1983ApJ...264..206J _1- The AstrophysicalJournal,264:206-214,1983January1 © 1983.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. made estimatesoftheagesglobularclusters,andboth find thatthereisasubstantialrangeintheirages difficulties forgalacticformationtheoriesinwhichthe correlated withmetallicity,aresultwhichwouldcause galaxy. Inaddition,theirageestimatesaresubstantially globular clustersformedinarapidlycollapsingproto- constant isaslargeif=95kmsMpc larger thantheageofuniverseifHubble and Demarqueusedsomewhatdifferentprocedures,both must bespecifiedinordertoderiveitsage,but their methodsrequiredthatthecompositionofacluster (Aaronson etal1980).Furthermore,althoughCarney previously. Adecreaseinmetallicitywoulddramatically clusters arenotasmetalrichhadbeenthought Pilachowski, Snedon,andCanterna(1980)Cohen thereby removingthecorrelationofagewithmetallicity increase theestimatedagesofmetal-richclusters, (1980) haveconcludedthatthe“metal-rich”globular diagrams ofclusterswiththeoreticalisochronesrequires but alsoasomewhatsubjective judgmentofthebestfit. not onlyanassumptionastothecluster’scomposition The purposeofthispaperis to showthat,byreducing (but leavingtheconflictwithalargeHubbleconstant). the informationinaC-Mdiagram toafewnumerical color ofthegiantbranchat some absolutemagnitude) quantities (suchasthemain-sequence turnoffcolororthe Recently Carney(1980)andDemarquehave The usualapproachforcomparingcolor-magnitude © American Astronomical Society • Provided by theNASA Astrophysics Data System 1 possible tosolvesimultaneouslyforage,heavy-elementabundance,andheliumabundance.This the meancolorindexorabsolutemagnitudeatvariouspointsalongprincipalsequences.By relating thesequantitiestotheanalogousparametersderivedfromtheoreticalisochronesitis analysis leadsustoconcludethatthereisnocorrelationofglobularclusteragewithcomposition the substantialobservationalandtheoreticaluncertaintiespreventaconclusivestatement, and thattheoldestopenclustersareaboutone-halfageofglobularclusters.Although that theglobularshaveanageofabout16.6±0.5Gyr,andmetal-richclusters47Tue evidence suggeststhattheopenclustershaveahigherheliumabundancethanglobularclusters, and M71have[Fe/H]~—0.9.Changesinthemetallicityscaleormixinglengthcouldsubstantially Subject headings:clustersglobular—opencosmologystarsabundances is aslarge100kms~Mpc"\thenfundamentalchangesinstellarevolutiontheoryarerequired. corrections andwouldyieldclusterpropertiesinconsistentwithobservation.IftheHubbleconstant alter thesevalues.Nevertheless,globularclusteragesasyoung10Gyrwouldrequirelarge From publishedcolor-magnitudediagramsof23globularandopenclusterswehavemeasured I. INTRODUCTION THE AGESANDCOMPOSITIONSOFOLDCLUSTERS stars :evolution—interiors Received 1982February1;acceptedJune21 Yale UniversityObservatory Pierre Demarque Kenneth Janes Boston University ABSTRACT AND 206 measured fromthetheoreticaldiagrams,simultaneous which canbecompareddirectlywiththesamequantities been usedbyTwarogandAnthony-Twarog(1981)to reliability estimated.Asomewhatsimilarapproachhas age andcompositionestimatescanbemadetheir published anextensivegridoftheoreticalisochrones results are,ingeneral,consistentwiththosefoundhere. study theagesandmetallicitiesofopenclusters;their which theylatertransformedintotheM-(B—V)plane can, inprinciple,becompareddirectlywithobserved color-magnitude diagrams,andinordertofacilitatethis values ofcolorandabsolutemagnitudeatvariouspoints comparison wehavereducedeachisochronetoasetof (Ciardullo andDemarque1979,hereafterCD9).These magnitudes 0,4-1,4-2,4-6andtheabsolutemagnitude color indexatthemain-sequenceturnoffandabsolute along thesequence.Specifically,wemeasured(B—V) at theturnoffandinflectionpointbetween turnoff andthebaseofgiantbranch. v originals ofthefiguresinCD9forisochroneswith The colorindexparameters (B—V),and and 0.30;age=2,5,10, 15,and20or22Gyr. Z =0.04,0.01,0.004,0.001,0.0004, and0.0001;Y=0.20 versus heavy-elementabundance (Z)andsmoothcurves (B—V), whichrepresentthe giantbranch,wereplotted 0u 2 Ciardullo andDemarque(1977,hereafterCD7) The valuesoftheseparametersweremeasuredfrom II. PARAMETERIZATIONOFISOCHRONES 1983ApJ...264..206J heavy-element abundance,logZ,forisochronesof2,5,10,15,and20Gyr.(left)HeliumY=0.2.(right)0.3. Fig. 1.—Thegiantbranchcolorindex(B—V),fromtheCiardulloandDemarque(1979)isochronesmeasuredatM=0,plottedvs. 0v © American Astronomical Society • Provided by theNASA Astrophysics Data System Fig. 2.—Thegiantbranchcolorindex(B—V)measuredasin1butatM=1,plottedvs.logZ uv Fig. 3.—Thegiantbranchcolorindex (B—V),measuredasinFig.1butatM=2,plottedvs.logZ 2v 1983ApJ...264..206J heavy-element abundancesZ,asshown,andforheliumabundance Ciardullo andDemarque(1979)isochronesplottedvs.log(age)for 208 Y =0.2(top)and0.3(bottom). Fig. 4.—Themain-sequenceturnoffcolorindex(B—V)fromthe Fig. 6.—Sameas4fortheabsolute magnitudeattheinflectionpointbetweenturnoffandbase ofthegiantbranchM Fig. 5.—Sameas4fortheturn-off absolutemagnitudeMvs.log(age) t vi vt © American Astronomical Society • Provided by theNASA Astrophysics Data System JANES ANDDEMARQUE The turnoffparameters(B—V),Mandwere each ofthefiveagesandforbothvaluesY(Figs.1-3). were drawntorepresentthecolorversusZsequenceat plotted versuslog(age)forthevariousvaluesofZ magnitude diagramhasbeenparameterizedinthesame estimate ofZ,Y,andageforanyclusterifitscolor- are affectedbyZandonlyslightlyageorY,theturnoff fashion astheisochrones.Thegiantbranchparameters (B—V) wasplottedversusYatvariousvaluesofZ (Figs. 4-6).Finally,themain-sequenceparameter main sequenceparameterisaffectedbyYandZ.Thus, parameters areaffectedbothbyageandZ,the (Fig. 7). be usedtoestimatetheassumedheliumabundance,but, return toFigures1-3foranotheriteration.Figure7can the ageestimatesfromFigures4-6,and,ifnecessary, helium abundance,findZfromFigures1-3,thenrefine one canmakearoughestimateofcluster’sageand necessary toassumeaheliumabundance. required toobtainmeaningfulresults,itisgenerally since main-sequencephotometryofhighqualityis taken atfacevalue,thismethodleadstoasimultaneous solution forY,Z,andage.Unfortunately,thesubstantial tvtvi 6 Figures 1-7permitonetomakeasimultaneous If theobservedC-Mdiagramsandisochronesare Vol. 264 1983ApJ...264..206J tially overwhelming.Onthetheoreticalsideitisnot theoretical andobservationaluncertaintiesarepoten- possible totryallcombinationsofparameters, Varner 1980showthatitprobablyactuallyvarieswith to scale-heightratio(a)wasarbitrarilysetequalone. but somenumericalexperimentsindicatetheextentof Ciardullo andDemarque(1979)isochronesvs.theheliumabundance depth inastar),itisessentiallyfreeparameter.CD9 Since theactualvalueofaisunknown(Deupreeand 0.02 magredderrelativetothestandardmix.Since suspected forglobularclusters,andplausiblealterations solar abundanceratios,butnonsolarratiosarewidely some oftheuncertainties. found thatavalueof=1.5yieldedgiantbranches magnitude enhancementinNorCcausesMand For example,Demarque(1980)hasinvestigatedthe in abundanceratioscouldsubstantiallyaffecttheresults. with abetterfittooldopenclusters,andtheywere to become0.15magfainterand(B—V) results ofvaryingtheabundanceratios[C/Fe]and enhancement wouldcauseaclustertoappearbetoo other parametersarenotseriouslyaffected,suchan able tointroducearelationaltertheeffectivetempera- [N/Fe] andfindsthat,forasyntheticclusterwith tures oftheoriginalisochronestosimulateanewvalue old byabout15%. Y forvariousvaluesofZ,asshown. log a=+0.05forZ0.0001isochronewouldaffect of a.Usingthisrelation,wefindthatachange No. 1,1983 the giantbranchparameters by about—0.04magand the theoreticalisochroneswould inturncauseanactual cluster toappearmoremetal richby0.12inlogZand Y =0.25,Z0.004,andanageof15Gyr,order older by0.05inlog(age). (B—V) byabout—0.01mag. Thesecolorchangesin vivt t t In theoriginalCD7isochrones,mixing-length The CD9isochronesareallbasedonmodelswith Fig. 7.—Themain-sequencecolorindex(B—V)fromthe 6 © American Astronomical Society • Provided by theNASA Astrophysics Data System OLD CLUSTERS evaluate quantitatively.Theyincludeuncertaintiesinthe plane thatdependonthemodelatmospheresand bolometric correctionsused(seeCD9)andacertain transformation fromtheM-Tplaneto-(B—V) clusters andmodelswithappropriateparameters.Thus, from alteringatoforcegoodfitbetweenoldopen in anabsolutesense,theuncertaintiesvalues amount ofinconsistencyandcircularitythatalsoresults corrections tothemodelsaresuchthat,ifacorrection theless, forthesakeofcomparisononeclusterwith of therelationsinFigures1-7aresubstantial.Never- another, itisimportanttorecognizethattheeffectsof properties in§IV. reduces thederivedageofacluster,itwilltendto constraints tobeputontherangeofreasonablecluster diagrams havebeenpublishedwhichgoasfaintthe main-sequence turnoff.Furthermore,thedataarefar increase itsmetallicity.Itisthisfactwhichpermitssome from uniformbothwithrespecttoqualityandin coverage oftheC-Mdiagram;therearehints magnitude ofmetal-poorRRLyraestars(Ftypeclusters) the tabulationbyHarris(1980),whogavevaluesfor distances andreddeningsarewellknown.Inspiteof and introducingscaleerrorsinothers,notallofthe affecting theshapesofdiagramsinsomecases systematic errorsinsomeofthephotometry,possibly vQff corrections tothepublishedphotometryinorder these difficulties,wemadenoattempttomakeany The lattercategoryincludesPal12,47Tue,andM71. is assumedtobeM=+0.6andforthemetal-richRR Janes (1979),KalinowskiandAdler summarizes theavailableclusterdataforglobularand avoid introducinganybiasintheanalysis.Table1 The distancemoduliformostoftheopenclusterswere Lyrae stars(Gtypeclusters),M=+0.9(Harris1976). be amajorfactorinthefollowingdiscussion. errors aresmall;sointhereddeningshouldnot Racine (1979)andtheopenclusterreddeningsfrom old openclusters. determined followingtheprocedureoutlinedbyJanes (visual) magnitudeofthehorizontalbranch.Theabsolute and, exceptforM71,NGC6791,andTrumpler5,the matched totheHyadesmainsequenceaftermakinga (1982). Mostoftheclustersarerelativelyunreddened, correction forthedifferenceincompositionbetween estimated inadvance,butthe correctionsweresmall cluster andHyades.Strictlyspeaking,thisintroducesa (1979). Inthismethod,aclustermainsequenceis little circularreasoningsincethecompositionmustbe branch hasM=+0.9. estimated byassumingthat theclumpongiant distance modulioftwoclusters (Mel66andTr5)were and donotsignificantlyaffect thepresentresults.The v v v Other theoreticaluncertaintiesaremoredifficultto A relativelysmallnumberofcolor-magnitude The globularclusterdistancemoduliarederivedfrom The globularclusterreddeningsarefromHarrisand III. PARAMETERIZATIONOFCOLOR-MAGNITUDE DIAGRAMS 209 1983ApJ...264..206J NGC 104(47Tue). NGC 288 distance ofanindividualclusterwill,course,affect the accuracyofclusterdistances.Anerrorin NGC 5053 NGC 3201 NGC 5139(œCen). but theremayalsobeerrorsintheoverallclusterdistance all oftheparametersforthatcluster(except[B—V]), NGC 5904(M5) NGC 5272(M3).... data. Harris(1976)estimatesanuncertaintyof±0.2 NGC 6341(M92).. NGC 6205(M13).. which isthereforealowerlimittotheuncertaintiesin mag intheabsolutemagnitudesoffieldRRLyraestars, scale thatwouldintroducesystematicerrorsintoallthe NGC 6752 NGC 6397 cluster distances,butthepresentdistancescaledoesagree NGC 7099(M30).. NGC 7078(M15).. NGC 6838(M71).. 210 diagram torepresentthebestestimateofprincipal globular clustermainsequences. with Carney’s(19796)comparisonoffieldsubdwarfsand Tr 5 Pal 12 NGC 2682(M67) NGC 2506 NGC 2420 NGC 2243 NGC 188 were measuredfromthisline.Thevaluesaregivenin sequences ofthecluster,andvariousparameters et al.1976.(6)CannonandStewart1981.(7)JohnsonSandage1956.(8)1970.(9)Arp1962.(10)Baumal1959.(11)Alcaino NGC 6791 cluster sequencesistheresult ofacombination assumption thatthedispersion inthedataalong Table 1.Thevalidityofthisapproachrestsonthe Canterna 1980.(17)McClureandTwarog1977.(18)Kalinowski1979.(19)vandenBergh(20)etal.1974.(21) al. and Liller1980«.(12)Carney1979«.(13)ArpHartwick1971.(14)SandageKatern1977.(15)Alcaino19806.(16)Harris Mel 66 photometric errorsandapossible intrinsicdispersionin stellar properties,but,if there wereasignificant t proportion ofundetectedcompanion stars(eitheractual 1981. (22)Racine1971.(23)Anthony-Twarogetal.1979.(24)Kinman1965. The reliabilityoftheclusterparametersisdefinedby References.—(1) BesserandHartwick1977.(2)AlcainoLiller1980c.(3)Olzewskietal1981.(4)(5)Walker For eachcluster,alinewasdrawnthroughtheC-M © American Astronomical Society • Provided by theNASA Astrophysics Data System Cluster (m-M) E(B-V)(B-V)(B—V) v012t6 13.16 14.15 14.70 16.03 14.51 15.00 13.92 13.20 12.30 14.50 14.35 15.26 13.55 14.60 16.20 12.60 13.00 12.0: 11.90 11.10 13.80 13.60 9.65 0.03 0.04 0.21 0.03 0.01 0.11 0.01 0.03 0.03 0.18 0.01 0.02 0.28 0.12 0.02 0.05 0.02 0.06 0.64: 0.08 0.05 0.11 0.14 Photometric ParametersofClusters JANES ANDDEMARQUE 0.93 0.72 0.82 0.86 0.86 0.88 0.86 0.77 0.73 0.88 0.80 0.75 0.98 1.12 1.13 00 23 36 62 10 Globular Clusters Open Clusters TABLE 1 0.93 0.67 0.74 0.82 0.78 0.76 0.76 0.80 0.73 0.69 0.77 0.70 0.66 0.93 0.96: 0.87 0.88 0.91 1.30 1.11 1.00 1.32 1.02 binaries oraccidentalcombinationsofstellarimages), the measuredmain-sequenceandturnoffcolorswouldbe the giantbranches,andpossiblymainsequences,of systematically tooredbysomesmallamount.Certainly some globularclustersareintrinsicallybroadened,but, we haveassumedthatthesephenomenacanbetreated as randomuncertaintiesindefiningtheparametersof in theabsenceofanyclearevidencetocontrary, the clusters. more thanonce,permittingonetomakeanestimateof Table 1.Inordertogetalargersample,wehave the accuracyofphotometricparametersgivenin given inthecatalogofPhilip,Cullen,andWhite(1976) measured thegiantbranchparametersforallclusters and inmorerecentreferenceslistedbyHarris(1980). estimates canbetranslatedinto estimatesoftheaccuracy error ofeachparameter(see Table2).Theseerror From thedispersioninvalues,weestimatetypical of themeasurementsY,Z, andage(alsoinTable2). certainties forindividualclusters are±0.15inlogZ, From thesevalues,weestimate thatthetypicalun- Some oftheglobularclustershavebeenobserved 0.83 0.62 0.67 0.79 0.71 0.72 0.71 0.74 0.67 0.65 0.70 0.66 0.61 0.82 0.93: 0.80 0.99 0.82: 0.89 0.81 0.91 1.08 1.21 0.54 0.40 0.45 0.35 0.38 0.42 0.43 0.40 0.32 0.39 0.40 0.35 0.50 0.50 0.50 0.57: 0.40 0.60 0.51 0.52 0.34 0.38 0.70 0.67 0.69 0.53 0.63 0.53 0.67 0.58 0.62 0.80 0.86 0.86 0.78 0.77 0.94 0.62 3.50 3.70 3.95 3.45 3.75 M: 3.40 3.50 3.45 3.40 3.50 3.45 3.40 3.30 3.80 3.55 2.10 2.35 3.10 3.1: 2.95 3.90 3.65 3.10 v 4.40 4.00 4.00 4.40 4.65 4.05 4.15 M 4.10 4.25 4.00 3.95 4.40 4.10 4.00 4.10 3.85 3.7: 4.25 2.90 3.40 3.40 3.10 3.20 v( Vol. 264 Refs. 8, 14 10, 8 2, 3 7,8 22 21 20 24 23 12 13 11 15 19 18 17 16 4 9 6 5 8 1 1983ApJ...264..206J No. 1,1983 course, theuncertaintiesindistance,reddening,and the modelsthemselves. the observationaldatapermitonetocalculatecluster properties, subjecttothevariouscaveatsdescribed sequence color(B—V),weassumedthatallofthe above. Becauseofthelargeuncertaintiesinmain- globular clustershavethesameheliumabundance (Y =0.2)andthattheopenclustershaveY0.3.For ±0.06 inlog(age),and±0.15neglecting,of 6 The theoreticalrelationsinFigures1-7togetherwith NGC 5053. NGC288 .. NGC 104.. NGC 6397. NGC 6205. NGC 5904. NGC 5272. NGC 5139. NGC 3201. NGC 6838. NGC 6752. NGC 6341. NGC 7099. NGC 7078. Tr 5 Pal 12 NGC 188.. NGC 2682. NGC 2420. NGC 2243. NGC 6791. NGC 2506. Mel 66 © American Astronomical Society • Provided by theNASA Astrophysics Data System IV. DISCUSSIONOFCLUSTERPROPERTIES Cluster M 50.15...±0.06 (B-V)o 200.03±0.17±0.02±0.03 M 60.15...±0.06 (B-V) 150.03±0.22±0.02±0.03 (B-V^ 200.03±0.19±0.02±0.03 (B—V) 60.03...±0.07 (B-V) 40.05...±0.12 vi vt 2 t 6 3 AssumingatypicalclusterwithZ=0.0004,age=15Gyr,Y0.2. 0.0007 0.0032 0.0003 0.0003 0.0001 0.0003 0.0004 0.0001 0.0004 0.00004 Parameter ClustersErrorlogZ(age)Y 0.0033 0.00005 0.0011 0.0058 0.010 0.023 0.0032 0.0026 0.00003 0.0008 0.0004 0.0003 0.0002 0.0004 0.0003 0.0002 0.00006 0.0026 0.0006 0.00006 0.00003 0.0014 0.0046 0.032 0.0079 0.0024 0.013 0.0042 0.026 0.0076 Effects ofPhotometricErrors No. ofTypical— 0.0017 0.0024 0.0007 0.0006 0.0001 0.0003 0.0005 0.0006 0.0022 0.0009 0.0003 0.0002 0.0002 0.00005 Zb- v 0.0018 0.0068 0.022 0.0043 0.0069 0.0026 0.0063 0.013 0.050 OLD CLUSTERS Cluster Properties Globular Clusters Open Clusters TABLE 2 TABLE 3 0.0010 0.0027 0.0004 0.0005 0.0004 0.00005 0.0002 0.0002 0.0001 0.0004 0.0006 0.0027 0.0001 0.00004 0.0014 0.0056 ± 0.027 ± 0.0039 ± 0.0069 ± 0.0025 ± 0.017 ± 0.038 ± 0.0080 ± the initialsolutionwealsoassumedglobularandopen cluster agesof15Gyrand5Gyr,respectively.With these assumptions,Figures1-3yieldthree(partly) of thegiantbranchparameters,(B—F),(B—V)and independent estimatesoflogZfromtheobservedvalues turnoff parameters(B—V),Mandleadtothree estimates oflog(age).Forthoseclusterswithderived the processisrepeateduntilgiantbranchparameters (B—V). TheaveragevalueoflogZ,alongwiththe the main-sequenceparameter(B—V)andestimated and heavy-elementabundances.Finally,insomecases and turnoffparametersyieldself-consistentvaluesofage ages significantlydifferentfromtheinitialassumption, 0u tvivt 2 6
1983Apj...264..206J the Astrophysical Journal, 264:206-214
