1989AJ 97.1688B a) THE ASTRONOMICALJOURNAL ies ofglobularclusteragesprovidetwokeyobservational but systematicerrorsarenotimportantaslongallclusters the Galactichaloformed,andprovidesafundamentalcon- probably themostreliableindicatoroftimeoverwhich age betweentheoldestandyoungestglobularclustersis of thehaloandmodelsuniverse:(1)Thedifferencein data pointsoftenusedtoconstrainmodelsoftheformation dated componentoftheGalactichalo.Consequently,stud- Taylor 1987;Sandage1988).Toaddressthesecondpoint recent discussionsofvariouscosmologicalmodels(e.g., observational lowerlimittotheageofuniverse,and straint onanymodelsoftheearlystagesincollapse requires agedeterminationsofhighaccuracy,withallsys- ages derivedforglobularshaveplayedaprominentrolein Galaxy. (2)Theageoftheoldestclusterisarguablybest cluster agesisadifficulttask,andonethathasanunfortu- dressed byadifferentialcomparisonoftheclustersNGC studied areaffectedidentically. point requiresmeasuringclusterageswithhighprecision, tematic errorsintheanalyseseliminated.Toaddressfirst present acompletehistoryhere. VandenBerg(1983)com- required inordertomakeastrongstatementconcerning ties inmakingclusteragedeterminations,and(3)arguethat minations, (2)presentanoverviewoftheprimarydifficul- tion will(1)giveabriefsummaryofrecentclusteragedeter- cussions ofmanyaspectstheobservationsforeach requires somewhatinvolved(andoccasionallytedious)dis- sequently, afairpresentationofthedataandconclusions nately strongdependenceonanumberofsmalldetails.Con- 288, NGC362,and1261.Thederivationofrelative contract withtheNSF. tional OpticalAstronomyObservatories, operatedbyAURA,Inc.under main-sequence photometryinglobulars andconcludedthat piled andcomparedtoisochrones allofthethenavailable the globularclustersystem,and noattempthasbeenmadeto relative clusterages. a differentialstudyofcarefullychosengroupclustersis clusters, aswellalargenumberofcaveats.Thisintroduc- THE AGEOFGLOBULARCLUSTERNGC288,FORMATIONGALACTICHALO, VisitingAstronomer,CerroTololo Inter-American Observatory,Na- 1688 Astron.J.97 (6),June1989 Dominion AstrophysicalObservatory,HerzbergInstituteofAstrophysics,NationalResearchCouncilCanada,5071WestSaanichRoad,Victoria, Globular starclustersarethemostconspicuousandeasily There havebeenmanystudiesfocusedontheagespreadin In thispaperthequestionofrelativeclusteragesisad- © American Astronomical Society • Provided by the NASA Astrophysics Data System branch morphology. billion yrolderthanNGC1261.ThisimpliesthattheformationtimeforGalactichaloissignifi- gies oftheclustersPal12,NGC288,362,and1261,allwithsimilarmetalabundances, cantly longerthanafreefalltime.Considerationoftheinferredagesandhorizontal-branchmorpholo- that aremostnaturallyexplainedifNGC288issome3billionyrolderthan362and—1to2 A differentialcomparisonofpreciseCCDphotometryintheglobularclustersNGC288,362,and NGC 1261showsthatdifferencesexistinthepositionsofmain-sequenceturnofftheseclusters suggests thatagemaybetheparameterthat,afteroverallmetalabundance,mostdetermineshorizontal- I. INTRODUCTION AND THESECONDPARAMETER British ColumbiaV8X4M6,Canada 0004-6256/89/061688-11 $00.90 a) Received 24January1989 Michael BoLTE VOLUME 97,NUMBER6 ABSTRACT best ofthephotographicstudiesitwasnotpossibletodistin- to 1983.Withhindsight,itnowseemsclearthateveninthe also includesasummaryoftheworkonclusteragesprevious there wasasmalldispersionintheageofclusters.Thiswork ble withCCDdetectors.Determiningthelower-main-se- ble accuratephotometryoftheage-sensitiveturnoffregion guish agedifferencesatthe4billionyrlevel.Anenormous and NGC362)bycomparingpublishedcolor-magnitude photometry ofNGC288withpublished for manyclusters.Asimportant,accuratephotometryofthe tudes wasmadepossiblebytheavailabilityofCCDdetectors improvement intheaccuracyofphotometryatfaintmagni- there isevidenceforagedifferences betweenclustersaslarge diagrams (CMDs)toasingleset ofisochronesandconclude gayears olderthanNGC362.King,Demarque,andGreen NGC 362andconcludethat288couldbeseveralGi- ter system.Pound,Janes,andHeasley(1987)comparetheir most recentstudiesfavorasignificantagespreadintheclus- branches. with poorlypopulatedorextremelybluehorizontal cluster’s distanceindependentofhorizontal-branchconsid- quantum efficiencyandlinearresponseofCCDsmadepossi- and sophisticatedreductionsoftwarein1983.Thehigh photometry ofPal12andshow thattheVmagnitudediffer- lani (1988)andStetsonetal. (1989) presentindependent age variationisthedistantcluster Pal12.GrattonandOrto- as 5Gyr.Thestrongestcaseto dateforacluster-to-cluster with galactocentricdistanceinthesensethatinnerhalo few criticalinterclustercomparisons.Gratton(1985)used measurements inanumberofindividualclusters,withonly erations. Thisiscriticaltoestimatingtheagesofclusters quence positionofaclusterallowstheestimation unevolved mainsequenceinthenearerclustersisalsopossi- ence betweenthe horizontalbranchandmain-sequence servations andconcludedthatthestronggalactocentricgra- range ofagesandweregenerallyyounger.Peterson(1986) clusters werecoevalwhiletheouterhaloshoweda and main-sequenceturnoff.Hefoundatrendinclusterages difference inVmagnitudebetweenthehorizontalbranch published clusterphotometrytocompileagesbasedonthe dient inclusteragefoundbyGrattonwasnotsupported.The carried outasimilarstudyusinglargerbaseofclusterob- ( 1988)deriveagesforseveralclusters(includingNGC288 The emphasisofthefirstCCD-basedstudieshasbeen © 1989Am.Astron. Soc.1688 JUNE 1989 1989AJ 97.1688B the Pal12CMDindicatethatissome30%younger clusters M5and47Tucanae(NGC104).Bothfeaturesof for clusters.Furthermore,thesestudies(particularlyStet- also theclusterdistanceandreddening,metalabun- ages isthefactthatmain-sequence-tumoffpositionin than 47TueorM5. anomalously brightandbluecomparedtothewell-studied son etal.)demonstratethattheturnoffpositionofPal12is turnoff inthisclusterissmallcomparedtotheaveragevalue ments heavierthanheliumtohydrogencomparedtheso- the distancemodulusby—0.15magorchanging[M/H] yr producesaneffectintheCMDcomparabletochanging dance ofthestarsincluster.Anagedifference2billion CMD ofaclusterdependsnotonlyontheage,but distance andageerrorsof—0.15mag—2Gyr,respec- sequence, errorsinthereddeningof0.03magtranslateinto the lowermainsequenceofclustertoafiducialPopII lar value.Ifthedistancetoaclusterisdeterminedbyfitting where [M/H]isthelogarithmicratiobynumberofele- distances, reddenings,andmetallicitiestobetterthanthe few billionyearsrequiresthemeasurementofrelativecluster tively. Therefore,tomeasureagedifferencesontheorderofa values quotedabove. 1689 MICHAELBOLTE:NGC288 —0.25 dex(atametalabundanceof[M/H]—1.2), brightnesses andcolorsiscommon(thehistoryofphotome- different studiestoasinglestandardphotometricsystem.In tive clusteragesisthedifficultyoftypingphotometryin a numberofclustersforwhichindependentphotometric Janes, andHeasley1987)).Anuncertaintyofthissizeis studies exist,disagreementatthe0.05maglevelinmeasured try inNGC288isanexcellentexampleofthis(Pound, 0.05 magin2?—Kresultsanerrortherelativedistance ages bycomparingclusterlower-main-sequencepositions quite serious.Forthetechniqueofestimatingrelativecluster for Stetsonetal.)reliedonpublishedphotometryfroma moduli of—0.25mag.Theprecedingstudies(exceptinpart very differenthorizontal-branchmorphologies),anerrorof variety ofsources.Inseveralcasesthephotometryinasingle be gainedthroughtheeliminationofexternaluncertainties cluster wasdrawnfrommorethanonesource,typicallymix- ing CCDobservationsofmain-sequenceandturnoff-region observational techniques.Thereissignificantadvantageto ages canbeminimizedbyacarefulchoiceofclustersand stars witholderphotographicobservationsofonthe (it isnecessarytousethistechniquecompareclusterswith out differentialstudieswithhomogeneousdatasets.Inthe in photometriczeropointandcolorcalibrationsbycarrying giant andhorizontalbranches. and NGC288to1261,theobservationsforeachclus- ter pairweremadewiththesameinstrument,frames present study,forthecomparisonsofNGC288to362 cluster photometrywascalibratedwiththesamestandard- were obtainedonthesameobservingrun(ornight),and clusters ofasimilar,well-measuredmetalabundance.Al- star observations.Thereisfurtheradvantageinchoosing metallicity correlation,thiswill isolatethedistancemodulus though itremovesthepossibility ofinvestigatinganage- tion oftheturnoffinV(B— V)plane.Moresubtlead- and ageasthetwomajorvariables thatdeterminetheposi- dance havetodowiththemethods ofdeterminingcluster vantages ofcomparingclusters withsimilarmetalabun- distances. The primary fiducialmarksusedto obtaindis- The primarysourceofuncertaintyinestimatingcluster © American Astronomical Society • Provided by the NASA Astrophysics Data System A secondmajorsourceofuncertaintyindeterminingrela- Some oftheuncertaintiesindeterminationrelative the ZAHBandmetalabundanceisanunresolvedissueat sequence ofclusters.Therelationshipbetweenthelevel zontal branch(ZAHB)andthepositionoflowermain tances toclustersaretheapparentlevelofzero-agehori- ture todate.The[M/H]-(l?—V)colorrelationmustbe ever, thepreciserelationshiphasbeenestablishedonly sequence, isdefinitelyafunctionofmetalabundance;how- when comparingclustersofsimilarmetalabundance.The Pechi 1988;Hesser1988)whichisconvenientlybypassed this point(see,e.g.,Jonesetal.1988;RenziniandFusi- cal checkonthemodelresultshasnotappearedinlitera- through modelcalculationsatthistime.Adefinitiveempiri- second fiducialmark,thepositionofunevolvedmain sequence intheCMDmagnifies(B—V)uncertainties known quiteaccuratelybecausethesteepslopeofmain quence positionstomeasurerelativeclusterpositions.For when attemptingaverticalslidingfitofclustermain-se- this lastreasonitisalsoimportanttochooseclustersfor analysis thathavesecureE(B—V)determinations. observing runsattheCerroTololoInter-AmericanObserva- tory. ThefirstrunwasinAugust1985usingthe4mtele- 362, andNGC1261.Thedatawereobtainedontwoseparate scope, thesecondwasinSeptember1986using1.5m ed inBoite(1987a),1988,1989),andMar- calibrations, andphotometryofindividualstars,arepresent- telescope. Thedetailsoftheobservations,reductions,and leau (1989)forNGC362,288,and1261,re- that willbedrawn. calibrations, asthisiskeytothereliabilityofconclusions spectively. Wereviewbelowtheintegrityofphotometric before midnightandapparentlyclearaftermidnight,when bration ofthephotometryinNGC288requiredconfirma- were obtainedonthesecondnight,whichwaspartlycloudy and onenonphotometricnight(4).TheNGC288data conditions earlierinthenight,weconsideredthatcali- stars observedimmediatelybeforetheNGC288framesand the NGC288fieldswereobserved.Sixphotometricstandard four standardstarsobservedimmediatelyaftertheNGC288 3 ),onenightofquestionablephotometricquality(night2), showed largescatter;however,reductionof24photometric tion.Fields inNGC288wereobservedontwonightsofthe photometric nightsoftherun.Still,becausecloudy frames wereconsistentwiththecalibrationsolutionderived this fielddidnotoverlapwiththe19854msoadirect run demonstratedphotometricconditions.Unfortunately, standard starsobservedinthecourseofnight31986 from standard-starobservationsthetwodefinitely for the1985fieldand1986 matchwithintheexpect- tions ofthemainsequenceand subgiantbranchmeasured star-by-star comparisonisnotpossible.However,theposi- ed errorsofafewpercentinV and B—V.Wetakethisasa confirmation thatthe19854m photometrywasinfactob- 1985 runconsistedoftwophotometricnights(nights1and tained throughclearskiesand that thecalibrationissecure lines derivedfor thetworuns. at the0.02maglevel.Figure1 shows theNGC288fiducial 1986 1.5mrun.Reductionofstandardsononethenights We presentphotometryofthreeclusters,NGC288, Frames wereobtainedinNGC2881985and1986.The II. OBSERVATIONS a) NGC288 1689 1989AJ 97.1688B 1690 MICHAELBOLTE:NGC288 points, andcolorcoefficientsshowedrmsresidualsof0.012 4 mrun.Thatnight28standaredstarswereobservedand branch. Weconcludethatthe NGC 362photometryisas in Vand0.0142?—V.Thiscalibrationwasappliedtothe solutions forextinctioncoefficents,instrumentalzero run. Thissamecalibrationwasappliedtodataobtainedthat NGC 362dataandthe288obtainedduringthat tial comparisonsofthisstudyfor theobservationsfrom run. Furthermore,althoughit is notcriticaltothedifferen- accurate aspossiblegiventheavailable datafromthe1985 tion isfoundinthecomparisonmadebetween1985Pal bration. Furthersupportoftheaccuracy1985calibra- This givessupporttotheexternalaccuracyof1985cali- are indistinguishableformagnitudesbrighterthanV~22. quence fiduciallinesderivedinthetwoNGC7099studies field inNGC7099.TheirFig.3showsthatthemain-se- night inNGC7099(Boite1987a)andPal12(Stetsonetal. to -1.5%inVmdB-V. photometry ofPal12tobeontheLandoltstandardsystem presented byStetsonetal.(1989).Thisstudyfoundthe1985 branch andslightlyredderat thepositionofgiant pair hasbeenaddedtotheoriginalNGC362study.The ing thestandard-starcalibrationsolution.Photometryfrom frames completely,anduseddifferentsoftwarefordetermin- evaluation oftheNGC362frames.Wehaverereducedthese sults forthelowermainsequence upthroughthesubgiant one additionaloverlappingfieldandashort-exposure-frame Bolte’s (1987a)NGC362photometry.Thispromptedare- Straniero (1988)suggeststhatacorrectionisrequiredto “new” resultsareindistinguishablefromthepublishedre- 1985 runtobecalibrated toanabsolutesystem, thecircum- (1988) obtainedindependentlycalibratedphotometryofa 1989). Subsequently,Richer,Fahlman,andVandenBerg 12 photometryandCFHTofthesamecluster overlap spatially. CTIO 1.5mobservingrun.Thefieldsobtainedduringthetworunsdonot 288 starsobtainedduringthe1985CTIO4mobservingrunand1986 Fig. 1.ComparisonoftheridgelinesmeasuredfromphotometryNGC The NGC362datawereobtainedonnight3ofthe1985 © American Astronomical Society • Provided by the NASA Astrophysics Data System Nevertheless, astudyofNGC362reportedbyChieffiand b) NGC362 B-V 0.010, respectively,indicatingthattheobservingconditions the Landoltstandardsystem.TheVandB—V errors forthecalibrationsolutionnightare0.008and used tocalibratethe1986NGC1261and288data vations of24photometricstandardstarsthatnightwere B-V. were photometric. on theLandoltsystemtowithinatleast0.02maginVand from thesamerunindicatesthatNGC362photometryis stantial evidencefromtheNGC7099andPal12photometry branch, andfirst-ascentgiantbranchbyfiducialridgelines. ly fromclustertocluster.Thisisparticularlythecasewhen As isthecaseforeveryaspectofanalysis,thesefiducial represent theclustermainsequence,turnoffregion,subgiant 1.5 mrunonthesamenightasNGC288frames.Obser- relative clusterdistancesaretobedeterminedbycomparing sequences mustbedeterminedverycarefullyandconsistent- ters. BecausethemainsequenceisquitesteepinCMD, the positionsofunevolvedmainsequencesclus- B —V.Thisprocedureismeanttoremoveanybiastoward errors intheverticalshiftsrequiredtomatchmain-sequence small errorsinB—Vpositiontranslateintomuchlarger constructed bydrawinglinesthroughthehighestdensityof positions. Themain-sequencefiducialsusedherehavebeen points, essentiallyusingthemodeofdistributionin presence ofbinarystarsinanytheclusters.Figure2shows locating themain-sequencefiduciallinebelowturnoff. larger distanceandbecausethedatawereobtainedwith turnoff. InthecaseofNGC1261,becausethisclusterisata posed. ForNGC288and362thereislittleuncertainty the photometryfromeachclusterwithridgelinessuper- the redsideofmainsequencethatwouldresultfrom brought toNGC288and362asa“second-parameter The positionoftheturnoff,however,isveryclearlydelineat- smaller telescope,thereissignificantlymoreuncertaintyin in tracingthemainsequencestoafewmagnitudesbelow been anumberofgoodstudies published inwhichthemetal very differenthorizontal-branch morphologies),therehave ferences inthepositionsoftheirprincipalsequences.Two ed. abundances oftheseclustershave beenmeasured.TableI pair” (twoclusterswithapparentlysimilarmetallicitiesbut to themoremetal-poorcluster.Becauseofattention sequence andgiantbranchatagivenmagnitudecompared dances) areexpectedtohavecoincidentunevolvedmain- NGC 362,and1261iscrucialtointerpretinganydif- ties, themoremetal-richclusterwillhaveareddermain plane. Forthecaseoftwoclusterswithdifferentmetallici- sequence andgiant-branchpositionsintheM-(B—V) clusters withidenticalmetallicities(andheliumabun- summarizes theresultsfromabundance studiesthatinclude values aretheaveragetaken fromtheliteraturefor at leasttwoofthethreeclusters. TheZinnandWest(1984) several different typesofanalysesexcludingQ . Theother V0 39 The NGC1261frameswereobtainedduringthe1986 In ordertocomparethephotometryforclusters,we Knowledge oftherelativemetalabundancesNGC288, III. CLUSTERSEQUENCERIDGELINES IV. CLUSTERMETALABUNDANCES c) NGC1261 1690 1989AJ 97.1688B clusters, theverticaldispersions andtrendsinTableIare notes. Forthepurposesofadifferential comparisonofthe values arefromstudiesthat brieflydescribedinthetable probably more important thanthehorizontal dispersions 1691 MICHAELBOLTE:NGC288 the horizontal-andgiant-branchridgelinesfromHarris(1982). quence ridgelinessuperimposed.Thedashedinthecenterpanelare Fig. 2.Color-magnitudediagramsforeachclusterwiththemain-se- © American Astronomical Society • Provided by the NASA Astrophysics Data System be thesamefor differentclusters,orthatany differences in branch, andbeforeevolvingto higherluminositiesupthe branch (ZAHB)andmakesa well-definedfiducialmark. tude lessthanthattowardNGC362andwewilladopt able, themostreliablemethodistomeasurerunofred- morphology (HarrisandvandenBergh1974).Whenavail- tra afterremovaloftheeffectsdifferenthorizontal-branch maps, andcomparisonofintegratedclustercolorsspec- methods employtheBursteinandHeiles(1982)reddening denings fromCMDmorphology.Possiblymorereliable make someinferencesconcerningtherelativeclusterred- metallicity effects,althoughforthecasesweconsiderhere, be knowntoS0.02mag,anunfortunatelystringentrequire- E(i? —V)0.02forNGC1261. ward NGC1261maybeafewhundredthsofmagni- and Heiles(1982)arethattheforegroundreddeningto- van denBergh(1974)andthereddeningmapsofBurstein intrinsic colorsversusspectral-typemethodofHarrisand the SGPandNGC288,Hesseretal(1987)for104, determined (see,e.g.,Pound,Janes,andHeasley(1987)for denings inthedirectionsoftheseclustersareunusuallywell with clustersofsimilarmetalabundance,wecanandwill quences intheCMDarecompromisedbyconfusionwith comparing thecolorsofvariouspointsonclusterse- ment. Thosemethodsthatestimaterelativereddeningsby cial linerequiresthattheintrinsic luminosityoftheZAHB asymptotic giantbranch.Forthe ZAHBtobeavalidfidu- after theheliumflashat top ofthefirst-ascentgiant monly interpretedasthelocationofzero-agehorizontal ward NGC288and362,respectively.Although and McNamaraFeltz(1980)fortheSMC).Wewill the well-studiedclusterNGC104(47Tucanae),red- posed ontheSmallMagellanicCloud(SMC),andisnear percent isverydifficult.BecauseNGC288situated however, eliminatingexternalerrorstothelevelofafew stars andUBVorStrömgrencolors.Eveninthebestcases, dening withdistanceinthedirectionofclusterusingfield main-sequence fitting,therelativeclusterreddeningsmust ever, forthepurposeofderivingrelativeclusterdistancesby reddening inthedirectionofeachiscertainlysmall.How- Stars arethoughttobeginhelium corefusionatthispoint, red sideoftheinstabilitystrip.Thislowerboundaryiscom- ters exhibitasharplydefinedlowerenvelopeofstarsonthe stars inallbutthemostdistantclusters,and(3)manyclus- very precisephotometryispossibleforhorizontal-branch attractive because(1)itisindependentofreddening,(2) align thehorizontalbranchesofclusters.Thismethodis moduli ofclustersistomeasuretheverticalshiftrequired adopt £(5—V)=0.015and0.040forthereddeningsto- near theSouthGalacticPole(SGP)andNGC362issuper- these clustersisapparentlylessthan0.2dex. consistently foundtobeslightlymoremetalpoorthanNGC measured foreachcluster,mosttechniquesNGC288is and trends.Althoughthereisarangeinthevaluesof[M/H] 362 orNGC1261;however,thedifferencein[M/H]for 1261 isnearontheskytoNGC362,indicationsfrom The clustersarelocatedatahighGalacticlatitudeandthe The traditionalmethodtodeterminerelativedistance a) Horizontal-BranchConsiderations VI. RELATIVEDISTANCEMODULI V. REDDENINGVALUES 1691 1989AJ 97.1688B 1692 MICHAELBOLTE:NGC288 parameters bewellunderstood. the intrinsicluminosityduetodifferentvaluesforcluster fraction Ythemassofheliumcore,and[O/Fe](see, perature dependsprimarilyon[Fe/H],thehelium-mass nambé 1987).Thecontroversyovertheextenttowhich e.g., IbenandRood1970;SweigartGross1978;Tor- stepped bychoosingclustersthataresimilarinmetallicity. between anyofthethreeclustersunderconsiderationhere tion rangefrom0.0(Jones,Latham,andCarney1988)to Recent estimatesoftheslopeAf(HB)-[Fe/H]rela- fore, withanupperlimitforthedifferencein[Fe/H] ZAHB Mis0.04mag. horizontal-branch morphologyforclustersthatcontainRR that Y=0.24±0.01withnodependenceonmetallicityor in Y.Caputoetû/.(1987)alsousedtheRmethodtoestimate and noevidenceforasignificantcluster-to-clustervariation Buzzoni etal.(1983)findameanvalueof7=0.23+0.02 come by.Basedontheresultsofso-called“Rmethod” A [Fe/H]=0.2dex,thelargestexpecteddifferencein ple ofhorizontalbranchandgiantstars,arenot NGC 288andderive7=0.23+0.03.Ourdatain the Buzzonietal.andCaputo al.resultswefeelitreason- sufficient toestimateRor7accurately. However,basedon Lyrae stars.Buonannoetal.(1984)applytheRmethodto tal branchstardependsmoststrongly on7andonlyweakly able toassumeasinglevalueof 7forallthreeclusters. f on [M/H]andthetotalstellar massattheclusterturnoff. [Fe/H] affectsthehorizontalbranchhasbeenlargelyside- ~0.2 (see,e.g.,King,Demarque,andGreen1988).There- F (Iben 1968)appliedto15clusters,includingNGC362, 1261 donotrepresentanysortofacomplete(orlarge)sam- v (e.g., SweigartandGross1978), thecoremassofahorizon- The luminosityofZAHBstarsatagiveneffectivetem- © American Astronomical Society • Provided by the NASA Astrophysics Data System Evidence forheliumabundancesinclustersishardto According toredgiantandhorizontal-branch models a 6 6 thesevaluesassume[M/H]=—0.8for47Tucanae CHF =Canterna,Harris,andFerrall(1982);4Äresolutionspectra basedonthemeasurementsofasingleRRLyraestar ZW =ZinnandWest(1984);compilation Smith =(1984);Qjg Grat ton=(1987a;1987b);4Aresolutionspectra Geisler =(1986;1988);WashingtonPhotometry CS =CostarandSmith(1988);AS CD =CaldwellandDickens(1988);0.5Âresolutionspectra NGC 288-1.4-1.0-1.38....-1.30-1.20 NGC 362-1.1-0.9-1.15-1.20-1.03-1.29 NGC 1261-1.08-1.0....-1.21-1.30 a Cluster CHFCDCSGeislerGrattonSmithZW Table I.Metallicityestimates. only considerthepossibledifferencesduetodifferentcluster For ourcaseofsimilarcluster[M/H]and7values,weneed turnoff massesresultingfromanyagedifferencesbetween only asmallamountinthecourseofseveralbillionyears. mass ofstarsattheturnoffaglobularclusterchangesby leisurely paceforstarsnearthemassofSun,total the clusters.Becausestellarevolutionproceedsatsucha Z =0.001isochronesfromVandenBergandBell(1985)in- For example,examinationoftheturnoffmassesfor from the12Gyrisochroneto18isochrone.Accord- dicates thattheturnoffmasschangesfrom—0.89to—0.80 noff-mass differencewillresultinacore-massof ing tothemodelstabulatedinSweigartandGross,thistur- less than0.01whichwill,inturn,resultanegligible ZAHB luminositydifferenceforclustersofthesetwoages. of thebestavailableinformationconcerningoxygenabun- two starsinNGC288andonlyasinglestar362.As estimated byPilachowski,Sneden,andWallerstein(1983), reason toassumeotherthanaconstant [O/Fe]—+0.3for the haloingeneral(see,e.g.,Sneden1985),thatthereisno dance intheseclustersspecifically,andmetal-poorstars was thecaseforheliumcontent,weconcludeonbasis spectively. TheGrattonresultisbasedonmeasurementsof Fe] -+0.5and0.2forNGC288362,re- Fe]—f-0.4 forbothclusters,whileGrattonfinds[O/ studies byPilachowskiandhercollaboratorsfind[O/ Pilachowski andSneden(1983),Gratton1987a).The NGC 288and362,theabundanceofoxygenhasbeen these threeclusters. vious paragraphisthattherelative distancesofNGC288, posing theCMDsofclusters andmakingaverticalslid- ing fitoftheZAHBs.Thisprocedure isstraightforwardfor NGC 362,and1261can bedeterminedbysuperim- The finalparametertoconsideris[O/Fe].Forstarsin The overallconclusionfromthe considerationsofthepre- 1692 1989AJ 97.1688B but thesensitivityofderiveddistancestoB—Vcolors branches evenlarger.Withsuch apparentlysimilarmetal two clustersshouldhavethesame colorexcess;however, must beborneinmind. abundances, thegiantbranches areexpectedtocoincide. that wouldmakethecolordifference betweenthegiant ZAHB fitisreddeningindependent) inthesensethat two methodsmaybetheresultof usinganincorrectvaluefor main-sequence-fitting methodisexcellentfortheNGC288/ consistency checksthatalleviatethisproblemsomewhat, mation forseveraldifferentregionsintheCMD,thereare derived distancemodulusof0.1mag.Becausewehaveinfor- NGC 1261comparisonandreasonablygoodforthe precision ofthephotometry—willresultinanerror the orderofuncertaintyinE(i?—F)valuesor AE(Æ -F)forNGC362and NGC1261(recallthatthe in thecolorofmainsequence0.02mag—whichison ness ofthemainsequenceinF(2?—F)plane.Anerror 362/NGC 1261comparison.Thediscrepancybetweenthe branches, theonlytechniqueusedtoestimaterelative the smalldifferencesinE(2?—V)relativedistancemod- until themainsequencesarecoincident. uli arederivedbyverticallyslidingthesuperimposedCMDs suming thesameYforallthreeclusters,thisleavesonly abundance ofstarsinthecluster.Givenrelative[Fe/H] the [Fe/H]ofstarsincluster,valueE(i?—F) primarily bytheapparentdistancemodulustocluster, tions. distances willbematchingthelower-main-sequenceposi- tance modulusis(m—M)=1.33. are insimilarevolutionarystages.Theindicatedrelativedis- horizontal-branch starsofsimilarcolorinthetwoclusters horizontal branchesforthecasewhereitisassumedthat relative distancemoduliasanunknown.Aftercorrectingfor and reddeningvaluesdiscussedinSecs.IVV,as- appropriate tothecluster,andalesserextenthelium unevolved mainsequence.Foranyclusterthisisdetermined can bederivedisthepositioninV(B—V)planeof For NGC288and362,withnooverlapofhorizontal Fig. 4showsthecomparisonofNGC288and1261 from horizontal-branchconsiderations.Thetoppanelof make areasonableguessastotherelativedistancemoduli blue ZAHBortheymayhaveevolvedtobrighterluminosi- ties. ForthecaseofNGC288and1261itispossibleto tionary statusofthebluehorizontal-branchstarsinNGC tent inthecaseofNGC288and362.(2)Theevolu- 288 andNGC1261isunknown—thesestarsmaybeonthe small forthecaseofNGC288and1261,nonexis- two reasons.(1)Theoverlapofthehorizontalbranchesis NGC 362or1261viathismethodismoredifficultfor redward oftheinstabilitystrip.Wefind(m—M) NGC 362and1261,whichhavewell-definedZAHBs 1693 MICHAELBOLTE:NGC288 288i61 362 — (mM)=1.31.AcomparisonofNGC288to l26 The consistencybetweentheZAHBmethodand Using themain-sequencecomparisontechnique,wefind The obviousdifficultyofthismethodisduetothesteep- A secondfiducialmarkbywhichrelativeclusterdistances (m —M)=-1.20mag. (m -M)(m-M)=1.29mag, (m —Af)M)=-0.10mag, © American Astronomical Society • Provided by the NASA Astrophysics Data System 3621261 2SS1261 2836 b)Unevolved Main-SequenceConsiderations branches areconsistentwiththeclustershavingsimilarmet- case fortheNGC288/NGC362comparison,thereisexcel- turnoff region,andsubgiantgiantbranches.Aswasthe NGC 288and1261aswelltheirmainsequences, abundance indicatedbythegiant-branchcolorsisthenin- sequences ).Thiscomparisonisnotacceptableastherelative NGC 362mainsequence(comparedtothe288cluster or fortheNGC362giantbranchandabluercolor eliminate thesedifferences,thisresultsinamuchreddercol- subgiant branches.Ifthedistancemoduliareadjustedto difference intheFmagnitudeofclusterturnoffsand very wellovernearly2mag.Thereis,however,a0.4mag and thepositionsofunevolvedmainsequencesmatch al abundances,withNGC288possiblythemoremetalpoor, that theNGC288turnoffisinfactsignificantlyfainter troscopic abundancemeasurements.Wefeelitmorelikely and bothCMDindicatorswouldbeinconflictwiththespec- common reddeninganddistance.Thepositionsoftheirgiant ments ini?—Fandrequiredtobringtheclustersa absolute visualmagnitudethantheNGC362turnoff. consistent withthatindicatedbythemain-sequencecolors, ridgelines forthetwoclustersaftermakingsmalladjust- those inNGC1261.Figure3showstheclustersequence most securebecausethedataintheseclustersaresuperiorto main-sequence ridgeline. measured HBstars,oranerrorinplacingtheNGC1261 level oftheZAHBNGC362duetosmallnumber Other possibleexplanationswouldbeanerrorinplacingthe bring theclusterstocommonreddening anddistance-modulusvalues. the NGC362ridgeline0.025magto blueand0.10magbrighterto Fig. 3.Ridge-linecomparisonofNGC 288andNGC362aftershifting The panelsofFig.4comparethehorizontalbranches The comparisonbetweenNGC288and362isthe VIL MAIN-SEQUENCECOMPARISONS b) NGC288/NGC1261 a) NGC288/NGC362 B-V 1693 1989AJ 97.1688B 1694 MICHAELBOLTE:NGC288 turnoffs andsubgiantbranches.Inthiscasethedifferenceis while theNGC1261starsin sameB—Vrangeareonthe firm criterionforrejectingthisvaluerelativedistance worse, but,withoutknowingtheevolutionarystatusof match shownintheupperpanelofFig.5isalsoclearly conflicts betweenthevariousCMDabundanceindicators. is possibletoassumealargerA(m—M)eliminatethe lent agreementatallpointsintheCMDexceptcluster tances totheclusterswouldbe indicated, whichwouldlead stars haveevolvedabovethe ZAHB whiletheNGC288 ZAHB, Fig.5wouldbeanacceptable fit.IftheNGC1261 stars measuredinNGC288haveevolvedabovetheZAHB, moduli. Forexample,ifthethreereddesthorizontal-branch stars with0.00