05'54" -72° 58'42" -68° 38'12" -6%°31'06" -63° 43'18" -68° 31'24" -69° IF48" -68° 21'36" -65° 2836" -66° 24'00" -69° 3L42" -71°28 48" -69° 12'42" -70° 59'12" -70° 09'36" -67°3118" -69° 45'06" -67° 11'12" -69° 08'06" -69° 24'24" -69° 39'24" -63° 51'18" -65° 21'54" -68° 45'12" -69° 07'36" -68° 4536" -68° 58'18" -83° 59'48" -69° 24'12" -64° 55'06" -66° 26'06" -66° 06'42" -67° 44'42" -74° \1'00" -70° 2630" -67° 03'06" -69° 59'06" -70° 35'06" -71°4018 Position (J2000.0) tfopt (deg)« 14.55 4.08 4.82 4.19 4.62 4.92 4.69 4.97 4.44 4.52 4.43 4.81 0.69 0.21 0.41 5.57 2.70 5.10 2.43 2.64 7.89 6.88 9.10 5.86 6.04 5.48 6.48 7.23 5.59 2.83 2.95 2.24 0.84 2.38 3.47 3.86 3.69 3.77 3.66 3.61 3.48 3.26 3.53 8.43 1.18 1.08 1.32 1.34 1.40 1.63 1.90 1.83 1.16 0 rot (deg) 14.78 4.03 4.85 4.00 4.00 4.29 4.37 4.15 4.59 4.23 4.40 4.16 4.00 4.37 4.23 0.15 0.72 0.95 5.47 5.44 2.96 6.29 7.85 5.33 5.46 5.43 5.89 6.69 2.92 2.75 2.96 5.03 2.34 2.80 0.58 2.01 3.61 3.02 3.17 3.11 3.04 8.38 8.47 1.54 1.53 1.77 1.90 1.09 1.37 1.82 1.01 1.82 1.70 006 +007 +007 +012 10.20 ±0.09 10.09 ±0.01 10.18 ±0.01 10.10 ±0.01 10.18 ±0.01 10.20 ±0.10 10.20 ±0.01 + yi0 yzu +010 y1 y:)A 89 7.06 ±0.30 7.50 ±0.20 7.42 ±0.30 9.30 ±0.30 7.70 ±0.05 9.13 ±0.30 7.60 ±0.20 7.60 ±0.20 7.70 ±0.20 7.60 ±0.20 7.60 ±0.20 7.60 ±0.20 6.99 ±0.30 7.30 ±0.20 7.20 ±0.20 8.74 ±0.30 8.12 ±0.30 8.28 ±0.30 8.12 ±0.30 8.50 ±0.30 8.82 ±0.30 8.00 ±0.10 8.20 ±0.10 10 15+ 10 22' 10.19: 10 25' 10 22' 1U. ioos iu.zz._oo8 iu.zd_ iu.zz_oj6 7.40+ 7.00" 9.08+ 9.30 ^•^-O.ll 9 a4+0.09 9.30+ 9.51 -0.13 9ig+o+o -o.i2 9 20' 9 aa+o.oo 9.33 -0.16 9 11+0.12 9.51" 9.11 -0.07 9 ci+0.06 09 6.48+!;+ 9.267“;” '+a24 log T (yr) rv+0.30 +0.30 O+0.12 +0.08 n+0.08 n n □+0.06 +0.06 +0.07 +0.06 +0.12 -0.10 —0.18 -0.07 —0.07 -0.10 -0.10 -0.16 -0.07 -0.09 o.io © 2003RAS,MNRAS 338,85-119 Age 11 11 11 14 13 13 13 13 13 11 11 ref. 4 4 4 4 4 4 4 4 4 4 4 5 5 5 2 5 5 5 5 5 2 5 5 5 5 5 5 5 2 2 3 3 3 3 3 3 3 3 3 1 1 * 0.00 to-0.40 0.00 to-0.40 ±0.01 ±0.20 - -0.4 -0.90 ±0.40 -2.08 ±0.20 -1.37 ±0.20 -0.50 ±0.20 -0.50 ±0.10 -0.52 -0.52 -0.12 ±0.20 -0.37 -2.11 ±0.10 -1.79 ±0.20 -1.87 ±0.20 -0.35 ±0.20 -1.54 ±0.20 -0.42 -0.57 ±0.17 -0.37 ±0.20 -2.17 ±0.20 -0.66 ±0.20 -2.06 ±0.20 -0.15 ±0.20 -0.42 -0.36 ±0.20 -0.60 ±0.20 -1.63 ±0.21 -0.47 -0.67 ±0.20 -0.45 -0.01 ±0.20 -1.97 ±0.20 -0.47 -0.60 ±0.20 -0.24 ±0.20 -0.44 -0.45 -0.23 ±0.20 -0.45 -0.45 -0.45 -0.55 ±0.20 -0.42 -0.55 ±0.23 -0.61 ±0.20 -0.32 ±0.20 -0.52 ±0.21 -1.81 ±0.20 -0.47 ±0.40 -1.92 ±0.20 -0.56 ±0.20 Metallicity [Fe/H] Met. 7,14 ref. 1,9 1,9 12 12 12 12 13 12 12 12 13 12 12 12 12 12 10 12 10 12 12 12 15 12 12 12 12 12 12 12 2 2 2 6 2 8 8 * * * * * * 2 0 0 3MNRAS.338. . .85M present aCMDforthisclusteralongwithCMDsandageestimates metallicity. Naturally,anysubsequent usemustbecarefullyjudged the purposeofestimatingmass-to-light ratioslaterintheanalysis- ple ofcomparableage.Weemphasizethatthesevalues,inparticular, these weaveragetheliteratureresultsforallclustersinoursam- from thediscussionofSiriannietal.(2000);seealsoHunter NGC 1805and1818weagaintaketherangesadoptedbydeGrijs tra ofOliva&Origlia(1998),andone(NGC1866)fromtheYLT Table 2.Weadoptanothertwoabundancesfromtheinfraredspec- tion of~0.2dex,whicharemoreconsistentwiththeothererrorsin tions of±0.03dexintheaveragesseveralobservationsforeach Jasniewicz &Thévenin(1994).Theauthorsreportstandarddevia- the sameseries(Suntzeffetal.1992).Afurtherthreeabundances The definitivestudyofLMCclustermetallicitiesisbyOlszewski 2.2.3 Clustermetallicities from thosefortheotherfiveclusters,soweaverageagesofthese fering fromseriousdifferentialreddening,isnotevidentlydifferent for fiveoldLMCclusters.TheCMDNGC1916,thoughsuf- not locateareliableageforNGC1916,butOlsenetal.(1998)do mates ofElson&Fall(1988),whoprovideanagecalibrationbased Finally, wefilltheremainingholesinoursamplewithageesti- thorough discussionandreviewofdeGrijsetal.(2002b)simi- three clusters.ForNGC1805and1818weadopttheagesfrom E91 fornineclustersandthoseofDirschetal.(2000)afurther We taketheagedeterminationsfromground-basedstudiesof ing inCMDs.Pre-eminentamongsttheseareHSTstudies,andwe lead wehaveadoptedwherepossiblefortheremainingclustersage provides ageestimatesfor15clustersinoursample.Followingthis homogeneous datasetwehavelocatedisthecolour-magnitudedia- literature, andinvolvealargevarietyoftechniques.Themostuseful Age determinationsforLMCclustersarewidelyscatteredacrossthe 2.2.2 Clusterages © 2003RAS,MNRAS 338,85-119 on thenatureofcalculationat hand. calculations, whichinanycaseare ratherinsensitivetotheadopted count forthis.Inthispaper,weadopt theseabundancessolelyfor are simplyrathercrudeestimatesand thatanyuseofthemmustac- et al.2001),andsimilarlyforR136weagainadopttheabundance et al.(2002b)aftertheirdetailedliteraturereview(seealsoJohnson discussed inSection2.2.2.FourcomefromthestudyofDirschetal. on abundancesderivedfromCMDfitsandcorrespondingtotheages of theseclusters;however,weprefertheirerrorspersingleobserva- also adoptonemetallicity(NGC1841)fromasubsequentpaperin observations ofthecalciumtripletinspectragiants.Fromthis et al.(1991)whoderivemetallicitiesfor~70LMCclustersfrom clusters toobtainanestimateforNGC1916. a distancemodulusof18.5usingtheirprescribedmethod.Wecould on alargesampleofliteratureCMDs.Wecorrecttheseestimatesto larly forR136wetaketheageasdiscussedbySiriannietal.(2000). age clustersandtheresultsofOlsenetal.(1998)forfiveoldclusters. adopt theresultsofRich,Shara&Zurek(2001)forfiveintermediate determinations basedonhigh-resolutionphotometricstudiesresult- gram (CMD)studyandagecalibrationofGeisleretal.(1997),which suitable abundancemeasurementsfromtheliteraturesoforeachof (1995). Fortheremaining14clusterswewerenotabletoobtain (2000), andtwofromtheHSTphotometryofRichetal.(2001).For studies suitableforourdataset.Forafewclusterswethereforerely spectroscopy ofHilletal.(2000).Thesecompletethespectroscopic (NGC 1850,2004,2100)aretakenfromthespectroscopicstudyof study weadoptmetallicitiesfor23oftheclustersinoursample.We © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 1 perfect forthecurrentdataset-withtwoframesperfield,each run automaticallywherepossible,withoutsacrificingdataintegrity. process byusingcalibrationsfromasingleepoch. baseline forcalculationandarethereforemoreaccurate.Bearingin brations. Thisispreferabletousingtheoriginaldataasreducedsoon before eachphotometrymeasurementusingthepixelsjustbeyond recursive locationandsubtractionofobjectsatincreasinglylower preparation utilitiesincludedwiththeHSTphotpackage.Thispro- through adifferentfilter.Conventionally,thiswouldmakethere- the samefield,regardlessoffiltercombination.Thismakesit This programfirstalignsaccurately(tofractionsofaWFCpixel) multiphot routinehasproventobethemostusefulforourdataset. the severelyundersampledPC/WFCpointspreadfunctions(PSFs) tailored tothereductionofWFPC2frames,routinelyaccountingfor HSTphot iswellsuitedforrunninginbatchmodeandspecifically large numberofobservationsrequiresthereductionprocesstobe mind thatourdatasetcoversaspanofmorethan5yearsHST As partofthearchiveretrievalprocess,allframeswerereducedac- 3 PHOTOMETRY the vignettedregionbetweenchips. the measuredprofileofanobject conforms to-theoptionsbeing from thePSFfittingofmultiphotareusedtokeepphotometry tions ofthecrowdedcentralregionsglobularclusters. for rapidlyvaryingbackgroundssuchasthoseexpectedinobserva- the photometryradius(Dolphin2000a).Thisisdesignedtoaccount multiphot thatcalculatesanadjustmenttothebackgroundimage threshold levels.Wesetaminimumlevelfordetection is similar,inprinciple,tothatofdophot,beingbasedaroundthe unique WFPC2PSFs.Thedetectionalgorithmusedbymultiphot multiphot isdesignedspecificallyformeasurementsinvolvingthe ing 2WFCpixeland3PCradii.Thisispresumablybecause that areatleastasnarrowthosefromaperturephotometryus- have foundthatPSFfittingproducesmainsequencesonourCMDs ting mode.Whileaperturephotometrymodeisalsoanoption,we image (usingaa-clippingalgorithm),andtherobustdetermination crrej), theremovalofhot-pixelsnotflaggedbydataquality these problemsareaccountedfor. moval ofcosmicraysandcross-identificationobjectscomplicated cording tothestandardHSTpipeline,usinglatestavailablecali- clean ofnon-stellarobjectsandspuriousdetections.Theobjectclas- data qualityimagethataccompanieseachobservation,afirstattempt cedure includesthemaskingofbaddataasflaggedbySTScI and thenperformssimultaneousphotometryonmultipleimagesof and theirvariationcausedbysubpixelpositioning.Inparticular,the observations, wealsomaintainthehomogeneityofourreduction after observationbecausethelatestcalibrationshaveamuchlonger of 3aabovethebackground.Inaddition,weenableafeature and measurement. of abackgroundimage-usedbymultiphotforstellardetection at theremovalofcosmicrays(usingaroutinebasedoniraftask and unreliable.Bysolvingthetwoframessimultaneously,bothof (Dolphin 2000a)tobethemostsuitablesoftwarepackage.Our stellar (oramarginallyresolved pair),extended(galaxy),or sification parameterisadeterminationastowhichprototypePSF Suchasknownbadpixels,saturated chargetraps,badcolumnsand For photometricmeasurementswehavefoundHSTphot The objectclassification,sharpnessandxparametersproduced Photometric measurementsaremadeusingmultiphotinPSFfit- Before startingmultiphoteachframeisreadiedwiththeimage Structure ofrichLMCclusters89 2 0 0 3MNRAS.338. . .85M -1 -3 jects withsharpnessbetween—0.6and+0.6x^3.5provided HST instrumentalsystemtotheJohnson-Cousinsbecause rected pixelcoordinates.Theonly resultsthatincorporateimage rations fromthese.Allcentringcalculations, annulusconstruction, pixel coordinatesforalistofstarstorelative broadly followthetechniquesoutlinedbyDjorgovski(1987). procedure issimilartothatforground-baseddata,however,andwe by thehighresolutionandpeculiarchipgeometryofWFPC2.The ric andastrometricaccuracyofmultiphottobe0.011-0.014mag brightness profiles,andwouldinsteadaddunnecessaryscatterto profile. Aftersomeexperimentation,wefoundthatselectingob- than takingthe(a,5)foreachstar andcalculatingangularsepa- tions usingtheWFCpixelscale of 0.0996arcsecpixel,rather the {a,5)socalculated.Toavoidthis,wetookcorrectedpixel information isnotalwaysreliable,andcanintroduceerrorsinto using thepositionalinformationinimageheaders.Thisheader then convertsthesecorrectedpixelcoordinatesto(a,¿)(J2000.0) the WFC2chip,makingappropriategeometriccorrections,and using theirafstsdastaskmetric,whichconvertschipand WFCs andtheseparationsbetweenchips.Thiswasachieved tial positioningofstarsfromchiptochip,weoverlaidauniform 4.1 Astrometryandcentredetermination in concept;however,practice,ourcalculationswerecomplicated 4 SURFACEBRIGHTNESSPROFILES the photometry.Dolphin(2000a)estimateslimitingphotomet- this transformationisnotimportantfortheconstructionofsurface from theDolphin(2000b)calibration.Wedonotconvert using groupsofisolatedstarsselectedaccordingtoasetstrict ters wereobservedinwarmconditions.Thestellarmagnitudesare April 23.Thisisespeciallyimportantforourdataset,since25clus- that is,observationstakenbeforetheWFPC2cool-downof1994 Notably, thiscalibrationalsoprovidescorrectionsfor‘warm’data- ically) (Dolphin2000a),andthe34throwerror(Shaklan,Sharman these valueswouldbesomewhatstricter. PSF, beingnegativeiftheprofileistoobroad,zeroobject measure ofhowsharpitsprofileisincomparisonwiththestellar and completenessareacorrections (seebelow)usedthesecor- coordinates frommetricforeach star andderivedangularsepara- optical systemofHST,thechangesinpixelscalefromPCto coordinate system,accountingforthegeometricdistortionfrom One problempresentedbythedatawascausedfour-chip Constructing asurfacebrightnessprofileforgivenclusterissimple on theWFCs),respectively. and 0.05pixels(2.5x10arcseconthePC5.4 criteria (Dolphin2000a).Finally,multiphotusesthezero-points also correctedforPSFresidualsandtoanapertureof0.5arcsec longest baselinecalibrationavailable-thatofDolphin(2000b). corrected forcharge-transferefficiency(CTE)effectsusingthe & Pravdo1995;AndersonKing1999).Themagnitudesarealso are fromPSFscorrectedforgeometricdistortion(Holtzmanetal. a mostlycompletestellarsampleforthepurposeofconstructing value simplymeasuresthequalityoffitPSFtoobject a perfectfitandpositiveiftheprofileistoosharp.Finally,x 90 A.D.MackeyandG.EGilmore structure ofWFPC2.Inordertomaintaintheaccuraterelativespa- surface brightnessprofiles.FortheconstructionofcleanCMDs, single pixel(cosmicray).Thesharpnessvalueforanobjectisa 1995a), thefilter-dependentplatescalechanges(determinedempir- The finalphotometricmeasurementsobtainedfrommultiphot © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 2 joined byanotherCCD,thenthenumberofsurroundingboxesis process thereforelosesitsvalue. brightness, addingtotheproblem.Thehighresolution,inparticu- pletely suitableforourdata.UnlikeGalacticglobularclusters,many by Djorgovski(1987).However,suchalgorithmswerenotcom- post-collapse core.Thereareseveralalgorithmsforlocatingthe pling methodisrobustandeasily adaptedforclustersofdifferent brightness calculated(asfortheboxes)inacircleofradiusrabout to mostclusters,becausethemagnitudeofsmoothingrequired lar, meansthatitisnotsufficienttosimplyapplyspatialsmoothing the sample.Inaddition,andcompoundedbyhighresolution Magellanic Cloudclustersdonothavesmoothprofiles,butinstead ter, oneexamplebeingthemirror-autocorrelationmethoddescribed ness profile,andthisinturncanleadtolargesystematicerrors header positionalinformationarethecalculatedcentrecoordinates Ormorecorrectly,thecentralsurface brightnesspeak. this procedureworkedwell;however,forclusterswithseverecentral to selectonlythesestarsforthecentredetermination.Ingeneral, to excludethefewbrighteststarsinaclusterfromabovecal- face brightnesspeak,itgenerallydoesnotcorrespondtotheoverall the brighteststarinacluster,andalthoughthisdoesrepresentsur- the highestsurfacebrightnessistakentobeclustercentre. less (fiveifthecentralboxisonanedge;threeitliesinacorner) tected) inthesubsequentcalculations.Ifboxwithhighest region fallsacrossmorethanonecharge-coupleddevice(CCD)- ness, andtheeightboxessurroundingit.Itdoesnotmatterifthis to theregioncoveredbyboxwithhighestsurfacebright- in thebox(includingcompletenesscorrections-seeSection4.2.2) face brightnessiscalculatedbyaddingupthefluxesforallstars cluster centres.Inthisprocedure,eachchipisfirstsplitintoboxes degrades theintrinsicaccuracyofcentredetermination,and ficult toapplysymmetry-algorithmsrobustlyanduniformlyacross centre ofaclusterthatrelyonthesymmetrypropertiesclus- cluster. Poorcentringwilltendtoartificiallyflattenasurfacebright- expressed in(o',á)(seeTable4Section5.1). very youngclusters). crowding, itwasnecessarytorelaxthelimitsandincludebrighter cluster weimposecolourandmagnitudelimitsontheCMD cluster). Main-sequencestarsaresuchanensemble,andsoforeach greatest densitycoincidentwiththesurfacebrightnesspeakof culations, andinsteaduseasubsamplethatshouldcloselytracethe cluster surfacebrightnesspeak.Toavoidthis,wewouldideallylike calculation. AfterNtries,thepointcorrespondingtocirclewith each point.Ifpartofonethesecirclesfallsofftheedgeachip we simplyaccountforthevignettedarea(wherenostarsarede- are clumpy,irregularandnotparticularlysymmetric,makingitdif- any structuralparametersderivedfromtheprofile,andmayob- or overavignettedregion,this‘lostarea’isaccountedforinthe amalgamated region,pointsarerandomlygeneratedandthesurface and theamalgamatedregioniscorrespondinglysmaller.Withinthis and dividingbytheareaofbox.Thesearchisthennarrowed of equalarea(~100WFCpixelsonaside).Foreachbox,thesur- small fieldofviewWFPC2,severalclustershaveverylowsurface scure importantdynamicalinformationsuchasthepresenceofa stars fromthegiantbranch(orupper mainsequenceinthecaseof surface brightnessprofileofthecluster(i.e.asamplethathasits surface brightnessfallsrightontheedgeofaCCD,whereitisnot Instead, weemployedaMonteCarlostylemethodtolocateour The nexttaskwastolocateaccuratelythecentreofanygiven While inelegantandcomputationally expensive,ourrandomsam- This routinehasthedisadvantagethatitisverygoodatfinding © 2003RAS,MNRAS 338,85-119 2 0 0 3MNRAS.338. . .85M because theshapeofWFPC2meansthatforallclusters,mostan- 4.2.1 Areacorrections regions isingeneralnotspherical(cf.E91)-hencewefitcircular both colourframesforafield.ForN=2000thecentringisrepeat- For agivenclusterwedeterminecorrected pixelcoordinatesforthe is complicatedbytheWFPC2chipgeometry(includingsmall in thefractionsofannulicoveredcauseartificialfluctuationsa through anannulusisdirectlyrelatedtothearea,variations nuli arenotcompletelycoveredbythefieldofview.Sinceflux ize thefluxinannulustothatforafullannulus.Thisisnecessary The areacorrectionA¡fortheithannulusisusedsimplytonormal- individually below. line themeaningofthesefactorsandtheirmethodscalculation the surfacebrightness/x/ofithannulusisgivenby there islittleevidencetosuggestthatthemassdistributionininner LMC clustershaveslightlyellipticalisophotesatextendedradii, therefore extendedtothemaximumradiipossible.Althoughmany the outer(lessdense)regionsofacluster.Thesetwoprofileswere to ~30arcsec.Thetwootherannulussetshadlargerwidthsof3 For eachframe(twopercluster),foursetsofcircularannuliwere 4.2 Annulusconstructionandfluxcorrections meaning thatwehavenotintroducedanylargeerrors.Wenote,how- lated centres(Table4)withthoseinTable2showsgoodagreement, image headerinformationisinaccurate.Acomparisonofourcalcu- from pixelcoordinatesto(a,8)mayintroducelargeerrorsifthe © 2003RAS,MNRAS 338,85-119 again ledustoresortaninelegant butrobustMonteCarloscheme. arbitrary natureofthesecondtwofactors fromclustertoonce camera andtherollangleofHST atthetimeofobservation.The and mustbedeterminedbeforetheannulusisconstructed.Weout- an annulusandthecompletenesscorrectionforastar,respectively, flux ofthejthstar.ThefactorsA¡andCjareareacorrectionfor where biand<2/aretheouterinnerradiiofannulus,re- Ui — of ellipticalannuliimpractical. of theimagesindatasetfullycoveranycluster,makinguse annuli. Inaddition,becauseofthesmallWFPC2fieldview,none and 4arcsec,respectively,wereusedprimarilyforsampling annuli werecalculatedtoaradiusof~20andthe2-arcsec widths of1.5and2arcsec,respectively,weredesignedfor constructed abouttheclustercentre.Twosetshadnarrowannulus are atleastasaccuratetheliteraturevalues. errors. Notwithstandingthis,weexpectthatourcalculatedcentres ever, thatthiscomparisonisnotsensitivetosmall(severalarcsec) approximately ±1arcsec.Asnotedabove,however,theconversion able toalimitingaccuracyofapproximately±10WFCpixels- consistency check,werunthecentringalgorithmindependentlyon concentration andrichnesssimplybyvariationofrN.Asa separations betweentheCCDs), centringoftheclusteron surface brightnessprofile,andmustthereforebeaccountedfor. spectively, AisthenumberofstarsinannulusandF¡ stars tocalculatethesurfacebrightnessforanannulus.Foreachset, sampling thecentralregionsofacluster.Tothisend,1.5-arcsec 16 CCDcornerpixelsthatdefine theWFPC2fieldofview,and s The processofdeterminingtheareacorrectionforanannulus Because ofthehighresolutionourimageswesimplycounted t(bf -af) © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem C E ;=i jFj, 0) 4.2.2 Completenesscorrections practice theprocesswashaltedatr=78arcsec. - noteparticularlythesmallseparationsofchipscausedby profile tobe~75-80arcsec. Figure 1.ObservationgeometryandareacorrectionpointsforclusterNGC multiphot. Foreachcluster,weset thisroutinetogenerate~3.5x nificant numbersofstarstobemissed byautomateddetectionsoft- Even withHSTresolution,crowding andsaturationcancausesig- At 100arcsectheareacorrectionfactorisapproximately4,andin falling inthefieldofviewhavebeenplotted.Theaccuracywith NGC 1841.Annuliofwidth4arcsechavebeendrawnaboutthe to besufficient.Toavoidintroducinglargeuncertaintiesintothe not. TheareacorrectionA¡fortheithannulusistotalnumber large numberofpointsarethenrandomlygeneratedoverthefull from thesewederivetheborderequationsoffourCCDs.A to aradiusof100arcsecandtherandompointsfallinginfieldview quantify thecorrectionweused artificialstarroutineattachedto these cancausetoanannulusoftherightradius,whichfallstangent. vignetted regionsmaskedbyHSTphot,andthesignificanterrors centre to100arcsec,andforeverysecondannulustherandompoints data wedonotuseannuliforwhichthefractioncoveredfallsbelow with anaccuracylimitedonlybythenumberofrandompoints.A computationally inefficient,thismethodisveryrobustandcaneasily determine whichpointsfallontheWFPC2camera,anddo are plottedforeverysecondannulus. and ismarkedwithasmallcross.Annuliofwidth4arcsechavebeendrawn ware suchasHSTphot.Thismissing fluxcanseriouslyaffectthe which theprocesshandlescomplicatedgeometryisquiteevident a third.Thislimitsthemaximumradiusforsurfacebrightness account forthearbitrarygeometryofanyparticularobservation, of pointsgenerateddividedbythenumber‘imaged’.Again,while area ofeachannulus,andusingtheCCDboundaryequationswe surface brightnessprofileofacluster andmustbeaccountedfor.To small amountofexperimentationshowed10000pointsperannulus 1841. ThecentreoftheclusterfallsonWFC3atpixelcoordinates(417,401) An exampleoftheprocessisshowninFig.1-apointingfor _i iI^ 71.5 71.471.371.271.1 Structure ofrichLMCclusters91 RA (a)(J2000.0) 2 0 0 3MNRAS.338. . .85M 56 /th starinanannulusistheinverseofcforappropriatebin.To y inuncrowdedregions(independentofchip),0.2magbright- regions ofthecluster.Ifincompleteness(orrapidspatialvariation pleteness functionsforthethreeWFCchips,whichimagedouter be functionsofbrightnessonly.ForNGC2213,crowdingandsat- pleteness functionshavebeenintegratedoverpositionandcolourto reflecting thefactthatincompletenesswasnotanissueforlarge recovered (unflagged)starsdividedbythetotalnumberof problems. resolution ofthepositionalbinningwasincreasedtoaccountfor ple. Forseverelycrowdedregions,however,thecompletenessmay implying thattheintegratedcompleteness inthecrowdedregion the PCimage,approximatelyhalf of thechipmaybenon-crowded, the non-crowdedregionsofPC tohavec~0.85atV24, less. Todemonstratethis,fromthe threeWFCfunctions,weexpect the completenessissolowthat measurements becomemeaning- in theverycentralregions,situationisevenworsethanthis- not adequatetofullydescribethecompletenessvariations.Infact, Fig. 2,NGC2005,isanexampleofthis.Theeffecttheextremely in comparisonwiththethreeWFCfunctions.Thesecondcluster the position-averagedPCfunctionwouldbesignificantlydegraded this. ThecoreoftheclusterisimagedonPCchip(solidline), uration arenotsignificant,andthecompletenessfunctionsreflect NGC 2005)areshowninFig.2togetherwiththePCF555Wimages majority ofclusters. limit (i.e.0.05^q0.5)hadanegligibleeffectonmostprofiles, less thanc\=0.25.Experimentationshowedthatvariationofthis this. Intheveryworstcases,inclusionofshortexposures(see the exampleforNGC2213,whichisatypicalclusterinsam- the positionalsense,isperfectlyadequatetoaccountforgradual means thatthebinningresolutiondescribedabove,particularlyin ness and0.25magincolour.Alargemajorityofoursamplesuffers magnitude andcolour.Binsizesaretypically160pixelsinx the imageandsolved(oneatatime)bymultiphot,usingsame limit andtwomagnitudesbelowthefaintforanimage, limits ofwhicharesettobetwomagnitudesabovethesaturation whereas wemeasureaspatiallyaveraged valueofc~0.45.From clear, anditisevidentthatapositionalresolutionof160pixels compact coreofthisclusteronthePCcompletenessfunctionis of completeness)wasasignificantissueinthecentralregions,then and thecompletenessfunctionforthischipmatcheswellcom- of thecentrestheseclusters.Foreasevisualizationcom- atively openclusterNGC2213andtheextremelycompact avoid largeuncertainties,weeliminatedanystarswithcompleteness generated inthatbin,andthecompletenesscorrectionCjfor Section 4.2.3below)usuallysignificantlyalleviatedanycrowding little ornocrowding,eveninthecentralregionsofacluster.This our classification,sharpnessandxselectioncriteria,againflagging output forrealstars,andwerunthisartificialphotometrythrough ered. Theoutputphotometryfileisexactlysimilartothemultiphot distributed accordingtothefluxofimage.Eachstarisplacedon and 0.5magbluerthanthebluestregion.Thestarsarespatially 0.5 magredderthanthereddestregionofCMDcluster 92 A.D.MackeyandG.EGilmore suffer rapidandsignificantspatialvariation,inthesecasesthe spatial variationsincompleteness.Thisisdemonstratedbelow, stars arebinnedaccordingtotheirx-andy-positiononthechip, stars thatareremovedfromthesample. settings asfortherealdata.Starsareflaggediftheynotrecov- 10 starsperCCD(i.e.~1.4xcluster)onaCMD,the 5 Examples ofthecompletenessfunctionsfortwoclusters(therel- The completenesscforagivenbinisthenumberofsuccessfully To determinethecompletenessfunctionforagivenchip,fake © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4.2.3 Shortexposures background fieldnearacluster.ThedegradationevidentintheWFC pleteness functionscanalsotellusasmallamountconcerningthe brightness-colour spacecan(anddo)havefullcompleteness.Com- being recovered.Certainly,however,individualbinsinposition- became useless. photometry becomessignificantand thesurfacebrightnessprofile brightness profilesshowasimilarshapeuptologre~0.8orr reduces thenoiseinshort-exposureprofile.Itisthensimpleto brighter bysometenthsofamagnitude.Thisoffsetisproduct brightness profileconstructed.Whenplottedovertheoriginalsur- process. Foragivencluster,theshort-exposureimageisreduced for theveryold,compactclustersNGC1754,1835,1916,2005 As discussedinSection4.2.2,ninecaseswhereseverecrowding NGC 2213isquitesparse. this, wehadtouseadditionalinformationfromashortexposure must bec<0.05atV~24(cf.Fig.3b).Inacasesuchas the crowding,measurementsaretaken fromtheshortphotometry Further evidenceofthiscanbeseeninFig.3(a).Thetwosurface for thisclustersufferedseriousincompletenessinthecentralregion. incompleteness atsmallradii. using photometryforstarswithr^fromtheshortexposure measure theradiusratwhichincompletenessbecomesanissue the calculations,asdiscussedbelowinSection4.2.4,andsoalso This isequivalenttoremovingthebrighteststarsinclusterfrom fore includingmorebrightstarsinitsprofilethanthelongerimage, face brightnessprofile,theshort-exposureprofileisfoundtohave in exactlythesamemannerasoriginalimage,andasurface R136. NGC1786requiredcorrectionbutnoadditionaldatawere complete thesurfacebrightnessprofiles.Thisoccurredspecifically very neartheEMCbar).Bycomparison,fieldpopulation dense fieldpopulationintheregionofthiscluster(NGC2005lies completeness functionsforNGC2005isprimarilycausedbythe ever reachesc=1-thisiscausedbytheintegrationovercolour eventually turnsoverbecauseof the amountofmissingflux.Not vious Section4.2.2weshowedthatthelong-exposurephotometry exposure. Thiskeepsscattertoaminimumwhilealleviatingthe limit Viimontheshort-exposurephotometrytocutoutbrightest exclusion oflargenumbersfaintstars,whicharenotmeasured whereas thelargerscatteriscausedbybothinclusionofmany crowding norsaturationareanissue),butwithalargerscatterand and 2019,theveryyoungclustersNGC1984,2011,2156 of animage,weusedinformationfromshort-exposureimagesto and/or saturationsignificantlydegradedthecompletenessinparts and position,sincebadpixelsbrightstarspreventallfake on ascaleshorterthan~6arcsec, or~130pixels.Toaccountfor only isthecompletenessverylow inthisregion,butitmustvary and thetwoprofilesbegintodeviate,formacompositeprofile on theshortimage.Toeliminateoffset,weimposeabrightness of thebrighteststarsincluster(seealsoSection4.2.4)and of theshorterimagehavingabrightersaturationlimitandthere- a shapematchingthatoftheoriginalatlargeradii(whereneither available. (see Section4.2.3,below),otherwisethesurfacebrightnessprofile ~ 6.3arcsec.Atthispointincompleteness inthelong-exposure (with Vnimposed)andtheremainderr>)fromlong stars, andvaryViuntiltheprofilesoverlapintheirouterregions. dVev 555 dev dev mdcv im We notethatnoneofthecompletenessfunctionsplottedinFig.2 Fig. 3showsanexampleofthisprocessforNGC2005.Inthepre- To addtheshort-exposuredataisarelativelystraightforward © 2003RAS,MNRAS 338,85-119 2 0 0 3MNRAS.338. . .85M profiles. Formostclusters,saturated starsarenotasignificantfactor. 4.2.4 Saturatedstars profile inthisregion. pleteness functionshavebeenintegratedoverpositionandcolour in ourimages.Suchstarswerenot measuredbymultiphotand using onlytheshort-exposurephotometryforsurfacebrightness the short-exposurephotometrywithincentralregionaccounts the long-exposurephotometryisveryevident.Italsoclearthat to beafunctionofbrightnessonly.Theterribleincompletenessin Fig. 3(b),whichshowsthecompletenessfunctionsforlong- NGC 2005isextremelycompact,onascalelessthan~160pixels,while2213wellresolvedeveninitsverycentre. magnitude only.ShownabovethecompletenessfunctionsarePCF555Wimagesofcoreeachcluster,withexposuretimes120s(NGC2213) line, forWFC3bytheshort-dashedlineandWFC4dottedline.Thefunctionshavebeenintegratedoverpositioncolourtobeafunctionof V555 Figure 2.CompletenessfunctionsforNGC2213(left)and2005(right).ThefunctionthePCisdenotedbysolidline,WFC2long-dashed © 2003RAS,MNRAS 338,85-119 Of the53clustersinsample,30 hadlessthanfivesaturatedstars were thereforenotincludedintheconstruction ofsurfacebrightness At thisstagewecommentbrieflyon thetreatmentofsaturatedstars very wellforthisincompleteness,andwearethereforejustifiedin and short-exposurephotometry,forr<.Asbefore,thecom- within 6.3arcsec.Theadvantagegainedfromthisisevidentin and 500s(NGC2005).Theimagesareslightlycroppedtobeapproximately730pixels(33.2arcsec)onaside.Itisclearfromthesethatthecore of deY © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem tion listedinTable3istiny(although largerthanfortheother39 images (otherwiseshort-exposuredatawouldhavebeenobtained- timate ofthetotalnumbersaturatedstarswithintwocoreradiifor thousand starsweremeasuredinthecentralregionsofeach. neglect didnotsignificantlyalterthesurfacebrightnessprofiles these clusters,thepresenceofsofewsaturatedstarsmeantthattheir either giantsoruppermain-sequence starsandareinverybrief(but clusters). The14clustersinTable3 areeitheryoung(r<100Myr) grade thequalityofimagesormeasurementsmadefromthese culations, forthefollowingreasons.First,theirpresencedidnotde- each cluster.Wefeltcomfortableleavingthesestarsoutofthecal- derived fortheseclusters,especiallygiventhatonaverageseveral within approximatelytwocoreradiiofthecentre.Whendatafrom or veryold(r>10Gyr).Insuch clusters,thebrighteststarsare see Section4.2.3).Secondly,itisclear thatforeachcluster,thefrac- saturation (seeSection4.2.3),thisnumberroseto39.Forallof short exposureswereincludedtocircumventextremecrowdingand The remaining14clustersarelistedinTable3,alongwithanes- Structure ofrichLMCclusters93 2 0 0 3MNRAS.338. . .85M profiles withoutcompromisingthe measurementofstructuralpa- by theoutputofanessentiallyrandomly distributedtinyfractionof photometry toremovetheoffsetbetweentwosurfacebrightnessprofiles. noise totheprofile. the starsinacluster-practice,this simplyaddslargeamountsof make sensetomeasureasurfacebrightness profilethatisdominated ters theyarein.Theythereforemaynot,ingeneral,representthe the originalexposure(solidcircles)andshort(opensquares).Thedottedlineshowsapproximateradiusatwhichprofilesstarttodeviate, NGC 2005.Ourlong-exposureimageofthecorethisclusterisshowninFig.2.(a)Surfacebrightnessprofilesforallfourannuluswidths,calculated from Figures. Anexampleoftheinclusioninformationfromashortexposuretoalleviatesignificantincompletenesscausedbycrowding,inthiscase for dynamical time-scales(e.g.themedianrelaxationtime)ofclus- very luminous)phasesofevolution,especiallycomparedwiththe over colourandpositionwithinrdevtobeafunctionofV555only.TheverticaldottedlinemarksthebrightnesslimitVnimposedonshort-exposure (b) Completenessfunctionsfortheshortexposure(solidline)andoriginal(dashedwithinrdevThecompletenesshavebeenintegrated 94 A.D.MackeyandG.EGilmore spatial distributionoftheunderlyingstellarpopulation.Itdoesnot m Removing thesestarsfromthecalculations provideslessnoisy c b NGC 1805 NGC 1786 NGC 1711 NGC 1466 within twocoreradii. extremely largecoreradius. no shortexposurewasavailable.^NGC1841hasan within twocoreradii.Thisfigureisanestimate NGC 2257 NGC 2210 NGC 2172 NGC 2164 NGC 2159 NGC 2031 NGC 1898 NGC 1866 NGC 1841 NGC 1818 Cluster Table 3.Clusterswithmorethanfivesaturatedstars core radii.Ndividedbythetotalnumberofstars since NGC1786suffersfromextremecrowdingand s Approximate numberofsaturatedstarswithintwo © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 10.20 10.20 10.15 10.09 10.18 10.10 log r 7.60 7.70 7.60 7.40 7.70 7.00 8.20 8.12 (yr) J c -50 -20 45 25 30 30 30 35 35 30 35 30 10 15 -0.008 0.001 0.005 0.033 0.016 0.022 0.012 0.006 0.009 0.003 0.016 0.034 0.018 0.002 brightness valuesfortheseeightsectors(Djorgovski1987).This 4.2.5 Errorestimation reflects theunderlyingstellardistribution.Specifically,Elsonetal. rameters. Elsonandcollaboratorsforexample(Elsonetal.1989; is essentialinthecaseofEMCclusters, manyofwhicharepatchy ness ofanannulus,butalsoitserror byanappropriateamount.This technique ensuresthattheinternalerrorofanannulusreflects ternal errorfortheannulusisstandarddeviationofsurface in eachusingequation(1)withthefactorssettounity.Thein- To estimatetheinternalerroraforanannuluswedivideditinto the underlyingstellardistributionofeachcluster. that leavingthebrightest(saturated)starsoutofconstructionpro- it isevidentfromthefinalresultspresentedinFig.6(seeSection5.1) necessary toremovequitesomanystars,inthecaseslistedTable3, mentation onourpartshowedsimilarresults.Whilewedonotfindit their ‘cleaned’profiles)reducedthescatterinparametermea- ing theirsurfacebrightnessprofiles,inordertomakesuretheprofile E91 ;Elson1992)routinelyremovethebrighteststarswhencalculat- the errorbarssocalculatedwere considerablysmallerthanthe clumps ofstarsorsinglebrightwillincreasethesurfacebright- error causedbythediscretenessoflightdistribution-thatis, eight sectorsofequalarea,andcalculatedthesurfacebrightness cess hasresultedinclean,low-noiseprofiles,whichshouldreflect derived structuralparametersbyasignificantamount.Someexperi- eters bymorethan5percent.Elson(1992)removedthebrightest of thatannulus-importantgiven our fourdifferentannulussets. and irregular.Similarly,theerror for anannulusreflectsthewidth again, thisprovidedmuchsmootherprofileswithoutalteringthe surements by~40percentonaveragewithoutalteringtheparam- (1989) foundthattheremovalofthesestars(inconstruction 120 starsperclusterintheconstructionofhercleanedprofiles- l In theouterregionsofmostclusters, however,wefoundthat © 2003RAS,MNRAS 338,85-119 2 0 0 3MNRAS.338. . .85M 4.3.1 KingversusEFFprofiles point-to-point scatterwell. persists. Itisbecauseofthelowdensitytheseclusters-stars - somecoverupto9magwhileothersonly2or3mag.Thiscan but itcanbecomesignificantintheouterregions.Thebackground random scatterinthepoints.AsanexampleseeFig.5(seeSec- is thereforeusefultodefinetheconcentration parameterc=log(r Provided r,thecoreradiusmaybetakenasat Traditionally, thesurfacebrightnessprofilesofoldglobularclusters 4.3 Profilefittingandbackgroundsubtraction their surfacebrightnessesandcorrespondinglyresultinerrorsthat to besmall.Oneshouldalsoexaminethebrightnessrangeofaprofile least someofthesameinformation,soonewouldexpecttheirscatter this, itisimportantthatonlythepointsinasingleannulussetare is causedbytherelativelylownumbersofstarsinlargeouter Poisson errorstendtooverestimatethescatterbetweenpoints-this in theouterregionstheyarePoissonerrors,withasmoothtran- in thecentralregionsofaclustererrorsaresectorerrors,while the sectorerror,wetookPoissonerrorinstead.Thiscondition from Poissonstatistics.Whenthisbecamesignificantlylargerthan To solvethisproblem,foreveryannuluswealsocalculatedtheerror tends tobemuchmoresmoothlydistributedthantheclusteritself, ters. Thisbackgroundisnegligibleintheinnerregionsofacluster, This effectiscoupledwithfieldstarcontaminationformanyclus- therefore donotreflectanylarge-scalevariationsforthatannulus. full area,theerrorsarecalculatedoveronlyathirdofareaand nuli, sothatwhilethefluxforsuchanannulusisscaledto nique describedinSection4.3.2butalsoillustratesthepresentissue tion 4.3.2),whichdemonstratesthebackgroundsubtractiontech- © 2003RAS,MNRAS 338,85-119 tors (EFF87;Elsonetal.1989;E91) haveshownthattheseclusters are measured(cf.EFF87),implying ratios10

MO ^ Fo( - ) +0 \a J

/xo(f) (22/r — \yyl1 + (¡> (5) with equation (4) substituted for a. We first fit an EFF model to the inner region of a cluster profile using the two narrow annulus sets, to estimate /x0 and rc. In this re- gion (r < 30 arcsec) the background contribution is negligible, in all cases being at least 5 mag below the central surface brightness. The background therefore does not affect a measurement of the central surface brightness /x0 nor the core radius rc, which is essentially the shape of the profile in the inner region. Hence it is a good approxima- tion to determine these without subtracting any background. Next we use these estimated values and fit a two-parameter model (y, 0) r (arcsec) of the form of equation (5) to the outer region of the profile, using the two wider annulus sets and ensuring r a. This allowed us to de- Figure 5. Background fit for NGC 2005. Models of the form of equation (5) termine 0 and subtract it from every annulus. After the background were fitted to the profiles with annulus widths of 3 arcsec (filled triangles) and subtraction, we calculate the Poisson errors for each point and sub- 4 arcsec (filled circles) beyond r = 20 arcsec. The two estimated parameters stitute as appropriate (see Section 4.2.5). Finally, we fit another EFF were a ~ 4 arcsec and po ~ 16.9. The solid line shows the average of the two best-fitting models, used to determine the background level Tbg = —2.5 log model to the new subtracted profiles, using all four annulus sets, and 0 = 21.83, marked with an arrow. Errors shown are those determined from thereby determine the best-fitting parameters. This method allows the light distribution (Section 4.2.5) rather than the Poisson errors, which are us to treat severely contaminated clusters (e.g. NGC 1898 and 1916) necessarily calculated after the background subtraction but before the final equally with clusters that have no evident background contribution fit (see the text). Note the apparent underestimation of the scatter at large (e.g. Hodge 11 and NGC 1841). radii. © 2003 RAS, MNRAS 338, 85-119

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 2 0 0 3MNRAS.338. . .85M 2 published surfacebrightnessprofiles, concentratedmainlyinfour profiles. Thereismuchtobelearnedfromsuchdetaileddata,cover- regions -thisiscausedbytheeffectsofcrowding,evenincluding potentially introducedbythebackgroundfittingarenotincludedin Metaxa etal.1988;Chrysovergis al.1989).Itisusefultocompare large studies-thoseofEFF87,Mateo (1987),E91(seealsoElson At leastthree-quartersoftheclustersstudiedinthispaperhave 5.1.1 Comparisonwithpreviouswork however, splitthesampleintosubgroupsandobtainsomeimmediate ing manyaspectsofglobularclusterandEMCastronomy.Wecan, in thesampledonothavepreviouslypublishedsurfacebrightness use HSTdata.Inaddition,approximatelyaquarteroftheclusters face brightnessprofiles,andasfarweareaware,theonlyoneto R136, whichalsorequiredshort-exposurephotometry,shouldbe for theseclusters,andtheclustersNGC1835,2005,2019 the profiles(NGC1754,1786,1916)areincompleteintheirinner EFF profileisalsoplotted,thecoreradiusindicatedandbest- the fourannulussetsonsameaxes,todemonstratehigh The background-subtractedF555Wsurfacebrightnessprofilesfor the estimation. We determinederrorsinthethreeparametersobtainedfromfinal iteration weaveragetheindividualfits,weightedbytheirxvalues. to maintainindependencebetweendatapointswefiteachannulus logically wellbehaved,thismethodwasaccurateandefficient,with is thenexpandedaboutthisparametercombinationandtheiteration the otherparametersareasdefinedinequation(3).Arefinedmesh this value,Nisthetotalnumberofannuliinsetquestion,and © 2003RAS,MNRAS 338,85-119 validity ofourreductionprocedure. our resultswiththosefromthese papers andtherebyestablishthe et al.1989),andKontizascollaborators (Kontizasetal.1987a,b; our resultswiththosefromtheseveralotherpublishedlarge-scale and interestingresults,whichwediscussbelow.Wefirstcompare considered upperlimits. was unavailableforNGC1786,however).Thederivedcoreradii cluster andthemaximumradialextentrofeachprofile.Three along withtheircorrespondingerrors,thecalculatedcentreofeach fitting parameterslisted.TheseresultsaresummarizedinTable4 degree ofconsistencybetweenthem.Foreachcluster,thebest-fitting each ofthe53clustersarepresentedinFig.6.Weplot 5.1 Profilesandstructuralparameters 5 RESULTS errors inthebest-fittingparameters.Systematicsuchasthose dence ofthepoints.Theerrorsthusdeterminedrepresentrandom was doneseparatelyforeachannulussettomaintaintheindepen- fits tothebackground-subtractedprofilesusingabootstrapmethod of usingfourannuluswidthseffectivelycountseachstartimes, convergence typicallywithin10iterations.Becauseourtechnique continued untilconvergence.Giventhatourparameterspaceistopo- where /z,isthesurfacebrightnessofithannulus,crerrorin studies. supplementary photometryfromshortexposures(aexposure (Press etal.1992,p.691)with1000recursionsperfit.Again,this set individuallyasappropriate.Toobtainthebest-fittingcurveforan X a m l 2 This isoneofthelargestpublishedstudiesEMCclustersur- E iV a © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Hi -¡¿(ri,/ip,a,y) (6) 8 7 8 9 parameter measurements. barely largeenoughformeaningfulstatistics.Extendingtheaver- radii fromMateoallcorrespondto upper-limitmeasurementsinour but alsomovemostoftheotherpointstoleftandawayfrom between thetwostudies(124Mq.Thismaygosomewaytowardsexplainingthe with m>15Mq,butincreasingtor=0.97arcsecusingstars et al.(1996)findconsiderableevidenceformasssegregationin because ourselectedannuluswidthsmeanthatwearenotequipped derived fromHSTobservations.Ourmeasuredcoreradiusofr= 0.25 arcsecbasedonapurepower-lawsurfacebrightnessfit,again also usingHSTobservations.Campbelletal.(1992)measurer= finds r=1.3arcsecfromground-baseddata,whileElsonetal. at largeradii. an EFFprofileintheouterregion.Best-fittingparametersforeachoftwo outer region,whilethedashedlinerepresentsanEFFprofileincoreand sets, asinFig.6.Weshowtwodifferenttwo-componentprofiles.Thesolid of R136/NGC2070.Thefourdifferentpointstylesrepresenttheannulus (1992) findr=0.5arcsecfromHSTobservations.Malumuth& 1992; Malumuth&Heap1994)-mostlytheargumentsaredepen- 1.3 arcsecisconsistentwiththatofMeylan,butconsiderablylarger 112 A.D.MackeyandG.FGilmore c c c c c c c c c Similarly, thereissomeargumentintheliteratureastowhether © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4 4 probably mass-segregatedbutnotpost-corecollapse(accordingto relaxation timeatthemedian(half-mass)radius(theirequation5) power-law profilesareshownasistheslopeiß)andbreakradius by Brandietal.(3x10Mqand 1.1pc,respectively).Following relaxation time(intheformofMalumuth&Heap1994,butsee power-law structureinthecentralregionofprofileisaresult by apowerlaw(althoughinthecaseofBrandietal.,thisisonlyfor profile canhelpshedsomelightontheissue.IfR136isaPCCcluster Binney &Tremaine1987,p.527,corecollapseoccursat12-19 time -comparabletotheageofcluster.Theyalsocalculate four timeslarger,andacorrespondinglylargercentralrelaxation the magnitudescale,slopesofpower-lawmodelasplottedis2.5ß. Figure 12.Power-lawfittotheinnercoreofR136.Thefourdifferentpoint for thehalf-massradius,obtaining r~1.25pc.Boththisradius masses ofalltheclustersstudiedin thispaper.ForR136weobtain mass) radius.Equation(7)isessentiallyequivalenttoequation(4.5) Tremaine 1987;Meylan1987): that theEFFprofilefitsequallywell,unlikeforbestoldPCC measured fortheoldPCCcandidates.FromFig.12itisalsoclear is plottedinFig.12,alongwiththebest-fittingpower-lawmodel then itsprofileshouldshowacuspsimilartothoseobservedforthe than anupperlimitforthecoreradiusofR136,oursurfacebrightness time istoolongforcorecollapsetohavetakenplace. the mostmassivestarsinsystem,butthatmedianrelaxation median relaxationtimes).Similarly,Brandietal.(1996)showthat from Brandietal.InSection5.2 we deriveestimatesforthetotal where Nisthetotalnumberofstarsandmtypicalstellarmass, with theargumentofBrandietal.Wecancalculatemedian candidates. ItislikelythenthatinthecaseofR136apparent 2.6 arcsec.Thisisonlymarginallyconsistentwiththevaluesofß dynamical masssegregationislikelytohaveoccurred,atleastfor and obtainasimilarestimate,thereforeconcludingthatR136is (arrow), justasforthePCCcandidateclustersinFig.10.Again,becauseof styles representthefourannulussets,asinFig.6.Thebest-fittingEFFand and thetotalmassareentirelyconsistent withthevaluesobtained M ~2.5x10Mq,andusingthis andequation(11)wecansolve Mtot isthetotalmassofclusterandrmedian(orhalf- also, forexample,Spitzer&Hart1971;1987;Binney of thebrighteststarsinclusterresidingthisspace,consistent and EFFmodel.Wemeasureaslopeß=1.17withthebreakatr~ and Brandietal.(1996)showthattheprofileofR136canbefitted old clustersdiscussedinSection5.1.3.BothCampbelletal.(1992) such apower-lawcuspandbreak.Thecentralregionoftheprofile stars withm>40Mq).Weobserveasmallamountofevidencefor h tot h Even thoughourresolutionisnotquitesufficienttoprovidemore 83/2 6.5 x10/r\ ln(0.4A0 ymJ h r l°gio( /arcsec) © 2003RAS,MNRAS 338,85-119 (V) 2 0 0 3MNRAS.338. . .85M 5 3 7 4-3 4 6 8 8 4 y-2 jected, whichisdonebymeansofanAbelintegralequation(EFF87; provided y>2,otherwisethelimit isdivergent. relevant observationalquantity.Thisgives By takingthelimitroo,wecan alsoobtainanestimateforthe the measuredsurfacebrightnessprofile,gives Evaluating theintegralforr=,maximumradialextentof luminosity densityandisgivenby for theluminositydensityj(r)ofclusterinquestion.Weobtain We canuseourmeasuredstructuralparameterstoobtainluminosity time-scale downtothesizerequiredmakeR136dynamicallyold the clustersstudiedinthispaper.Usingourderivedvalueofpo~ following sectionwealsoestimatethecentralmassdensitiesforall timate thecentralrelaxationtime(informofCampbelletal. time tooccur,butbothcalculatedvaluesofarguestronglyagainst Brandi etal.weadoptm~0.5MqandthereforeestimateAf5x © 2003RAS,MNRAS 338,85-119 asymptotic clusterluminosityL^: where iistheradialvariableandxline-of-sightvariable. within acylinderofradiusralongthelinesight,sincethisis closed luminosityLasafunctionofradius,weintegrateequation(9) where Fisastandardgammafunction.Toobtainthemeasureden- C(r) butwithindexy+1.Inequation(9),jorepresentsthecentral which hasthesamefunctionalformassurfacebrightnessprofile and massestimatesforeachcluster.Equation(3)mustfirstbedepro- 5.2 Luminosityandmassestimates enough tobeintheepochofcorecollapse(Co~1x10yr). Co ocr,thetruecoreradiuswouldhavetobeatleastfivetimes considerably longerthantheestimatedageofcluster.Giventhat of r~0.32pc,weobtainí1x10yrform0.5Mq,again 3 x10MqpcforR136,andourupperlimitthecoreradius where risthecoreradiusandpcentralmassdensity.In Co ^3x10 core collapsehavinghappened.Inconfirmationofthis,wecanes- gests thatforthesestars,dynamicalmasssegregationhasindeedhad 2.1 x10yr,whichiscomparabletotheageofcluster.Thissug- 2.1 x10yr,verysimilartotheestimateofBrandietal.(t~2.5 Loo Jo j(r) =jo1+— see alsoBinney&Tremaine1987,Section4.2andAppendix1.B.4) smaller thanourupperlimitinordertobringthecentralrelaxation Em L(r) =Anj, 1987; Meylan1987): 1992, butalsosee,forexample,Spitzer1987;Binney&Tremaine 10 yr).Forthemostmassivestars(i.e.m~40Mq)weobtaint 10. Substitutingthesevaluesintoequation(7)providesuswitht~ m m c cr0 cQ rh rh rh CoFKy +l)/2] — 2 27t/Xo F9v/2.2\)/2l ItCIJLqO aV^r(y/2) ’ y ■ 4-3 y a^ 5 X10Mqpc © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2aY nr [a -(a+''m) 10 Mq Po l\\ +- -C+l)/2 0.06 pc !2 1/2 +f ln(0.4A0 1.4 -(K+P/2 yr, ài dx. (13) (12) (ID (10) (8) (9) -12 pc. Thistakescareofaandr,buttoconvert/xLqis presumably afairlygoodapproximationtotheformationofrich range ofmetallicitiesandanyongoingstarformation.Weproceed plying theappropriateluminosityequationsbyaveragemass-to- has significantlyhigherreddening,withE(B—V)=0.38(Hunter Holtzman etal.,andTij,sZfromtable7of more complicated.WefirstneedtoknowtheVmagnitudeof modulus tobeDM=18.5,whichimpliesascaleof4.116arcsec units. Asalways,toconvertparsecswetaketheLMCdistance When calculatingLwetakerfromTable4.Inordertouse relatively insensitivetothechosen abundance. Forcompleteness,we Fig. 13,itisclearthatformostoftheevolution,M/Lratio tios obtainedfromthesemodelsarepurelytheoretical,theydoagree Tout &Gilmore(1993)overthemassrange0.1-120Mq.There using thesimplestpossiblemodel-apopulationofstarsformed for factorssuchastheinitialmassfunction(IMF)ofsystem,a thesis codeofFioc&Rocca-Volmerange(1997)(pegasev2.0, light ratioM/Lfortheclusterinquestion.Thedensityp(r)then to convert/zphysicalunits. et al.1995).Armedwiththesenumbers,weusetherelation central surfacebrightnessforeachclustermustbecorrected et ah,weobtain=+4.85.Alternatively,usingequations(11) where thenotationisasinHoltzmanetal.(1995b).Usingouras- equations (10),(12)and(13),wemusthave/¿o,arinphysical erature -itissufficienttobeable todifferentiatebetween‘metal calculated asaveragesratherthan being takendirectlyfromthelit- dance, weareconfidentinusingeven thoseabundancesthatwere 2. Becauseoftheinsensitivity calculationtotheselectedabun- well withobservations(see,e.g.Parmentier&Gilmore2001).From given byequation(13)timesthisratio. equation (12)multipliedbyM/Landtheasymptoticmassis from equation(10).Similarly,themassMinsiderisgivenby corresponds toequation(9),withthecentraldensitypoobtained average inthedirectionofEMC(cf.EFF87).R136,however, absorption, andweuseE(B—V)=0.10,whichisareasonable and (12)fromDolphin(2000b)providesanidenticalresult.The WFPC2 =SMAG-TxSCOL a standardcolourB—V=+0.65andcombineequation(7) Sun. WeassumeanabsolutestandardmagnitudeofV=+4.82and adopt themetallicityforeachcluster basedontheestimatesinTable as afunctionofclusterageinFig.13.Althoughthemass-to-lightra- of theclustersample:Z=0.0001([Fe/H]^-2.25);0.0004 are fouravailableinitialabundancesthatcoverthemetallicityrange and stellarspectratomakethedetailedcalculations,accounting log ßo=0.4[l+-ß(0)+DM sumed standardsolarmagnitudeandcolour,Zfromtable6of (8) fromHoltzmanetal.(1995b): ([Fe/H] ^—0.33).TheM/Lyvaluesforeachmetallicityareplotted ([Fe/H] ^-1.65);Z=0.004-0.64);and0.008 stellar cluster.Fortheinitialburst,weassumeIMFofKroupa, simultaneously inoneinitialburstandwiththesamemetallicity- stellar populationasafunctionoftime,usinglibrariesisochrones 1999). Thiscodedeterminestheintegratedpropertiesofasynthetic m0 S2FFS 5 m v v 0 m v m hFS 555 FG The calculatedvaluesforandLarelistedinTable6. To estimateM/Lforeachcluster,weusetheevolutionarysyn- We calculatemassanddensityestimatesforeachclusterbymulti- m v 2- + 3.1£(ß-V)]log(4.116)Lqpc(15) 2 - T^xSCOL+Z,(14) fsFGFS Structure ofrichLMCclusters113 2 0 0 3MNRAS.338. . .85M NGC 2257 NGC 2249 NGC 2231 NGC 2214 NGC 2213 NGC 2210 NGC 2209 NGC 2193 NGC 2173 NGC 2172 NGC 2164 NGC 2162 NGC 2159 NGC 2157 NGC 2156 NGC 2155 NGC 2153 NGC 2136 NGC 2121 NGC 2100 NGC 2031 NGC 2019 NGC 2011 NGC 2005 NGC 2004 NGC 1984 NGC 1916 NGC 1898 NGC 1868 NGC 1866 NGC 1860 NGC 1856 NGC 1850 NGC 1847 NGC 1841 NGC 1835 NGC 1831 NGC 1818 NGC 1805 NGC 1786 NGC Mil NGC 1754 NGC 1718 NGC 1711 NGC 1651 NGC 1466 SL855 SL842 SL663 Cluster Table 6.Luminosityandmassestimatescalculatedusingthestructuralparametersfrombest-fittingEFFprofiles. 114 A.D.MackeyandG.FGilmore © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 4.19 ±0.06 4.00 ±0.04 4.32 ±0.04 4.02 ±0.03 4.01 ±0.03 4.14 ±0.03 2.32 ±0.01 2.50 ±0.05 2.78 ±0.03 2.75 ±0.02 2.61 ±0.03 2.72 ±0.03 2.83 ±0.02 2.52 ±0.02 2.33 ±0.01 2.80 ±0.04 2.06 ±0.01 2.69 ±0.01 2.54 ±0.02 2.26 ±0.04 3.49 ±0.02 3.71 ±0.04 3.70 ±0.10 3.02 ±0.03 3.38 ±0.02 3.06 ±0.02 3.07 ±0.02 3.35 ±0.03 3.03 ±0.02 3.42 ±0.02 3.40 ±0.02 3.58 ±0.02 3.10 ±0.03 3.02 ±0.04 3.74 ±0.04 3.12 ±0.02 3.12 ±0.06 3.88 ±0.05 3.92 ±0.03 3.24 ±0.04 3.07 ±0.02 3.50 ±0.02 3.28 ±0.01 3.28 ±0.02 3.06 ±0.02 3.35 ±0.02 1.52 ±0.01 1.73 ±0.02 1.86 ±0.02 (Lq pc“) log /x" Adopted -0.33 -0.33 -0.33 -0.33 -0.33 -0.33 -0.64 -0.33 -0.64 -0.64 -0.33 -0.64 -1.65 -0.33 -1.65 -0.64 -0.64 -2.25 -1.65 -0.64 -0.64 -0.64 -0.64 -0.33 -0.33 -2.25 -1.65 -0.33 -0.33 -0.33 -1.65 -0.33 -1.65 -0.33 -0.64 -0.33 -2.25 -0.33 -0.33 -0.64 -1.65 -0.33 -0.64 -0.33 -0.33 -2.25 -0.33 -0.64 -0.33 [Fe/H] Adopted M/L 0.11 0.13 0.69 0.11 0.11 0.11 0.69 0.16 0.07 0.20 0.05 0.08 0.05 0.40 0.18 0.22 0.18 0.10 0.09 2.75 0.32 0.08 0.05 0.67 0.12 2.80 0.70 0.48 0.69 0.11 0.87 0.61 3.80 3.56 3.37 3.13 3.56 3.29 3.36 3.43 3.37 1.33 1.33 1.14 1.14 1.14 1.33 1.00 1.19 v Zi4 07 zJ Z/4 +014 +009 08 z7 07 U 01 Z 7 01 Z +019 07 i/ 7 4.10 ±0.07 2.81 ±0.04 2.02 ±0.10 -0.06 2 14+- 2.90 ±0.06 -^0.06 2 <0+0.07 -0.13 2 74- 2.40 ±0.08 2.75 ±0.12 2.94 ±0.10 2 46- 2.97 ±0.04 2.44 ±0.03 2.16 ±0.08 2.66 ±0.06 0.85 ±0.08 2.10 ±0.06 2.65 ±0.06 2 40+- - -0.06 2 74+0- -^0.09 0 49+- 0.60 ±0.07 2.44 ±0.06 2.71 ±0.09 2.46 ±0.06 2.81 ±0.05 0.82 ±0.09 ’ —0.08 r\ r%rj-\-0.09 3.13 ±0.09 3.80^ 3.75 ±0.09 3.62 ±0.12 3 42+- -^°-0.08 3.50 ±0.06 3.30 ±0.08 3.77 ±0.07 3.06 ±0.06 3.28 ±0.10 3 45- 1.88 ±0.07 1.61 ±0.09 1.15 ±0.09 1.85 ±0.04 1 6R+- 1.55 ±0.12 1.19 ±0.06 i '7'7+0.20 -0.18 1.99 ±0.08 -0.18 —0.07 —0.06 ¿ z y ö 6 014 7 4 069 Z +052 601 4 045 045 Dz:) 456 022 jau 020 Z7 03 024 7ZO 4.93 ±0.104.89±0.09 +-yj_Q2'i 4 95+0.41 4.82 ±0.13 4.92+ 4.87+ 4.86 ±0.11 4.74; 4.O2; 4.88 ±0.15 4.66 ±0.13 4.62 ±0.15 4.95 ±0.10 ^•^-0.20 4 49+0.22 ^•-0.27 4 99+0.35 ^•^-0.15 4 48+0-1 4.61 ±0.15 4 59+- 4.77+ 4.131 ^•-0.32 4 77+0.38 -^0.26 5.38 ±0.085.260.06 7 26+' °-^-0.32 6 42' -±3 '6+¡S 5.27 ±0.135.24±0.12 —*-u.iu 5.30 ±0.13 5.05 ±0.20 5.04+ 5.14 ±0.16 5 19+- 5.11 5 46+' -0.6 5.01 ±0.09 '-('ä 5.27 ±0.13 5.24 ±0.17 j.ju_o_44 5 56+’ J.OO—o_45 -0.19 5 io+- 4 94+0.27 5.52^'g 4.68í“;| D._0i4 2.25_o_42 ¿T OO+0.15 5 34+0-43 5 63+- 5 S2+- c 77+0.15 c OO+0.19 r 9C+0.36 ■—0.87 -u.z/-U.IJ z 7 7 log Loo —0.12 7+0.13 7+0.33 zi+0.26 7+0.26 '—0.32 7+0.35 -0.23 (Lq) +0.34 + 1/4 +0.24 -0.42 -0.34 -0.22 -0.59 0.24 yi 12 01 yö 16 7 /z 26 Zi +009 7Z 009 4 0 01 Hz z 1 017 0 4 19 0-21 U 6 01 Z),Zi z j37 wi 6 4 55+0.12 ^•-0.1 4 91+0.09 4 57+0- 4 75+- ^•-0.17 4 9Q+o. 4 70+0-0 ^•-0.28 4 72+0- 4.72 ±0.13 ^•-o.t 4 21- ^•-o.io 4 72+- 4.63 ±0.12 -^-0.35 4 44+-29 4 54+- "'”—0.09 4 Q9+O.O8 ^•—0.13 4 22+°+ 4.25 ±0.14 4.67+ 4.39+ 4.93 ±0.07 4 46+' 4.52 ±0.12 4 51++° 4.61 4.041 4.86^;“ 4.99 ±0.15 442+0. 4 85+ ^•^-0.17 4 4Q+0-1 4.80+¡];^ 5 63+' -0.1 5.11 ±0.10 j.u_o_i2 5.23 ±0.11 5.22 ±0.16 5.46+ 5.03+ -0.17 3.88; 7 Q7+O.2O < Q7+Ö.13 r 7i+0.09 5 02^- 5 09+°-i r 07+0.16 7 y i 7 / —0.08 log L 7+0.14 -0.13 q+0.12 4+0.26 °-0.23 7+0.12 O+0.13 /r+0.22 ^-O.lS m —0.16 1+0.15 —0.14 _.21 0 '-0.15 —0.14 —0.28 -0.15 (Lq) 0.22 -0.20 246 u3J 0 Z 7 2 Z 013 z3Z 09 9 zu 020 7 07 1OU 17 4.32 ±0.07 4.33 ±0.09 4.17 ±0.12 4.63 ±0.07 2.58 ±0.04 2.76 ±0.06 2.30 ±0.08 -o!7 -0.9 0 33++° 0.73 ±0.07 2.12 ±0.06 2.40 ±0.06 0.60 ±0.09 ’ —0.08 7 77+0.09 2.06 ±0.08 0.92 ±0.07 "^°-0.13 7 cq+0.14 2.33 ±0.09 ’° —0.12 2 64+- -0.9 7 77+0.10 2 96+- 3.79 ±0.10 3 98+0-1 3.34 ±0.05 -^0.8 1.69 ±0.03 1.50 ±0.08 1.62 ±0.06 1.29 ±0.08 1.60 ±0.06 1.55 ±0.06 1.75 ±0.06 1.68 ±0.04 1.61 ±0.12 1.73 ±0.06 1 60+' 1.93 ±0.04 1.86 ±0.10 1 1S+0.0 1 63+- 1.74 ±0.09 1.27 ±0.09 1.70 ±0.08 1.45 ±0.12 1.64 ±0.10 -0.18 1.76 ±0.09 ^^-O.OÓ 1.94 ±0.06 -°0.6 © 2003RAS,MNRAS 338,85-119 4U 041 015 + :)U 045 O:>i 069 J,HZ :>ö 034 4 41/ 022 44ö 33 024 045 ,JZ 052 021 036 014 7 43 4.53 ±0.10 4.63 ±0.084.520.06 -+-0.27 -r.^o_027 —0.13 4 30+' 4 97+0.48 4.81 ±0.13 4 13+- 4.75+ 4.08 4.35 ±0.13 + --0.31 4 50+- 4.56 ±0.15 4.12 ±0.09 4.31 ±0.13 4.90+ 4.45 ±0.17 -0.87 6 51+' ’—0.32 5.83 ±0.13 5.57 ±0.20 4.21 ±0.16 5.31 ±0.11 +--0.59 4 58+’ 5.23+ 5.41 ±0.15 5.48 ±0.10 d.u^-oó '+o:io s-o+oi '°/,.¿ 5 69+’ -0.30 4 48+0- 5 13+- 9.ÖÖ_o 19 4 42+0-24 3.52 ±0.13 5.39+ 5.10+ 5 24+- ■2—0.15 7 ^7+0.16 3 47+0.38 j.jo_o_28 7 70+O.35 5.79+0.15 j.oO—0 42 5 42+- 5 12+- 5 03+- 3.65 ±0.15 ■2-°-2-0.13 3 63+' 3.97+ < AQ+0-20 < 49+O.2 5 1Ö+0- -0.14 c qq+0.19 1 z u u 14 ö 7 7 —0.19 log Moo q+0.33 -0.22 n+o.26 —0.23 +0.26 7+0.35 7+0.24 ^-O.U r+0.13 0+/ —0.24 2-0.42 -0.32 -0.32 n (Mq) -0.63 —0.34 0.44 öy 47i 09 ö 01 Ui 01 u 17 3 z/ 6 0 16 J Z yU 3ö 01 7Z J 3iZ 6 012 0-21 015 4.49 ±0.09 ^•-o.n 4 89+0-10 4 Q7+0.13 -o.i 4 71+0.09 4.01 ±0.10 4.02+ + •22-0.10 4 33+- 4 13+0.16 +-+—0.12 4 48+- +--0.13 4 01+' 4.25 ±0.14 4.75+ 4.04 ±0.07 +-2-0.18 4 30+°‘ 4.27 ±0.11 4.73+ 4.42 ±0.16 +•^-0.13 4 9Q+0-11 +■2—0.23 431+0.22 +--0.13 4 33+0.12 ^•-0.17 4 27+°+ Z).uu_ 14 5.79 ±0.12 J.JU-O 17 5 50+ 5.26+ -+2-0.09 5.57 ±0.15 ^■ —0.16 + -0.13 3 90+0-12 ■-®o.i 7 Q6+0.09 3 45+- 2--0.15 7 77+0.13 3.43+ 3.56 ±0.12 ■2--0.1 7 cc+0.10 3.88+ ■-0.20 7 17+0.19 3 ^o+°+ 5 OO+ c 43+O.O8 5 40+ c 77+0.12 5 29+- 0 z ö log M m (Mq) —0.21 7+0.20 ^+0.09 <+0.14 2-0.13 7+0.12 7+0.15 —0.28 n+0.26 —0.14 -0.10 -0.15 -0.16 2 0 0 3MNRAS.338. . .85M justified. between thesevaluesandtheasymptotic values;however,forclus- poor’ ([Fe/H]^-2.25)and‘metalrich’-0.33).We large (e.g.NGC1856),andtheextrapolation r^oomaynotbe ters withy^2,thevalueofL©©(and M©©)canbecomeunreasonably nosities andmasses.Formostclusters thereisnotagreatdifference luminosity andmassovertheradialrangeweactuallymeasure, tidal limitinformation.Thereisverylittledifferenceintheresult Table 6. tio fromtheappropriateevolutionarysynthesismodel.Theadopted then usetheageestimatesfromTable2toobtainamass-to-lightra- line); [Fe/H]=-0.64(shortdashes);and-0.33(dottedline). the clustersample:[Fe/H]=—2.25(longdashes);—1.65(solid using theIMFofKroupaetal.(1993)overmassrange0.1-120Mq,and ulation modelsofFioc&Rocca-Volmerange(1997)(pegasev2.0,1999), Figure 13.Mass-to-lightratiospredictedfromthesingle-burststellarpop- luminosity andmassincludingNGC2070.^CorrectedforreddeningusingE(B—V)=0.38(seethetext). is, thoseparameterslistedinTable4.Giventhebreaktoashallowerprofileatr—15arcsec,weprobablyunderestimateL©©andM©©-asymptotic ^Corrected forreddeningusingE(B—V)=0.10.^Luminosityandmasscalculatedthestructuralparametersderivedinnerregionsonly-that R136^ HODGE 14 HODGE 11 HODGE4 © 2003RAS,MNRAS 338,85-119 as such,theseprovidereliablelower limitsfortotalclusterlumi- equation (13).WeprovideestimatesofLandMtoshowthe dred arcsec(areasonabletidalcut-off),andtheresultobtainedfrom obtained fromusingequation(12)withanrvalueofseveralhun- estimates oftotalclusterluminositiesandmassesintheabsence abundances, andvaluesforM/L,pM©©Marelistedin calculated forthefouravailableabundancesthatcoverrangespannedby Cluster Table 6-continued m m v0m The valuesofL©©andM©©areintendedtoprovidereasonable © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem c 2 5.98 ±0.04 2.58 ±0.04 2.85 ±0.02 2.46 ±0.02 (L pc“) 0 log /xf; loTrs gio (/y) Adopted -0.33 -0.64 -2.25 -0.33 [Fe/H] M/L v 0.02 0.88 3.25 1.21 3 6.17 ±0.08 2.02 ±0.10 2.08 ±0.07 1.59 ±0.09 (Lq pc“) log jo 4.38; 6.25 5.11 5.31 lOg Lqq (Lq) pronounced intheyoungestclusters,wherebrightstarsarerela- rather simplyusedallthoseavailable intheHSTarchive-ef- reduction artefact,orarisingfrom aselectioneffect.Inaddition, reduction processoraselectioneffect(i.e.wesystematicallymissed parameters -namelythatthespreadincoreradiusincreasessig- properties oftheLMCclustersystem.Suchananalysisisbeyond present inthecalculatedvaluesforM/L. ing massgivestotalsstillwithinthequoteduncertaintiesforsuch tively massive.Atworstwemiss~30starsfromanyyoungcluster, than wouldbeexpectedwerethebrighteststarsincludedinpro- fect, arandomsample.Thisadds weight totheargumentagainsta fact thatweconfirmexactlytheresultofElson,usingalarger(and tive oftruestructuralevolutioninLMCclustersastheygrowolder, trend hasbeendiscoveredpreviouslyanddiscussedbyElsonetal. ters olderthanlogr~9thefullrange^0-8pciscovered.This young clustershavecompactcoreswithr<2.5pc,whileforclus- nificantly withincreasingclusterage.Withoutexception,allofthe the sample(Fig.14),aclearrelationshipexistsbetweenthesetwo With alargesamplesuchasthis,thereistheopportunityforfull AGE RELATIONSHIP the calculatedparametersowingtorandomerrorsinvalues clusters. TheerrorslistedinTable6representtheuncertainties which resultsin<600Mqbeingneglected.Additionofthismiss- files). However,thiseffectisnotparticularlysignificant.Itmost causes someluminosity(andmass)tobeunaccountedforinseveral distinct) sample,space-basedobservations,anduniformlyselected the scopeofpresentpaperandwillbepresentedinfuture. 6 THECORERADIUSVERSUS we didnotchooseouryoungclusters inasystematicfashion,but and reduceddataisanargument against therelationshipbeinga all theyoung,lowsurfacebrightnessclustersfromoursample).The or ismerelytheresultofasecondarycorrelation,product and ground-basedmeasurements. We do,however,observeoneparticularlynoteworthytrend. 6, inasearchforcorrelationsandphysicalinsightintotheoverall as thoseintroducedbyanysaturatedstarsorthatmightbe of /x,yanda.Wedonotaccountforanysystematicerrorssuch surface brightnessprofiles(thatis,thezero-point76555(0)isfainter sition ofbrightnesslimitsonothers(seeSections4.2.3and4.2.4) selection effectbeingresponsible for theobservedupperenvelope; (1989), E91andElson(1992),usingacombinationofliteraturedata statistical analysisoftheparameterspresentedinTables2,4and v c c 0 +0.21 +0.34 +0.26 +0.22 -0.19 -0.28 -0.22 -0.45 The presenceofsaturatedstarsonsomeimages,andtheimpo- The keyquestioniswhetherthisobservedrelationshipindica- When thecoreradiusisplottedagainstageforallclustersin +018 4/y 01 ^.iO_o 19 4 16’ -0.12 4 79+- 9+0.13 6.01 ±0.13 4 5 log L m (Lq) 0.14 Structure ofrichLMCclusters115 3 4.47 ±0.08 2.59 ±0.07 1.96 ±0.10 1.67 ±0.09 (M© pc-) log Po +021 +026 4 55- 4 OO+0.34 2>.03_o2 5 63’ 5 4Q+0.2X -2 log Moc (Mq) n io +018 3 4.31 ±0.13 ¿klU—o 19 4 ^o- 4.671 5.31 log M m (Mq) 7+0.13 1+0.11 —0.12 -0.14 2 0 0 3MNRAS.338. . .85M 10 presented inMeylan1993).There is noevidenceforanysignificant radius evolveswithage.However,Elsonobservednosuchcorrela- possibility thatacorrelationbetweenmassandcoreradiusbe- product ofdatareductionoraselectioneffect,E91discussesthe brightness youngclusterswithlargecoresintheLMCsystem.Itis points markingclusterswithradiismallerthan~1pcshouldbeconsidered intrinsic differencebetweenthemasses ofthelargestnewlyformed more massatlargeradii,wherewedidnotobserve,thanacluster nient parameterforeliminatingtheagebiasinLand(i.e.young Figs 15and16,respectively.Whileisnotalwaysareliable tions inhersampleof10youngclusters. ters (withsmallercores)formedrecently,itmightseemthatthecore massive clusters(withlargercores)andless tween massandagemightberesponsible-thatis,ifbothmore for long,andsotheirpresence(orotherwise)doesnotaffectthe likely, however,thatsuchdiffuseclusterswouldnotremainbound however, wecannotguaranteethattherearenotverylowsurface upper limits,asdiscussedinSection5. literature estimatesfromTable2,andthecoreradiiaslistedin4.The Figure 14.Coreradiusversusageforallclustersinthesample.Agesare evidence forastrongcorrelation.While itistruethatthoseclusters clusters andtheoldin sample. InFig.16wealsoseeno are nolow-massoldclusters(adetailed discussionofthiseffectis faded andprobablydispersedbyage 10yr-explainingwhythere attribute thistothefactthatlow-massyoungclusterswillhave and thatalltheoldclustersseemtohavelargermasses;however,we age. Itistruethatthereareafewyoungclusterswithlowmasses, with y~4,andconsequentlywillprobablyhaveacorrespondingly observational biaspresentinM(i.e.aclusterwithy~2willhave clusters areintrinsicallymoreluminousthanoldclusters),andany extrapolation tothetruemassofacluster,weuseithereasconve- discussion andconclusionsbelow. small M.)InFig.15,weseenosignificantcorrelationofmasswith (much larger)sample,tolookforcorrelations.Theseplotsare smaller cores)wereformedinthepast,butonlylessmassiveclus- 116 A.D.MackeyandG.FGilmore m m m Similarly, weplotagainstage,andMrforour Given thattheradius-agerelationshipdoesnotseemtobe œc © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 8 bifurcation ataroundseveralx10 yr.Thisbifurcationgrowsinto Figure 15.Asymptoticmassversusageforallclustersinthesample.Again, ine closelythedistributionofclusters, whichseemstoexhibita Fig. 14representsrealevolutionin thestructureofclustersasthey more massivethanmostoftheclusters withsmallercoreradii. Figure 16.Asymptoticmassversuscoreradiusforallclustersinthesample. Table 6. ages aretheliteratureestimatesfromTable2,whilemasses grow older.Giventhis,itisuseful toreturnFig.14andexam- with largecoreradiiallseemtoberelativelymassive,theyarenot Core radiiarefromTable4,andmasses6. We thereforeconclude,likeElson, thatthetrendobservedin © 2003RAS,MNRAS 338,85-119 2 0 0 3MNRAS.338. . .85M 8 810 _(1+T) be sosignificantthatratherthanundergoing corecollapse,acluster provides adetailedreview,andmorerecentlydeGrijsetal.(2002c) better than99.5percent.Thebifurcationisthereforestatistically mass losstobelessmassive.Upper-sequence clustersaretherefore massive, whereasonewouldexpect aclusterdissolvingbecauseof Fig. 16showsthatclusterswithlarge coreradiiareallrelatively they divergefromthestandardsequencebeyondafewx10yr,to FMC clusters.Thisrenderstheclustersthatfollowupperbranch E91 matchthelowersequenceofFig.14sowelladdsplausibilityto to reproducethelowerregionofFig.14forasuitablecluster these twomechanismsindetail,tomeasuretheirrelativeeffects ters. WearecurrentlyemployingV-bodysimulationstoexplore might simplyreflectthespreadinorbitalradiibetweenclus- the comparativeevolutionofGalacticglobularclustersasIMFvari- is thatthescatteraresultofclustersamplebeingspreadover this alonecouldreproducetherequiredscatter.Asecondpossibility mass wouldcauseaspreadinthelowersequence-itmaybethat ter (E91),andthespreadininitialmass(Fig.15).Variations this probablyreflectsthedifferentformationconditionsofeachclus- youngest clustersinthepresentsamplehaveaspreadcoreradii- that acombinationofotherfactorsisinsteadresponsible.Eventhe Fig. 14)musthavehadverysimilarIMFs.Itthereforeseemslikely have shownthatasampleofsixFMCclusters(widelyscatteredin is pointingtowardstheuniversalityofIMF-Gilmore(2001) not clear.BecausetheIMFslopegovernsrateofexpansion, Fig. 14. follow tracksthatmatchwelltheshapeoflowerbranchin is, themoresevereearlymassloss.Asclustergrowsolder heavily weightedthehigh-massendofmassfunctionacluster the massfunction;see,e.g.Chernoff&Weinberg1990).Themore the initialmassspectrumpresentincluster(i.e.slopeof including allclustersolderthan1Gyr,thesignificanceincreasesto mately the99percentlevel.Ifweincreasesamplesizeby that theyarenotdrawnfromauniformdistribution,atapproxi- © 2003RAS,MNRAS 338,85-119 are onthevergeofdissolution-afteracertaintime,masslosscan finish intheupperright-handsideofplot?Possibly,theseclusters especially intriguing.Whatmakestheseclustersdifferent-whydo our argumentthattheradius-ageplottracksphysicalevolutionof and toseewhethereither(oracombinationofboth)isable ations betweenclusters.ThespreadinthelowersequenceofFig.14 Gilmore (2001)showsthattidalforcesareatleastassignificantin a considerablerangeofdistancesfromtheFMCcentre(Table2). variations couldberesponsible.However,moreandevidence Clusters withIMFslopessimilartothatfortheSalpeter[x with differentIMFslopes,plottedovertheequivalentofFig.14. collapse. E91presentFokker-Planckmodelsofevolvingclusters and evolves,theexpansionslowsiseventuallyreversedbycore causing theclustertoexpand.Therateofexpansionisregulatedby cluster sufferssignificantandrapidmasslossfromstellarevolution, dard pictureof(isolated)clusterevolution,whereanewlyformed distribution ofcoreradiiforallclustersolderthan10Gyr,shows of olderclusterswithcoreradiiintherange3-6pccouldbea a largeseparationby10Gyr.Itispossiblethattheapparentdearth scale 10-10yr,whichisfartoo longfordissolution.Inaddition, simply dissipates.However,theupper sequencecoversthetime- sample. = 1.35,wheretheIMFisgivenbyOam]andsteeper significant. small-sample effect.AsimpleKolmogorov-Smirnovtestonthe The factthatthemodelsofisolatedevolvingclusterspresentedby There isanoticeablescatteraboutthissequence,butitscause The lowerbranchintheradius-agediagramrepresentsstan- © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 7 6 10 A-body simulations(e.g.Wilkinsonetak,inpreparation)toexplore reason. Giventhis,wesuggesttwowaysinwhichupper-sequence probably notundergoingdissolution,butareexpandingforanother process ashomogeneouspossible withoutsacrificingdatain- be quantitativelyeliminated.Wearecurrentlycarryingoutdetailed parts. Atidalforcestrongenoughtosignificantlyalterthecore be required,andthisisstatisticallyveryunlikely.Inthecaseof probably gravitationallyboundandinteracting.Aninteractingpair therefore thatsignificantclusterexpansioncanbedrivenbybinary important inthecontextofhaltingcorecollapse,binarystarsalone holds here.Similarly,althoughthebinarystarfractioninaclusteris it becomesunboundafteronlyaveryshorttime(~10yr).Our ter withaveryflatIMFsufferssuchextremeearlymasslossthat lifetime ofthecluster(aswouldberequiredfortoevolve not isolated). they havebeeninfluencedbysomeexternalprocess(i.e.are they have(orhad)radicallydifferentstellarpopulations,or We havecompiledapseudo-snapshot datasetoftwo-colourobser- 7 SUMMARYANDCONCLUSIONS this further. the contextofcoreexpansion,andsoneithermechanismcanyet the mergerofdoubleclusters,nomodelshavebeenexploredin from thecentreofaclusterandthereforemainlyaffectouter tidal forces,itisuncertainastowhateffectsafieldcanhave is aresult-small-scaleexpansionimpliesmanymergerswould unlikely thattheyareallcoincidentalalignments-hencesome Bhatia &Hatzidimitriou(1988)haveshownthatitisstatistically that isobservedwithoutdestroyingtheclustersinquestion.Double- how eithermechanismcouldproducethescaleofcoreexpansion fraction. encounters, andanexpandingcoreradiusimplieslowerstellarden- extract energyfromthebinarystarsofaclusterrequiresclosestellar cannot drivethelarge-scalecoreexpansionwehaveobserved.To earlier argumentwithrespecttotheuniversalityofIMFalso expansion, buttherapidexpansionphasedoesnotlastentire cussed previously,theIMFslopeforaclusterregulatesitsearly either couldcausethedegreeofcoreexpansionobserved.Asdis- clusters mightbedistinguishedfromthe‘standard’-either tegrity. Wehavealsocompiledliterature estimatesfortheagesand vations fromtheHSTarchivefora sampleof53richLMCclusters clusters. However,itisunclearwhetherlarge-scalecoreexpansion cluster mergercanresultinasinglewithstructurethatis will mergeafterarelativelybriefperiod(Bhatia1990),andA-body de Oliveira,Dottori&Bica1998;Oliveiraetal.2000),and cluster pairsarerelativelycommonintheFMC(Bhatiaetal.1991; fields. Again,fromsimplephysicalarguments,itisdifficulttosee double clustersandtheeffectsofstronglyvariable,perturbativetidal along theuppersequence).Inaddition,asshownbyE91,aclus- on tryingtomakethiscompilation andthesubsequentreduction of aclusterwouldprobablydestroythecluster.However,aswith on aclustercore.Tidalforcesincreaseasthecubeofdistance stars overtherequiredtime-scale,evengivenanexceptionalbinary sity andthereforefewerencountersinagivenperiod.Itisunlikely slopes, andverylargebinarystarfractions.Itseemsunlikelythat spanning thefullagerange10-1 0 yr.Theemphasishasbeen stable after~200Myranddistinctfromthestructureoforiginal studies bydeOliveiraetal.(1998,2000)haveshownthatabinary Examples fallingintothefirstcategoryincludeveryflatIMF Two examplesthatfallintothesecondcategoryaremergerof Structure ofrichLMCclusters117 2 0 0 3MNRAS.338. . .85M Hubble SpaceTelescope,obtainedfromthedataarchiveat processes thatfallintothesecategories. populations, orbybeingsubjectedtoanexternalinfluence.Weare power-law slopeatlargeradii.Usingtheseparameterswehavealso Brandi B.etah,1996,ApJ,466,254 Binney J.,TremaineS.,1987,Galactic Dynamics.PrincetonUniv.Press, Bica E.L.D.,SchmittH.R.,DutraC.M., OliveiraH.L.,1999,AJ,117,238 Bica E.,ClariáJ.J.,DottoriH.,SantosJ.F.C.,Jr,PiattiA.E.,1996,ApJS, Bhatia R.K.,ReadM.A.,HatzidimitriouD.,TrittonS.,1991,A&AS,87, Bhatia R.K.,MacGillivrayH.T.,1988,A&A,203,L5 Bhatia R.K.,HatzidimitriouD.,1988,MNRAS,230,215 Bhatia R.K.,1990,PASJ,42,757 Anderson J.,KingI.R.,1999,PASP,111,1095 tract NAS5-26555. Universities forResearchinAstronomy,Inc.undertheNASAcon- This paperisbasedonobservationsmadewiththeNASA/ESA Hurley forusefuldiscussionsandsuggestions.ADMissupportedby We wouldliketothankMarkWilkinson,RicharddeGrijsandJarrod ACKNOWLEDGMENTS large diffusecores.Wesuggestthattheseclustersmustbedifferent moving totheupperright-handsideofdiagramandevolving hundred Myr,withmostclustersmaintainingsmallcoresconsistent this trendreflectsrealevolutioninclusterstructurewithage.The PCC state. two-component fittoitsprofile,andthatitisprobablynotyetina PCC objects,matchingthe20percentestimatedforGalactic interesting -thetwobestexamplesshowclearpower-lawprofiles in theirprofiles.Weseeevidencefordoubleclustersoursample young clustersinparticularexhibitingbumps,shouldersanddips http://www.ast.cam.ac.uk/STELLARPOPS/LMC_clusters/. tural parametersforeachcluster,includingthecoreradiusand metallicities oftheseclusters,againtryingtomaintainconsistency Campbell B.etal.,1992,AJ,104,1721 REFERENCES Space TelescopeInstitute.STScIisoperatedbytheassociationof a TrinityCollegeERSgrantandBritishgovernmentORSaward. currently employingA-bodysimulationstoexploreseveralphysical from the‘standard’clusters,eitherbyhavingexceptionalstellar with standardisolatedglobularclusterevolution,butseveral distribution ofclustersontheplotsuggestsabifurcationatseveral covering thefullrangeofcoreradiimeasured.Wehavearguedthat we seethatwhilealltheyoungclustershavecompactcores, globular clustersystem.WehavealsoshownthatR136requiresa we areabletoestimatethat20±7percentoftheseclusters at smallradii,withslopesß~0.7inthelog/x-logrplane.Our and post-core-collapseclusters.ThePCCcandidatesareespecially along withthesurfacebrightnessprofiles,areavailableon-lineat estimated thetotalluminosityandmassforeachcluster.Thesedata, as farpossible.FromtheHSTobservations,wehaveconstructed spread incoreradiusincreaseswithage,theoldestclusters sample covers12ofthe15definiteoldLMCglobularclusters,and surface brightnessprofilesfortheentiresampleandobtainedstruc- 118 A.D.MackeyandG.FGilmore If thecoreradiusisplottedagainstageforentiresample, The surfacebrightnessprofilesshowarichamountofdetail,with Princeton 335 102, 57 © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Elson R.A.W.,SchadeD.J.,ThomsonR.C.,MackayC.D.,1992,MNRAS, Elson R.A.W.,FreemanK.C.,LauerT.R.,1989,ApJ,347,L69 Elson R.A.W.,FallS.M.,FreemanK.C.,1987,ApJ,323,54(EFF87) Elson R.A.W.,FreemanK.C.,1985,ApJ,323,54 Elson R.A.W.,FallS.M.,1988,AJ,96,1383 Elson R.A.W.,1992,MNRAS,256,515 Elson R.A.W.,1991,ApJS,76,185(E91) Dutra C.M.,BicaE.,CiarlaJ.J.,PiattiA.E.,1999,MNRAS,305,373 Dolphin A.E.,2000b,PASP,112,1397 Dolphin A.E.,2000a,PASP,112,1383 Djorgovski S.,KingI.R.,1986,ApJ,305,L61 Djorgovski S.,1987,inGrindlayJ.,PhilipA.G.D.,eds,Proc.IAU Dirsch B„RichtlerT,GierenW.P.,HilkerM„2000,A&A,360,133 Rich R.M.,SharaM.M.,ZurekD.,2001, AJ,122,842 Press W.H.,TeukolskyS.A.,Vetterling W.T.,FlannertyB.P.,1992,Numer- Parmentier G.,Gilmore2001,A&A, 378,97 Meylan G.,DjorgovskiS.,1987,ApJ,322,L91 Meylan G.,1993,inSmithG.H.,BrodieJ.P.,eds,ASPConf.Ser.Vol.48,The Meylan G.,1987,A&A,184,144 Metaxa M.,KontizasE.,1988,A&AS,73,373 Mateo M.,1987,ApJ,323,L41 Malumuth E.M.,HeapS.R.,1994,AJ,107,1054 Lyngâ G„WesterlundB.E.,1963,MNRAS,127,31 Lugger P.M.,CohnH.N.,GrindlayJ.E.,1995,ApJ,439,191 Johnson R.A.,BeaulieuS.E,GilmoreG.E,HurleyJ.,SantiagoB.X.,Tanvir Jasniewicz G.,ThéveninE,1994,A&A,282,717 Hunter D.A.,ShayaE.J.,HoltzmanJ.A.,LightR.M.,O’NeilJr,Lynds Holtzman J.,BurrowsC.J.,CasertanoS.,HesterJ.J.,TraugerJ.T.,Watson Holtzman J.etal„1995a,PASP,107,156 Hodge P.W.,1960,ApJ,161,351 Hill V.,FrançoisP,SpiteM.,PrimasE,2000,A&A,364,L19 Fioc M.,Rocca-VolmerangeB.,1997,A&A,326,950 de VaucouleursG.,1957,AJ,62,69 de OliveiraM.R.,BicaE.,DottoriH.,2000,MNRAS,311,589 de OliveiraM.R.,DottoriH.,BicaE„1998,MNRAS,295,921 de GrijsR.,GilmoreG.F.,MackeyA.D.,WilkinsonM.I.,BeaulieuS.F., de GrijsR.,GilmoreG.F.,JohnsonR.A.,MackeyA.D.,2002b,MNRAS, de GrijsR.,JohnsonR.A.,GilmoreG.E,FraynC.M.,2002a,MNRAS,331, Chrysovergis M.,KontizasE.,1989,A&AS,77,357 Chernoff D.,WeinbergM.,1990,ApJ,351,121 Olszewski E.W.,SchommerR.A.,SuntzeffN.B.,HarrisH.C.,1991,AJ,101, Olsen K.A.G.,HodgeP.W.,MateoM.,OlszewskiE.W.,SchommerR.A., Oliva E„OrigliaL„1998,A&A,332,46 Kroupa R,ToutC.A.,GilmoreG.E,1993,MNRAS,262,545 Kontizas M.,HadjidimitriouD.,E.,1987b,A&AS,68,493 Kontizas M.,ChrysovergisE.,1987a,A&AS,68,147 King I.,1962,AJ,67,471 Gilmozzi R.,KinneyE.K.,EwaldS.P.,PanagiaN.,RomanielloM.,1994, Gilmore G.,2001,inTacconiL.,LutzD.,eds,StarburstGalaxies:Nearand Geisler D.,BicaE.,DottoriH.,ClariáJ.J.,PiattiA.E.,SantosJ.F.C.,Jr,1997, p. 333 p. 588 Johnson R.A.,SantiagoB.X.,2002c,MNRAS,inpress Univ. Press,NewYork ical RecipesinC:theArtofScientific Computing, 2ndedn.Cambridge N.R., ElsonR.A.W.,2001,MNRAS,324,367 R., 1995,ApJ,448,179 A.M., WortheyG.,1995b,PASP,107,1065 ApJ, 435,L43 Far. Springer-Verlag,Heidelberg,p.34 AJ, 114,1920 258, 103 228 515 Globular Cluster-GalaxyConnection.Astron.Soc.Pac.,SanFransisco, Symp. 126,GlobularClusterSystemsinGalaxies.Kluwer,Dordrecht, 331, 245 Suntzeff N.B.,WalkerA.R.,1998,MNRAS,300,665 © 2003RAS,MNRAS 338,85-119 2 0 0 3MNRAS.338. . .85M RohlfsK.,Kreitschmann J.,SiegmanB.C.,FeitzingerJ.V.,1984,A&A,137, © 2003RAS,MNRAS 338,85-119 Spitzer L.,1987,DynamicalEvolutionofGlobularClusters.PrincetonUniv. Sirianni M.,NotaA.,LeithererC.,DeMarchiG.,ClampinM,2000,ApJ, Shapley H.,LinsdayE.M.,1963,Irish,AJ,6,74 Shaklan S.,SharmanM.C.,PravdoS.H.,1995,Appl.Opt,34,6672 Press, Princeton 533,203 343 © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem This paperhasbeentypesetfromaTjhX/DTeXfilepreparedbytheauthor. Träger S.C.,KingLR.,DjorgovskiS.,1995,AJ,109,218 Westerlund B.E.,1990,A&AR,2,29 Suntzeff N.B.,SchommerR.A.,OlszewskiE.W.,WalkerA.R.,1992,AJ, Spitzer L.,HartM.H.,1971,ApJ,164,399 104, 1743 Structure ofrichLMCclusters119