A&Amanuscriptno. ASTRONOMY (willbeinsertedbyhandlater) AND Yourthesauruscodesare: ASTROPHYSICS 05(08.01.1;08.16.3;11.01.1;10.07.2) The red giant branches of Galactic globular clusters in the − [(V I) , M ] plane: metallicity indices and morphology 0 V IvoSaviane1,AlfredRosenberg2,3,GiampaoloPiotto1,andAntonioAparicio4 1 DipartimentodiAstronomia,Universita`diPadova,vicolodell’Osservatorio5,I-35122Padova,Italy 0 2 TelescopioNazionaleGalileo,vicolodell’Osservatorio5,I-35122Padova,Italy 0 3 OsservatorioAstronomicodiPadova,vicolodell’Osservatorio5,I-35122Padova,Italy 0 4 InstitutodeAstrof`ısicadeCanarias,ViaLactea,E-38200LaLaguna,Tenerife,Spain 2 n Received/Accepted a J 4 Abstract. Thepurposeofthisstudyistocarryoutathorough Table1.Theinputparametersfortheobservationalsample 1 investigation of the changes in morphology of the red giant 1 branch (RGB) of Galactic globularclusters (GGC) as a func- [Fe/H] v tionofmetallicity,intheV,Ibands.Tothisaim,twokeypoints NGC E(B−V) E(V−I) ZW CG RHS97 VHB 6 aredevelopedinthecourseoftheanalysis. 104 0.05 0.06 -0.71 -0.70 -0.78 14.05±0.05 6 2 (a)UsingourphotometricV,I databaseforGalacticglob- 288 0.03 0.04 -1.40 -1.07 -1.14 15.40±0.05 1 ular clusters (the largest homogeneous data sample to date; 362 0.05 0.06 -1.33 -1.15 -1.09 15.51±0.05 0 Rosenberg et al. 1999a) we measure a complete set of metal- 1261 0.01 0.01 -1.32 — -1.08 16.68±0.05 0 licityindices,basedonthemorphologyandpositionofthered- 1851 0.02 0.03 -1.23 — -1.03 16.18±0.05 0 giantbranch.Inparticular,weprovideherethefirstcalibration 1904 0.01 0.01 -1.67 -1.37 -1.37 16.15±0.05 h/ oftheS,∆V and∆V indicesinthe(V −I,V)plane.We 3201 0.21 0.27 -1.53 -1.23 -1.24 14.75±0.05 1.1 1.4 p showthatourindicesareinternallyconsistent,andwecalibrate 4590 0.04 0.05 -2.11 -1.99 -2.00 15.75±0.10 - 4833 0.33 0.42 -1.92 -1.58 -1.71 15.70±0.10 o each index in terms of metallicity, both on the Zinn & West 5272 0.01 0.01 -1.66 — -1.33 15.58±0.05 r (1984)andtheCarretta&Gratton(1997)scales.Ournewcali- ast brationsofthe(V−I)0,g,∆V1.2,(V−I)−3.0and(V−I)−3.5 55486967 00..0008 00..0100 --21..2923 -1.—59 --12..7133 1166..3600±±00..0150 indicesareconsistentwithexistingrelations. : 5904 0.03 0.04 -1.38 -1.11 -1.12 15.00±0.05 v i (b)UsingagridofselectedRGBfiducialpoints,wedefine 6093 0.18 0.23 -1.75 — -1.47 16.25±0.05 X afunctioninthe(V −I) ,M ,[Fe/H]spacewhichisableto 6171 0.33 0.42 -1.09 — -0.95 15.65±0.05 0 I r reproducethe whole set ofGGC giantbranchesin terms ofa 6205 0.02 0.03 -1.63 -1.39 -1.33 14.95±0.10 a singleparameter(themetallicity).Asafirsttest,weshowthat 6218 0.19 0.24 -1.40 — -1.14 14.70±0.10 thefunctionisabletopredictthecorrecttrendofourobserved 6254 0.28 0.36 -1.55 -1.41 -1.25 15.05±0.10 indiceswithmetallicity. 6341 0.02 0.03 -2.24 — -2.10 15.20±0.10 6352 0.21 0.27 -0.50 -0.64 -0.70 15.25±0.05 The usage of this functionwill improvethe currentdeter- 6362 0.09 0.12 -1.18 -0.96 -0.99 15.35±0.05 minationsofmetallicityanddistanceswithintheLocalGroup, 6397 0.18 0.23 -1.94 -1.82 -1.76 12.95±0.10 since it allows to easily map (V − I)0,MI coordinates into 6541 0.12 0.15 -1.79 — -1.53 15.40±0.10 [Fe/H],MI ones. To this aim the “synthetic” RGB distribu- 6637 0.17 0.22 -0.72 — -0.78 15.95±0.05 tion is generatedbothfor the currentlyused Lee et al. (1990) 6656 0.34 0.44 -1.75 — -1.41 14.25±0.10 distance scale, and for the most recent results on the RR Lyr 6681 0.07 0.09 -1.64 — -1.35 15.70±0.05 distancescale. 6723 0.05 0.06 -1.12 — -0.96 15.45±0.05 6752 0.04 0.05 -1.54 -1.42 -1.24 13.80±0.10 6779 0.20 0.26 -1.94 — -1.61 16.30±0.05 Keywords:Stars:abundances-Stars:PopulationII-Galaxies: 6809 0.07 0.09 -1.80 — -1.54 14.45±0.10 abundances-Globularclusters:general 7078 0.09 0.12 -2.13 -2.12 -2.02 15.90±0.05 1. Introduction In very recenttimes, new determinationsof Galactic globular cluster(GGC) metallicitieshaveprovideduswithnewhomo- Sendoffprintrequeststo:IvoSaviane Correspondenceto:[email protected] 2 IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters Fig.1.Graphicalrepresentationofthemetallicityindices(part1)thatweremeasuredontheselectedclusters.(Left)Theobserved CMDoftheintermediate-metallicityclusterNGC1851anditsfiducialRGB(solidline).Thefiduciallocuswasobtainedbyfitting Eq.(1)tothedata.ThetwocrossesmarkthecoloroftheRGBattheleveloftheHB,anditscolor2magsbrighterthantheHB. The slope of the line connectingthe two points is the S index. (Right) On the color de-reddened CMD other four indices are marked.Fromfaintertobrightermagnitudes,theRGBcolorattheleveloftheHB,andtheV magnitudedifferencebetweenthis pointandthoseat(V −I) =1.1,1.2and1.4..ThedashedlinerepresentstheadoptedHBlevel,V =16.18 0 HB geneous[Fe/H] scales.Inparticular,Carretta&Gratton(1997; exploitthemtoperformathoroughanalysisofthemorphology CG) obtained metallicities from high resolution spectroscopy oftheRGBasafunctionofthecluster’smetallicity.Asafirst for24GGCs, withaninternaluncertaintyof0.06dex.Foran step, we want to obtain a new improved calibration of a few even larger sample of 71 GGCs, metallicities have been ob- classicalphotometricmetallicityindices.Secondly,wewantto tainedbyRutledgeetal.(1997;RHS97)basedonspectroscopy providetothecommunityaself-consistent,analytic,familyof of the CaII infrared triplet. The equivalentwidths of the CaII giantbranches,whichcanbeusedintheanalysisofoldstellar triplet have been calibrated by RHS97 on both the CG scale populationsinexternalgalaxies. andtheolderZinn&West(1984;ZW)scale.Thecompilation by RHS97 is by far the most homogeneousone which is cur- 1.1. Metallicityindices rentlyavailable. Inthesameperiod,wehavebeenbuildingthelargesthomo- Photometricindiceshavebeenwidelyusedinthepasttoesti- geneousV,I photometricsampleofGalacticglobularclusters mate themeanmetallicitiesofthosestellar systemswheredi- (GGC)basedonCCDimagingcarriedoutbothwithNorthern rect determinations of their metal content are not feasible. In (Isaac Newton Group, ING) and Southern (ESO) telescopes particular,theyareusedtoobtain[Fe/H] valuesforthefarthest (Rosenberg et al. 1999b, 1999c). The main purpose of the globulars and for those resolved galaxies of the Local Group project is to establish the relative age ranking of the clusters, whereasignificantPopIIispresent(e.g.thedwarfspheroidal basedonthemethodsoutlinedinSavianeetal.(1997,1999b; galaxies). SRP97,SRP99)andBuonannoetal.(1998;B98).Theresults The calibration of V,I indices is particularly important, of this investigationare presentedin Rosenberget al. (1999a; since with comparable exposure times, deeper and more ac- RSPA99). Here suffice it to say that for a set of 52 clusters curatephotometrycanbeobtainedforthecool,low-massstars weobtainedV vs.(V −I)color-magnitudediagrams(CMD), in these broadbandsthan in B,V. Moreover,our hugeCMD whichcoveramagnituderangethatgoesfromafewmagsbe- databaseallowsatestofthenewCGscaleonalargebasis:we lowtheturnoff(TO)uptothetipoftheredgiantbranch(RGB). areabletocomparetherelationsobtainedforboththeoldZW At this pointboth a spectroscopicand photometrichomo- and new scale, and check which one allows to rank GGCs in geneousdatabasesareavailable:thepurposeofthisstudyisto the most accurate way. Indeed, the most recent calibration of IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters 3 theV,I indices(Carretta&Bragaglia1998)isbasedonjust8 2. Theobservationalsample clusters. Thirty-nine clusters have been observed with the ESO/Dutch 0.9m telescope at La Silla, and 16 at the RGO/JKT 1m tele- 1.2. OldstellarpopulationsinLocalGroupgalaxies scope in la Palma. This database comprises 75% of the GGC whose distance modulusis (m−M) < 16. The zero-point V A reliable metallicity rankingof GGC giantbranchesalso al- uncertaintiesofourcalibrationsare<0.03magforeachband. lowsstudiesthatgobeyondasimpledeterminationofthemean Three clusters were observed both with the southern and the metallicity of a stellar population. As an illustration, we may northerntelescopes,thusprovidingaconsistencycheckofthe recall the recent investigationof the halo metallicity distribu- calibrations:nosystematicdifferenceswerefound,atthelevel tionfunction(MDF)ofNGC5128(Harrisetal.1999),which of accuracy of the zero-points. A detailed description of the wasbasedonthefiducialGClinesobtainedbyDaCosta&Ar- observationsand reduction procedureswill be given in forth- mandroff(1990, hereafter DA90).These studies can be made comingpapers(Rosenbergetal.1999b,1999c)presentingthe morestraightforwardbyprovidingasuitableanalyticrepresen- singleclusters. tationoftheRGBfamilyofGGCs.Indeed,assumingthatmost A subsample of this databasewas used for the presentin- oftheGGCsshareacommonage(e.g.Rosenbergetal.1999a), vestigation.WeretainedthoseclusterswhoseCMDsatisfieda one expects that there should exist a “universal” function of fewcriteria:(a)theHBlevelcouldbewelldetermined;(b)the {(V −I)0,MI,[Fe/H]}abletomapany[(V −I)0,MI]coor- RGBwasnotheavilycontaminatedbyforeground/background dinatepairintothecorrespondingmetallicity(providedthatan contamination; and (c) the RGB was well defined up to the independentestimateofthedistanceandextinctionofthestar tip. This subsample largely overlaps that used for the age in- are available). We will show here that such relatively simple vestigation, but a few clusters whose TO position could not mono-parametric function can actually be obtained, and that bemeasured,areneverthelessusefulforthemetallicityindices this progress is made possible thanks to the homogeneity of definition. Conversely, in a few cases the lower RGB could bothourdatasetandanalysis. be used for the color measurements, while the upper branch Inordertoenforceaproperuseofourcalibrations,wemust wastooscarcelydefinedforareliabledefinitionofthefiducial clearly state that, in principle, the present relations are valid line. Two of the CMDs that were used are shown in Figs. 1 onlyforrigorouslyoldstellarpopulations(i.e.forstarsasold (NGC 1851) and 2 (NGC 104), and they illustrate the good as the bulk of Galactic globulars). At fixed abundance, giant qualityofthedata. branchesaresomewhatbluerforyoungerages(e.g.Bertelliet Thedatasetof31clustersusedinthispaperislistedinTa- al.1994).Moreover,inrealstellarsystemsAGBstarsarealso ble1.Fromlefttoright,thecolumnscontaintheNGCnumber, presenton the blue side of the RGB (cf. Fig. 2). Both effects the reddening both in (B − V) and (V − I), the metallicity must be taken into account when dealing with LG galaxies, accordingtothreedifferentscales,andtheapparentmagnitude since they could lead to systematic effects in both the mean ofthehorizontalbranch(HB).TheE(B−V) valuesweretaken abundancesandtheabundancedistributions(e.g.Savianeetal. fromtheHarris(1996)on-linetable1.The(V −I)reddenings 1999a). were obtained by assuming that E(V−I) = 1.28 × E(B−V) (Dean et al. 1978). The values of the metallicity were taken fromRHS97:theyrepresenttheequivalentwidthsoftheCaII 1.3. Layoutofthepaper infraredtriplet,calibratedeitherontotheZinn& West (1984) scale (ZW column) or the Carretta & Gratton (1997) scale Theobservationalsample,onwhichthisinvestigationisbased, (RHS97 column). Moreover, the original Carretta & Gratton is presentedin Sect. 2. Sect. 3 is devotedto the set ofindices metallicities(CGcolumn)arealsogivenfortheclusterscom- whicharetobecalibrated.TheyaredefinedinSect3.1.There- prisedintheirsample. liabilityofoursampleistestedinSect.3.3,wherewedemon- The HB level was found in different ways for clusters of strate that our methodology produces a set of well-correlated differentmetallicity.Forthethemetalrichandmetalinterme- indices. In Sect. 4 we show that, once a distance scale is as- diate clusters, a magnitude distribution of the HB stars was sumed for the GGCs, our whole set of RGBs can be approx- obtained, and the mode of the distribution was taken. Where imated by a single analytic function, which depends on the the HB was too scarcely populated, a horizontal line was fit- metallicityalone.Thisfindingallowsanewandeasierwayto tedthroughthedata.Thebluetailofthemetalpoorestclusters determinethedistancesandmeanmetallicitiesofthegalaxies does not reach the horizontalpart of the branch:in that case, oftheLocalGroup,extendingthemethodsofDaCosta&Ar- a fiducial HB was fitted to the tail, and the magnitude of the mandroff(1990),andLeeetal.(1993).Themetallicityindices horizontal part was taken as the reference level. The fiducial arecalibratedinSect.6,whereanalyticrelationsareprovided branch was defined by taking a cluster having a bimodal HB bothfortheZWandfortheCGscales.Usingtheseindices,we color distribution (NGC 1851, cf. Fig. 1) and then extending areabletotestouranalyticRGBfamilyinSect7.Ourconclu- itsHBbothtotheredandtotheblueby“appending”clusters sionsareinSect.8. beingmore and moremetalrich and metalpoor,respectively. 1 http://physun.physics.mcmaster.ca/Globular.html 4 IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters (V −I,V)planehere;however,inordertobeabletouseour metalrichestclusters,weredefinedSbymeasuringthesecond RGBpoint2magbrighterthantheHB.SinceSismeasuredon the apparentCMD, it is independentboth fromthe reddening andthedistancemodulus. The right panel of the same figure, shows the apparentV magnitude vs. the de-reddened(V −I) color. In this panel, 0 fourotherindicesareidentified,i.e.(V −I) ,∆V ,∆V , 0,g 1.1 1.2 and∆V .ThefirstoneistheRGBcolorattheleveloftheHB, 1.4 andtheotherthreemeasurethemagnitudedifferencebetween theHBandtheRGBatafixedcolor(V −I) = 1.1,1.2and 0 1.4mag.TheformerindexwasoriginallydefinedbySandage & Smith (1966) and the latter one by Sandage & Wallerstein (1960),inthe(B−V) ,V plane.Theothertwoindices,∆V 0 1.1 and ∆V , are introduced later to measure the metal richest 1.2 GCs.Theseindicesrequireanindependentcolorexcessdeter- mination. Finally,Fig.2showstheCMDofNGC104(47Tuc)inthe absolute (V − I) M plane: the adopted distance modulus, 0, I (m−M) = 13.35,wasobtainedbycorrectingtheapparent V luminosityoftheHBaccordingtoLeeetal.(1990;cf.Sect.6). By comparison,Harris’ catalog reports(m−M) = 13.32. Fig.2.Graphicalrepresentationofthemetallicityindices(part V 2)thatweremeasuredontheselectedclusters.Inthisfigure,the Two other indices are represented in the figure: (V −I)−3.0 absoluteCMDofthemetalrichclusterNGC104isplottedin and(V −I)−3.5.TheyaredefinedastheRGBcoloratafixed absoluteI magnitudeofM =−3.0(DaCosta&Armandroff the(V−I) ,M plane,adoptinganapparentdistancemodulus I 0 I 1990) or M = −3.5 (Lee et al. 1993). The latter index was (m−M)V = 13.35anda reddeningEV−I = 0.06(seetext also discussIed by Armandroff et al. (1993), and a calibration forthe discussion).Thisplotshowsthe ability of the analytic formulawas givenin Caldwell et al. (1998). This is based on functiontoreproduceeventhemoreextendedRGBs.Thetwo the DA90 clusters plus M5 and NGC 362 from Lloyd Evans crossesmarkthecoloroftheRGB atM = −3.0andM = I I (1983). −3.5. Sincethesetwoindicesaredefinedonthebrightpartofthe RGB,theycanbemeasuredevenforthefarthestobjectsofthe Thedetailsofthisprocedure,aswellastheerrorsassociatedto LocalGroup(LG).Duetothefastluminosityevolutionofthe theVHB inTable1,arediscussedinRSPA99.ForNGC1851, stars on the upper RGB, this part of the branch was typically VHB = 16.18±0.05wasadopted(dashedlineinFig.1),and under-sampled by the early small-size CCDs, so no wide ap- this value is just 0.02 mag brighter than the value found by plicationoftheseindiceshasbeenmadeforGalacticglobulars. Walker(1992)andSavianeetal.(1998). However,thisisofnoconcernforgalaxy-sizestellarsystems. Basedonthisobservationalsample,asetofmetallicityin- ItwillbeshowninSect.6thatgoodaccuraciescanbeobtained diceswere measuredon the RGBs of the clusters. In the next evenforGCs,providedthattheanalyticfunctionofEq.(1)is section, the indices are defined and the measurement proce- used. duresaredescribed.Consistencychecksarealsoperformed. 3.2. Measurementprocedures 3. Metallicityindices Colors and magnitudes were measured on a fiducial RGB, 3.1. Definitions whichhasbeenfoundbyleast-squarefittingananalyticfunc- Themetallicityindicescalibratedinthisstudyarerepresented tiontotheobservedbranch.Aftersomeexperimenting,itwas and defined in Fig. 1 and Fig. 2. The figures represent the foundthatthebestsolutionistousethefollowingrelation: CMDofNGC1851andNGC104indifferentcolor-magnitude y =a+bx+c/(x−d) (1) planes, and the crosses mark the position of the RGB points usedinthemeasurementoftheindices. where x andy representthe color andthe magnitude,respec- TheleftpanelofFig.1showstheapparentcolorsandmag- tively.OnecanseefromFigs.1and2thatthefunctionisindeed nitudes for NGC 1851: the inclined line helps to identify the able to represent the giant branch over the typical metallicity first index, S. This was defined, in the (B −V,V) plane, by rangeofglobularclusters.Moreover,itisshowninSect.4that, Hartwick(1968)astheslopeofthelineconnectingtwopoints whentheCMDsarecorrectedfordistanceandreddening,the on the RGB: the first one at the levelof the HB, and the sec- four coefficientscan be parametrizedas a functionof [Fe/H], ond one 2.5 mag brighter. We use the same definition for the sothatoneisabletoreproducetheRGBofeachcluster,using IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters 5 Table2.Themeasuredmetallicityindices ∆V (V −I) NGC (V −I)0,g S 1.1 1.2 1.4 @3.5 @3.0 104 0.99 4.13 0.78 1.27 1.87 1.94 1.57 288 0.95 6.39 1.25 1.75 2.36 1.51 1.35 362 0.90 7.28 1.67 2.09 2.57 1.45 1.28 1261 0.91 7.77 1.62 2.13 2.73 1.39 1.25 1851 0.97 7.41 1.23 1.82 2.55 1.45 1.31 1904 0.94 8.56 1.58 2.14 2.83 1.35 1.24 3201 0.99 8.72 1.19 1.91 2.71 1.39 1.27 4590 0.91 9.98 1.90 2.52 3.25 1.24 1.16 4833 0.92 9.25 1.80 2.36 3.12 1.28 1.19 5272 0.91 7.60 1.66 2.13 2.81 1.36 1.24 5466 0.91 9.85 1.93 2.50 3.18 1.24 1.16 5897 0.97 8.73 1.34 2.00 2.79 1.35 1.25 5904 0.93 6.91 1.41 1.91 2.55 1.44 1.30 6093 0.93 8.02 1.58 2.12 2.91 1.34 1.24 6171 1.07 5.66 0.31 1.09 1.93 1.67 1.49 6205 0.89 7.70 1.75 2.20 2.75 1.37 1.23 6218 0.95 7.09 1.34 1.88 2.51 1.46 1.31 6254 0.90 8.25 1.75 2.29 3.17 1.30 1.21 6341 0.88 9.92 2.15 2.69 3.40 1.21 1.13 Fig.3. The metallicity indices (V − I)0,g, (V − I)−3.0, and 6352 1.12 3.11 -0.16 0.52 1.30 1.99 1.75 (V −I)−3.5areplottedasafunctionoftheindexS.Thepoints are ordered such that the metal-poor to metal-rich cluster se- 6362 0.93 5.84 1.31 1.76 2.32 1.55 1.37 quencegoesfromlefttoright.Theverygoodcorrelationsbe- 6397 0.89 9.45 1.98 2.49 3.12 1.26 1.16 6541 1.01 8.59 1.03 1.77 2.67 1.39 1.29 tween(V −I)−3.0,(V −I)−3.5andS(thermsoftheparabolic fitsare2%and3%respectively),demonstratethattheseindices 6637 0.96 4.39 0.96 1.41 1.97 1.82 1.53 6656 0.86 10.32 2.27 2.69 2.96 1.24 1.12 areveryaccurate 6681 0.95 7.54 1.35 1.92 2.76 1.37 1.27 6723 1.01 6.02 0.76 1.38 2.18 1.55 1.41 Secondorderpolynomialswerefittedtothedistributions,and 6752 0.99 7.16 1.08 1.69 2.46 1.45 1.33 thermsofthefitwascomputedforeachindex.Inordertoin- 6779 0.94 8.74 1.60 2.18 2.94 1.32 1.22 tercomparethedifferentindices,arelativeuncertaintyhasbeen 6809 0.93 9.38 1.72 2.29 2.87 1.32 1.20 computedbydividingthermsbythecentralvalueofeachpa- 7078 0.88 9.82 2.10 2.62 3.27 1.23 1.14 rameter(thisvalueisidentifiedbyadottedlineineachfigure). Inthisway,thescatterofthemetalindexiis∆i/i=0.02, 0.02, 0.04, 0.06, 0.12, and 0.26, for the indices (V − I)−3, justoneparameter:themetallicity.Atanyrate,theindiceswere (V−I)−3.5,(V−I)0,g,∆V1.4,∆V1.2,and∆V1.1,respectively. measuredontheoriginalloci,sothatanindependentcheckof Thesevaluesconfirmthevisualimpressionofthefigures,that the goodness of the generalized hyperbolae can be made, by ∆(V − I)−3.0 and ∆(V − I)−3.5 are the lowest dispersion comparisonofthemeasuredvs.predictedindices. indices,followedby(V −I) and∆V . 0,g 1.4 Alltheindices’valuesthathavebeenmeasuredarereported Theindiceswillbecalibratedintermsof[Fe/H]inSect.6; inTable2.Inthistable,theclusterNGCnumberisgivenincol- however, before moving to this section, we want to present a umn1;thefollowingcolumnslist,fromlefttoright,(V−I) , new way to provide “standard” GGC branches in the (V − 0,g S,∆V , ∆V , ∆V ,andfinallytheRGB colormeasured I) ,M plane,alongthelinesoftheclassicalDaCosta&Ar- 1.1 1.2 1.4 0 I at M = −3 and −3.5. The Lee et al. (1990) distance scale mandroff(1990)study.UsingthisfamilyofRGBbranches,we I wasusedtocomputethelasttwoindices(cf.Sect.6). areabletomakepredictionsonthetrendofthealreadydefined indiceswithmetallicity;thesetrendscanthusbecomparedto the observed ones, and therefore provide a further test of the 3.3. Internalconsistencychecks reliabilityofourRGBfamily(cf.Sect7). Before discussing the indices as metallicity indicators, we checkedtheirinternalconsistency.WewillshowinSect.6that 4. Newstandardglobularclustergiantbranches theindexS isthemostaccurateone,asexpected,sinceitdoes notrequirereddeninganddistancecorrections.Therestofthe Da Costa & Armandroff(1990) presentedin tabular formthe indicesarethereforeplottedvs.S inFigs.3and4,andweex- fiducial GGC branches of 6 globulars, covering the metallic- pect that most of the scatter will be in the vertical direction. ity range −2.17 ≤ [Fe/H] ≤ −0.71. The RGBs were cor- 6 IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters Table3.Clustersselectedforthedeterminationoftheanalyticfits,listedforincreasing[Fe/H]values Cluster VHB E(B−V) E(V−I) [Fe/H]ZW [Fe/H]RCG [Fe/H]CG NGC104 14.05 0.050 0.064 −0.71 −0.78 −0.70 NGC5904 15.00 0.023 0.029 −1.38 −1.12 −1.11 NGC288 15.40 0.036 0.046 −1.40 −1.14 −1.07 NGC6205 14.95 0.000 0.000 −1.63 −1.33 −1.39 NGC5272 15.58 0.002 0.003 −1.66 −1.33 — NGC6341 15.20 0.010 0.013 −2.24 −2.10 — Table4.Thefiducialpointsforthe6selectedclusters NGC104 NGC288 NGC5272 NGC5904 NGC6205 NGC6341 I (V −I) I (V −I) I (V −I) I (V −I) I (V −I) I (V −I) 13.782 0.978 15.359 0.914 15.492 0.852 14.725 0.926 14.645 0.867 15.060 0.852 13.604 0.994 15.107 0.939 15.151 0.874 14.457 0.942 14.322 0.890 14.720 0.872 13.443 1.008 14.849 0.960 14.789 0.892 14.221 0.961 14.033 0.909 14.395 0.894 13.317 1.021 14.593 0.984 14.597 0.910 14.040 0.978 13.788 0.929 14.079 0.916 13.075 1.045 14.342 0.999 14.359 0.929 13.878 0.994 13.595 0.944 13.789 0.937 12.862 1.070 14.109 1.018 14.143 0.955 13.700 1.009 13.381 0.966 13.533 0.953 12.619 1.101 13.881 1.036 13.796 0.990 13.456 1.032 13.170 0.984 13.303 0.974 12.346 1.136 13.649 1.062 13.517 1.021 13.190 1.061 12.984 1.005 13.082 0.994 12.035 1.185 13.376 1.090 13.265 1.046 12.916 1.091 12.832 1.019 12.850 1.020 11.761 1.231 13.058 1.132 13.005 1.076 12.655 1.122 12.631 1.045 12.611 1.039 11.461 1.281 12.766 1.173 12.759 1.110 12.419 1.154 12.363 1.077 12.351 1.067 11.101 1.362 12.534 1.210 12.519 1.148 12.231 1.183 12.118 1.111 12.075 1.102 10.696 1.459 12.380 1.233 12.302 1.187 12.073 1.212 11.945 1.138 11.771 1.148 10.330 1.600 12.163 1.268 12.109 1.227 11.868 1.254 11.844 1.156 11.492 1.195 10.062 1.720 11.928 1.317 11.878 1.275 11.615 1.305 11.707 1.178 11.284 1.233 9.877 1.856 11.617 1.411 11.741 1.310 11.335 1.371 11.571 1.204 11.154 1.265 9.706 2.019 11.427 1.483 11.575 1.344 11.116 1.422 11.395 1.252 11.008 1.295 9.602 2.148 — — 11.494 1.377 10.902 1.489 11.141 1.312 10.854 1.320 9.524 2.315 — — 11.330 1.406 10.652 1.585 10.870 1.376 10.709 1.351 9.573 2.576 — — 11.240 1.447 10.457 1.680 10.643 1.444 — — 9.619 2.768 — — 11.112 1.488 10.343 1.742 10.552 1.492 — — — — — — 11.078 1.528 — — — — — — — — — — 11.047 1.546 — — — — — — rected to the absolute (V −I) ,M plane using the apparent Insuchcase,oneexpectsthatanyRGBstar’spositioninthe 0 I V magnitudeoftheHB,andadoptingtheLeeetal.(1990)the- absoluteCMD is determinedjustbyits metallicity,andthata oreticalHBluminosity.SincetheDA90study,these branches better statistical determination of the population’s metal con- havebeenwidelyusedforstellarpopulationstudiesintheLo- tent would be obtained by converting the color of each star calGroup.BasedontheseRGBs,inparticular,amethodtode- into a [Fe/H] value. With this idea in mind, in the following termineboththedistanceandmeanmetallicityofanoldstellar sections we will show that this is indeedpossible, at least for populationwaspresentedbyLeeetal.(1993). the bright/most sensitive part of the giant branch. We found that a relatively simple continuousfunction can be defined in Both DA90 and Lee et al. (1993) provided a relation be- the(V −I) ,M ,[Fe/H]space,andthatthisfunctioncanbe 0 I tweenthemetallicity[Fe/H]andthecoloroftheRGBatafixed usedtotransformtheRGBfromthe(V −I) ,M planetothe 0 I absoluteI magnitude(MI = −3and−3.5,respectively),and [Fe/H],MI plane. recentlyanewrelationfor(V −I)−3.5hasalsobeenobtained byCaldwelletal.(1998).Oncethedistanceofthepopulation isknown(e.g.via theluminosityoftheRGB tip),thenanes- Inordertoobtainthisfunction,wefirstselectedasubsam- timateofitsmeanmetallicitycanbeobtainedusingoneofthe pleofclusterswithsuitablecharacteristics,sothatareference calibrations.Itisassumedthattheageofthepopulationiscom- RGB grid can be constructed. The fiducial branches for each parabletothatoftheGGCs,andthattheagespreadisnegligi- clusterwerethendeterminedinanobjectiveway,andtheywere blecomparedtothemetallicityspread(RSPA99). correctedtotheabsolute((V −I) ,M )plane.Inthisplane, 0 I IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters 7 The DA90 fiducial clusters were NGC 104, NGC 1851, NGC6752,NGC6397,NGC7078andNGC7089(M2).NGC 104 is the only cluster in common with the previous study, and M2 is not present in our dataset. The other objects have been excluded from our fiducial sample since they have too large reddening values (E(B−V) > 0.05 for NGC 6397 and NGC 7078), or their RGBs are too scarcely populated in our CMDs(NGC1851andNGC6752).Nevertheless,thecalibra- tionsthatwe obtainforthe (V −I)−3.0 and(V −I)−3.5 are infairlygoodagreementwiththoseobtainedbyDA90(forthe smalldiscrepanciesatthehighmetallicityend,cf.Sect.6.2and 6.3),andinparticularwiththerecentCaldwelletal.(1998)cal- ibrationforthe(V −I)−3.5index. 4.2. Determinationofthefiducialloci TheridgelinesofourfiducialRGBsweredefinedaccordingto the following procedure. The RGB region was selected from the calibrated photometry, by excluding both HB and AGB stars. All stars bluer than the color of the RR Lyr gap were removed;AGBstarswerealsoremovedbytracingareference straightline in the CMD, and by excludingall stars blue-side Fig.4. The metallicity indices ∆V , ∆V , and ∆V as 1.1 1.2 1.4 ofthisline.Thisoperationwascarriedoutinthe((V −I),I) a function of the index S. The points are ordered such that plane, where the RGB curvature is less pronounced, and a the metal-poor to metal-rich cluster sequence goes from left straightlineturnsouttobeadequate. toright.Thedashedlinerepresentsasecondorderpolynomial ThefiduciallociwerethenextractedfromtheselectedRGB least-square fitted to the data. The typical relative uncertainty samples. The (V − I) and I vectors were sorted in magni- oneachindexhasbeenestimatedbytakingtheratiooftherms tude,andbinswerecreatedcontainingagivennumberofstars. ofthefitoverthevalueoftheparameteratthelevelofthehor- Within each bin, the median color of the stars and the mean izontaldottedline magnitudewereusedasestimatorsofthebincentralcolorand brightness.Thenumberofstarswithinthe binswasexponen- theanalyticfunctionwasfittedtotheRGBgrid.Theseopera- tially increased going from brighter to fainter magnitudes. In tionsaredescribedinthefollowingsections. this way, (a) one can use a small number of stars for the up- per RGB, so that the color of the bin is not affected by the RGBslope,and(b)itispossibletotakeadvantageofthebet- 4.1. Selectionofclusters ter statistics of the RGB base. Finally, the brightest two stars The clusters that were used for the definition of the fiducial of the RGB were not binned,and were left as representatives RGBs are listed in Table 3, in order of increasing metallic- of the topbranch.After someexperimenting,we foundthata ity. The table reports the cluster name, and some of the pa- goodRGB samplingcan beobtainedbytakingforeachbina rameters listed in Table 1 are repeated here for ease of use. number of stars which is proportionalto e0.2·i, where i is an Thevaluesofthereddeningwereinsomecaseschangedbya integer number. The resulting fiducial vectors were smoothed fewthousandthmagnitudes(i.e.wellwithinthetypicaluncer- usinganaveragefilterwithaboxsizeof3. taintiesonE(B−V)),toobtainasequenceoffiduciallinesthat TheRGBregionsofthe6clustersareshowninFig.5,to- movefrombluertoreddercolorsas[Fe/H]increases,andagain getherwiththefiduciallines:itcanbeseenthatinallcasesthe thecorrespondingE(V−I) valueswereobtainedassumingthat AGBs are easily disentangled from the RGBs. The values of E(V−I) = 1.28×E(B−V) (Deanetal. 1978).Indeed,dueto thefiducialpointscorrespondingtothesolidlinesinFig.5,are thehomogeneityofoursample,weexpectthatifamonotonic listedinTable4. color/metallicitysequenceisnotobtained,thenonlytheuncer- taintiesontheextinctionvaluesmustbetakenintoaccount. 4.3. Analyticfitstothefiducialloci In ordertosingle outthese clustersfromthetotalsample, somekeycharacteristicsweretakenintoaccount.Inparticular, The fiducial branches defined in Sect. 4.2 were fitted with we consideredclusters whose RGBs are all well-definedby a a parametrized family of hyperbolae. First, the RGBs were statisticallysignificantnumberofstars;theyhavelowredden- movedintotheabsolute(V−I) ,M plane.Thedistancemod- 0 I ingvalues(E(B−V) ≤0.05);andtheycoverametallicityrange ulus was computed from the apparent magnitude of the HB thatincludesmost of our GGCs (−2.2 ≤ [Fe/H] ≤ −0.7 on (cf. Table 3) and by assuming the common law M (HB) = V theZWscale). a[Fe/H] + b; in order to compare our results with those of 8 IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters Fig.5.TheRGBsoftheselectedclusters(crosses)andtheirfiduciallines(solidcurves).Theclustersarerepresented,fromleft torightandtoptobottom,inorderofincreasingmetallicity DA90, a = 0.17 and b = 0.82 were used, but we also ob- Thelistoftheparametersofthefitsinmagnitudeisreportedin tainedthe same fitsusing morerecentvaluesasin Carretta et Table5,togetherwiththermsoftheresidualsaroundthefitting al.(1999),i.e.a= 0.18andb =0.90.TheRGBwasmodeled curves.Thetableshowsthattheparameterddoesnotdepend with an hyperbola as in Rosenberg et al. (1999a), but in this onthechoiceofthedistancescale,asexpected.Eventheother case the coefficients were taken as second order polynomials coefficients are little dependent on the distance scale, apart in[Fe/H].Inotherwords,weparametrizedthewholefamilyof fromk .Itisaffectedbythezero-pointoftheHBluminosity- 3 RGBsinthefollowingway: metallicityrelation,andindeedthereistheexpected∼0.1mag differencegoingfromtheLDZtotheC99distancescale. M =a+b·(V −I)+c/[(V −I)−d] (2) I One could question the choice of a constant d, but after where sometrainingonthetheoreticalisochrones,wefoundthateven a=k [Fe/H]2+k [Fe/H]+k (3) allowing for a varying parameter, its value indeed scattered 1 2 3 very little around some mean value. This empirical result is b=k [Fe/H]2+k [Fe/H]+k (4) 4 5 6 a good one, in the sense that it allows to apply a robust lin- c=k [Fe/H]2+k [Fe/H]+k (5) earleast-squarefittingmethodforanychoiceofd,andthento 7 8 9 searchforthebestvalueofthisconstantbyasimplermsmini- d=k (6) mization.WechosetofittheM =f{(V −I) ,[Fe/H]}func- 10 I 0 IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters 9 Fig.6.Thefiducialpointsofourreferencesampleof6clusters Fig.7.SameasFig.6,fortheCGmetallicityscale.Themetal- plottedovertheanalyticfitsfortheZWmetallicityscale.The licity step between the analytic RGBs (dashed lines) is again analyticRGBs(dashedlines)havebeencalculatedatconstant 0.2dex.Ifcomparedtothepreviousfigure,thenon-lineartrend ∆[Fe/H] = 0.2dexsteps.Theobservedridgelineshavebeen oftheRGBcolorwith[Fe/H]canbeclearlyseen correctedforreddeningandabsorption+distancescale.Inthe upperpanel,thefitsintheV−I,M planeareshown,whilefits I intheV −I,M planeareshowninthelowerpanel.Different certaintiesinthedistancemoduliwithintheLocalGroup.We V symbolsidentifydifferentclusters:NGC104(opentriangles), further stress the excellent consistency of the empirical fidu- NGC288(opensquares),NGC5272(opencircles),NGC5904 cial branches for clusters of similar metallicity. We have two (solid squares), NGC 6205 (solid triangles) and NGC 6341 pairsofclusterswhosemetallicitiesdifferbyatmost0.03dex (solidcircles) (dependingonthescale):NGC288andNGC5904ontheone side,andNGC5272andNGC6205ontheotherside.Thefig- ures show that the fiducial line of NGC 288 is similar to that tion,andnotthe(V −I)0 =f(MI,[Fe/H])function,sincethe of NGC 5904, and the NGC 5272 fiducial resembles that of latteronewouldbedouble-valuedforthebrightestpartofthe NGC6205,furtherdemonstratingboththehomogeneityofour metalrichclusters’RGBs.Thischoiceimpliesthatourfitsare photometryandthe reliabilityof theprocedurethatis usedin not well-constrained for the vertical part of the giant branch, definingtheclusterridgelines. i.e.formagnitudesfainterthanMI ∼ −1.However,weshow Ifthecoefficientsofthehyperbolaearetakenasthirdorder inthenextsectionthatouranalyticfunctionisgoodenoughfor polynomials, the resulting fits are apparently better (the rms theintendedpurpose,i.e.toobtainthe[Fe/H]oftheRGBstars is∼ 0.05mag);however,the trendsofthe metallicityindices in far LocalGrouppopulations,and thusto analyzehowthey showanunphysicalbehavior,whichisasignthatfurtherclus- aredistributedinmetallicity. ters,havingmetallicitiesnotcoveredbythepresentset,would OursyntheticRGBfamiliesareplottedinFigs.6and7,for beneededinordertorobustlyconstraintheanalyticfunction. theLDZdistancescale.Intheformerfigure,theZWmetallicity Inthefollowingsection,theindicesarecalibratedinterms scaleisused,whiletheCGscaleisusedinthelatterone.The ofmetallicity,sothatinSect.7theywillbeusedtocheckthe figuresshowthatthechosenfunctionalformrepresentsavery reliabilityofourgeneralizedfits. goodapproximationtothetruemetallicity“distribution”ofthe RG branches.The rms valuesare smaller than the typicalun- 10 IvoSavianeetal.:TheredgiantbranchesofGalacticglobularclusters Table 5. The coefficientsthat define the functionsused to in- terpolateourRGBs(seetext);thetopheaderlineidentifiesthe twodistancescalesused,whilethetwometallicitiesareidenti- fiedinthesecondlineoftheheader LDZ C99 CG ZW CG ZW d 0.212 0.182 0.212 0.182 k1 -0.231 -1.338 -0.227 -1.336 k2 3.290 -0.069 3.314 -0.055 k3 -7.229 -9.547 -7.140 -9.465 k4 0.611 0.710 0.612 0.709 k5 0.551 0.883 0.556 0.881 k6 1.398 1.651 1.401 1.650 k7 0.380 0.525 0.381 0.524 k8 -0.135 0.206 -0.133 0.204 k9 6.194 6.806 6.195 6.805 rms 0.07 0.08 0.07 0.08 Table6.Coefficientsofthecalibratingrelationsfortheindices (see text for the definition of the equations). NGC 6656 was excludedfromthefits Fig.8. Calibration of the index S (cf. Fig. 1, left panel) as a functionof[Fe/H]ontheZinn&West(1984)scale(toppanel) index d.sc. metallicity α β γ rms fit andontheCarretta&Gratton(1997)scale(bottompanel).Lin- S CG -0.03 0.23 -1.19 0.13 2 ear (top panel) and parabolic (bottom panel) fits of the data ZW -0.004 -0.18 0.08 0.12 2 arealsorepresented.Theclustermarkedwithopencirclewas ZW -0.24 0.28 0.12 1 excluded from the fit (see text for details). Starting from this (V −I)−3.5 LDZ CG 0.00487 -0.0057 0.13 z figure(toFig. 11),the opensquaresconnectedbya solidline ZW -2.12 8.81 -9.75 0.13 2 representthemono-parametricapproximation(seeSect.4) C99 CG 0.0045 -0.0053 0.15 z ZW -2.05 8.57 -9.61 0.12 2 (V −I)−3.0 LDZ CG 0.0068 -0.0076 0.15 z ZW -3.34 12.37 -11.91 0.14 2 C99 CG 0.0065 -0.0073 0.15 z ZW -3.233 12.23 -11.96 0.14 2 ∆V1.4 CG -0.34 0.93 -1.37 0.16 2 ZW -0.063 -0.56 0.41 0.16 2 ZW -0.87 0.77 0.16 1 ∆V1.2 CG -0.36 0.55 -0.97 0.19 2 CG -0.69 0.0007 0.22 1 ZW -0.13 -0.38 -0.28 0.20 2 ZW -0.82 0.06 0.20 1 ∆V1.1 CG -0.30 0.09 -0.81 0.23 2 CG -0.59 -0.52 0.25 1 ZW -0.13 -0.42 -0.68 0.25 2 ZW -0.70 -0.56 0.25 1 (V −I)0,g CG 4.25 -5.37 0.32 1 ZW 5.25 -6.52 0.33 1 5. Calibrationoftheindices.Introduction In order to obtain analytic relations between the indices and the actual metallicity, our photometric parameters were com- paredbothwiththeZWandtheCGvalues.Asummaryofthe Fig.9. Calibration of the index (V − I)−3.0. The solid lines representtheequationsdescribedinthetext,whilethedashed resulting equations is given in Table 6. For each index (first column)bothlinearandquadraticfitsweretried,oftheform: curverepresentsthetheDA90calibration. [Fe/H]=α·index+βand[Fe/H]=α·index2+β·index+γ.