Mon.Not.R.Astron.Soc.000,1–12(1997) Printed5February2008 On the galactic disc age-metallicity relation Giovanni Carraro1,2, Yuen Keong Ng3 and Laura Portinari1,4 1 Department of Astronomy, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy 2 SISSA-ISAS, Via Beirut 2-4, I-34014 Trieste, Italy 3 Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy 8 4 Nordita, Blegdamsvej 17, DK-2100 Copenhagen Œ, Denmark 9 E-mail: carraro,yuen,portinari@astrpd.pd.astro.it 9 1 n submitted a J 1 ABSTRACT 2 Acomparisonismade betweenthe age-metallicityrelationobtainedfromfourdifferent types of studies: F and G stars in the Solar Neighbourhood, analysis of open clusters, 3 galacticstructure studies with the stellar populationsynthesis technique, andchemical v evolutionmodels.Metallicitiesofopenclustersarecorrectedfortheeffectsoftheradial 5 gradient, which we find to be −0.09 dex kpc−1 and to be most likely constant in time. 8 We do not correct for the vertical gradient, since its existence and value are not firmly 1 7 established. 0 Stars and clusters trace a similar age-metallicity relation, showing an excess of rather 7 metal-rich objects in the age range 5–9 Gyr. Galactic structure studies tend to give 9 a more metal-poor relation than chemical evolution models. Both relations do not ex- / plain the presence of old, relatively metal-rich stars and clusters. This might be due h to uncertainties in the ages of the local stars, or to pre-enrichment of the disc with p - material from the bulge, possibly as a result of a merger event in the early phases of o the formation of our Galaxy. r t Key words: Open clusters – Galaxy:abundances,gradients,chemicalevolution,gen- s a eral, structure : v i X r 1 INTRODUCTION of stars and therefore the result is less susceptible to indi- a vidualerrors. The age-metallicity relation (AMR) for nearby stars is a AnAMRcanalsobeobtainedfromstarcountsstudies, record of the progressive chemical enrichment of the star- based on the population synthesis technique (Bertelli et al. forminglocalinterstellarmediumduringtheevolutionofthe 1995, 1996; Ng et al. 1995, 1996, 1997). In such studies all galacticdisc,andsoprovidesusefulcluesaboutthestarfor- the stars along the line of sight are considered. The disc is mation and chemical evolution history of thelocal environ- sampled with respect to age and metallicity in layers with ment.Metallicity isusuallyidentifiedwiththe[Fe/H]ratio. specificeffectivethicknesses.Inthisway indicationsareob- Oxygenwouldactuallybeabettertracerand“chronometer” tained for thedisc’s chemical evolution. of metalenrichment(Wheeler etal. 1989), becauseit is the TheaimofthispaperistocomparetheAMRobtained mostabundantmetalanditisproducedonthewell-defined from variousmethods and tocritically discuss theprobable andshorttime-scaleoftypeIISNæ.Onthecontrary,ironis causes for the differences found. In Sect. 2 we start with a released byvarious sources (both typeII and typeIa SNæ) general overview of the various AMRs and improve them withratherdifferenttime-scales.Anyway,metallicityisgen- when possible. In Sect. 3 the relations are compared with erally determined bythe[Fe/H]ratio, sincethe[O/H]ratio eachotherandprobablecausesforanydiscrepancyareout- is much more difficult to measure in stellar atmospheres. lined. The results are finally summarized in Sect. 4. IntheSolarNeighbourhoodthemetallicity ofthestars can be studied in high detail (Edvardsson et al. 1993, hereafter Edv93ea), but the results are liable to large errors in 2 AGE-METALLICITY RELATION theindividualdeterminationsoftheage.Ng&Bertelli(1998, hereafterNB98)demonstratedthattheerrorsintheageare In this section we describe the AMRs considered for this mainly due to the large uncertainties in the individual dis- study. We start with the AMR obtained from stars in tances.Distancesneedtobeknowntoa5%accuracytoget the Solar Neighbourhood. Then we consider the AMR ob- reliable ages. In this respect, the ages and metallicities of tained from open clusters, by improving the results from clusters are more reliable, since one is dealing with a group Carraro&Chiosi (1994a, hereafter CC94a) with a larger 2 G. Carraro et al. Figure1.AMRfornearbystarsbyMeusingeretal.(1991;trian- Figure2.TheAMRfornearbystarsbyNg&Bertelli(1997).The gles)andEdvardssonetal.(1993,opensquaresandopencircles). agesarecomputedwiththedistancesobtainedfromtheHipparcos parallax(ESA1997).Theopencirclesindicatestaronornearthe mainsequencewithanuncertaintyintheagelessthan12%.Open cluster sample. We continue with the description of the starsareusedforgiantbranchstars.Theuncertainty inthe age AMR obtained from star counts analysis based on the stel- is less than 12% for the largesymbols and greater than 12% for lar population synthesis technique. Finally, we discuss the thesmallsymbols. AMR obtained from chemical evolution models. 2.1 The Solar Neighbourhood TheEdv93eadatasetwasre-analysedbyNB98bymeansof Twarog (1980) first showed that nearby stars display an Bertelli et al. (1994) isochrones, based on the latest opac- AMR, by applying uvby-β photometry and Yale isochrones ity tables. Near the main sequence, high age isochrones are to get the metallicity and the age for two wide samples of packed closely together and the deduced ages have consid- stars.Sincesingledatashowedaremarkabledispersion,age- erable uncertainties. The situation changes if a star is on bins and average metallicity per bin were used to deduce thegiant branch:its evolution is relatively fast and theun- the local AMR. The metallicity turned out to increase sen- certainty in the age becomes considerably smaller. For the sitivelyduringdiscevolution,rapidlyfrom 13to5Gyrago, determination of the ages, NB98 also took into account the and more slowly onwards. uncertainties on the effective temperature, metallicity and Twarog’s data were later re-examined by means of dif- distanceofeachstar;thedistancesofthestarsareobtained ferent photometriccalibrations with theVandenberg(1983, fromtheHipparcos (ESA1997)parallaxes.Inthisway,reli- 1985) isochrones, resulting in discordant AMRs. ableageswereobtainedforthestarsdisplayedwithbigsym- Carlberg et al. (1985) limited themselvesto only one of the bols in Fig. 2. The resulting AMR has a small, but distinct two samples from Twarog, hereby excluding around fifty of slope of ∼0.07 dex/Gyr when the stars older than 10 Gyr thelowest metallicity stars.Theyobtainedarelativelyhigh are considered. However, NB98 suspect that the ages for averagemetallicityforoldstarsandashallowerslopeofthe t >10 Gyr might be overestimated (∼2 Gyr), due to an AMRintheearlyphases,suggestingthatthediscevolution improper selection of the isochrones for these stars, which started with a high initial metallicity. are over-abundantin α-elements. It is noteworthy that this On the other hand, Meusinger et al. (1991) re-examined relationisessentiallynotdifferentfromtherelationonegets both samples from Twarog with Vandenberg’s isochrones when,forthestarswithreliableages,theagesfromEdv93ea andwithanewcalibrationforthemetallicityindexandim- are adopted; we refer to NB98 for additional details. proved model atmospheres. The resulting AMR was closer However, the most striking feature of the results men- totheoneobtainedbyTwarogandhadaconsiderableslope tioned above is the huge scatter around the average trend, toward old ages. This relation is displayed in Fig. 1. which makes the correlation between age and metallicity A new estimate of the local AMR, based on a sample rather weak, especially for stars with t<10 Gyr. Such a of 189 nearby F and G dwarfs, was performed by Edv93ea. spreadinthedatamustbeinpartintrinsic,andmanypossi- The metallicity is derived from the analysis of high resolu- blecauseshavebeensuggested:orbitaldiffusionofstarscou- tion spectra with theoretical LTE model atmospheres. The pledwithradialmetallicitygradients,localinhomogeneities agesweredeterminedfromfitsofthephotometricdatawith inthestar-forminggas,inhomogeneousaccretionofinfalling Vandenberg(1985)isochrones.TheresultingbinnedAMRis externalgas,overlappingofdifferentgalacticsub-structures, ingoodagreement,withinthelargedispersion,withthatby each with its own specific AMR. All the mentioned effects Meusinger etal. Figure 1showstheaveraged,binnedAMR may actually contribute to produce the observed scatter, (open squares) from Edv93ea together with the individual and the new challenge for chemical models is nowadays to data points. explainsuchalargespreadinthelocalAMR(seeSect.2.4). On the galactic disc age-metallicity relation 3 andKing5(Phelpsetal.1994),Collinder261(Mazuretal. Table1.Sampleof37clusterswith:agesdeterminedbythesyn- theticCMDstechnique(2nd column),spectroscopic metallicities 1995), and NGC 1245 (Carraro&Patat 1994). Table 1 lists in the Boston scale (Friel&Janes 1993, Friel 1995; 3rd column) ourupdated compilation for 37 clusters. andcorrespondingerrors(4th column),heightabovethegalactic InCC94a,theagesoftenclustersweredeterminedwith plane(5th column)andgalactocentric distance(6th column). stellar isochrones usingthesyntheticColour–magnitude di- agrams (CMDs) technique (Chiosi et al. 1989). This sam- Cluster age(Gyr) [Fe/H] r.m.s. z (pc) R(kpc)† ple defined a relation between age and ∆V (cf. Cannon 1970, Cameron 1985, Barbaro&Pigatto 1984, Anthony- Berkeley17 9.00 −0.29 0.13 170 11.2 Twarog&Twarog 1985). Theagesoftheremainingclusters Berkeley19 3.80 −0.50 0.10 300 13.3 Berkeley20 3.00 −0.75 0.21 2100 16.0 wereobtainedthroughinterpolation ofthisrelation,onlyin Berkeley21 3.10 −0.97 0.10 260 14.5 a few cases an extrapolation was applied. von Hippel et al. Berkeley31 4.00 −0.50 0.16 430 12.7 (1995)noticedforoneclusteradiscrepancybetweentheex- Berkeley32 3.00 −0.58 0.10 300 12.0 trapolated ∆V age with theage determined from thewhite Berkeley39 6.50 −0.31 0.08 705 11.7 dwarf cooling sequence. This however does not imply, as Cr261 7.00 −0.14 0.14 420 7.6 concluded by von Hippel et al. (1995), that the isochrone IC166 0.85 −0.32 0.20 10 10.7 agesareinerror.Itmainlydemonstratesthatonehastobe IC4651 1.60 −0.16 0.05 100 7.8 cautious with extrapolations. King5 0.80 −0.38 0.20 180 10.5 In this paper, the ages for all the clusters in Table 1 King11 6.00 −0.36 0.14 460 10.5 have been determined by fits with the Bertelli et al. (1994) M67 4.80 −0.09 0.07 415 9.1 Melotte66 5.46 −0.51 0.11 710 9.4 isochrones using the synthetic CMDs technique, following NGC188 7.50 −0.05 0.11 570 9.3 the procedure described by Carraro&Chiosi (1994a, 1995). NGC752 1.50 −0.16 0.05 145 8.7 We found for Berkeley 17 and Collinder 261 an age sensi- NGC1193 5.00 −0.50 0.18 1020 12.7 tivelydifferentfromrecentstudies(Phelps1997andGozzoli NGC1245 0.80 +0.14 0.10 460 11.1 et al. 1996 respectively). In the case of Berkeley 17 the dif- NGC1817 0.80 −0.39 0.04 410 10.3 ferent value can be ascribed to the use of different datasets NGC2141 2.50 −0.39 0.11 430 12.6 and different techniques (simple isochrones fitting against NGC2158 1.42 −0.23 0.07 95 11.6 syntheticCMDs). The same partly holds for Collinder 261. NGC2204 1.74 −0.58 0.10 1200 11.8 Weusedadifferentdataset andaslightly differentmethod. NGC2243 4.50 −0.56 0.17 1260 11.1 Gozzolietal.1996derivedtheagefromevolutionarytracks NGC2420 2.10 −0.42 0.07 655 10.3 NGC2477 0.60 −0.05 0.11 135 9.0 (Fagottoetal.1994),whilewedeterminedtheagefromsuit- NGC2506 1.90 −0.52 0.07 460 10.4 ably interpolated isochrones (Bertelli et al. 1994). Finally, NGC2660 0.70 +0.06 0.10 152 9.2 we performed simulations with synthetic CMDs and used NGC3680 1.80 −0.16 0.05 230 8.3 thecapabilityofourcodetointerpolatebetweenisochrones NGC3960 0.60 −0.34 0.08 180 8.0 ofdifferentmetallicities, adoptingforthesimulations ame- NGC5822 0.45 −0.21 0.12 45 7.9 tallicity Z corresponding to theobservational [Fe/H]. NGC6791 8.00 +0.19 0.19 1010 8.4 The main advantage of this compilation is the homo- NGC6819 2.05 +0.05 0.11 310 8.2 geneity of the sample: ages, metallicities and positions in NGC6939 1.40 −0.11 0.10 255 8.7 the galactic disc are all obtained in the same fashion. This NGC6940 0.60 +0.04 0.10 100 8.3 homogeneity is not guaranteed when using larger samples NGC7142 4.90 0.00 0.06 495 9.7 NGC7789 1.35 −0.26 0.06 165 9.4 as in Friel (1995), Piatti et al. (1995, hereafter P95ea) or Tombaugh2 1.75 −0.70 0.18 1030 15.6 Twarog et al. (1997). In addition, completeness is a cru- cialingredientinordertoexplorepossiblerelationsbetween † Riscomputed withR⊙=8.5kpcforthedistanceofthe theclusterpropertiesandtheirpositioninthegalacticdisc. Suntothegalacticcentreforconsistencywithpreviouswork. However, it is not possible to gather a complete sample for theold,openclustersinthegalactic disc,becauseof strong selection effects mainly related to the past dynamical his- 2.2 Open clusters tory of the galactic disc. Many old clusters have probably beendisrupted(vandenBergh&McClure1980;Friel1995). 2.2.1 Sample Takenthislimitation intoaccount,weusedastatistical ap- Mostoftheopenclustersconsideredinthispaper(Table1) proach tofindcorrelations between theclusters’ fundamen- are taken from the compilation presented by CC94a. We talparameters,i.e.age,metalabundanceandpositioninside selected from that sample all the clusters for which a ho- thegalactic disc. mogeneous metallicity determination was available: all the metallicitiesinTable1areinfactobtainedspectroscopically and they are in the Boston scale (Friel&Janes 1993, Friel 2.2.2 Multivariate analysis 1995).Therefore,withrespecttoCC94awedonotconsider here NGC 6603, IC 1311, NGC 7704, King 2 and AM 2, The search for correlations has been realized by means of sincefortheseclusterthelackofahomogeneousmetallicity MultivariateDataAnalysis(Murtagh&Heck1987)withthe estimatepreventsusfromobtainingtheiragewiththesame SPSSpackage(Nieetal.1975).Inparticular,weperformed method as for all theother clusters. the so-called Principal Component Analysis (PCA), which In addition, the CC94a sample has been updated including is designed to find the number of independent parameters here Berkeley 17 (Kaluzny 1994), Berkeley 20, Berkeley 31 characterizing multivariate data. This technique is widely 4 G. Carraro et al. 0.50 2000 16.0 0.25 14.0 0.00 1500 -0.25 12.0 1000 -0.50 10.0 -0.75 500 8.0 -1.00 6.0 0 0.0 4.0 8.0 0.0 4.0 8.0 0.0 4.0 8.0 age (Gyr) age (Gyr) age (Gyr) 0.50 0.50 2000 0.25 0.25 0.00 0.00 1500 -0.25 -0.25 1000 -0.50 -0.50 -0.75 -0.75 500 -1.00 -1.00 0 0 1000 2000 5.0 10.0 15.0 5.0 10.0 15.0 z (pc) R (kpc) R (kpc) Figure 3.RelationbetweenthefundamentalparametersoftheopenclustersamplegiveninTable1,seeSects.2.2.2&2.2.3fordetails. Solidlinesaretheprojectionsofthefirstprincipalcomponent: ([Fe/H]–t9),(z–t9),(R–t9),([Fe/H]–z),([Fe/H]–R),and(z–R). used in astronomy; for applications to other astronomical Table 2. Principalcomponents (ψ1,ψ2)and eigenvalues forthe problems we refer toMurtagh&Heck. open cluster sample listed in table 1, together with the values The crux of the method is to search for suitable linear (ψ1p,ψ2p)forthePiattietal.(1995)sample. coordinate transformations, which are by definition orthog- onal,andtodiagonalizethecovariancematrixfromanorig- lij age [Fe/H] z R λ variance(%) inal set of variables (x ,x ,...x ) to a new set of variables 1 2 n (ψ ,ψ ,...ψ ) with a zero mean value: ψ1 0.201 −0.849 0.755 0.914 2.167 54.2 1 2 n ψ2 0.938 0.284 0.256 −0.153 1.049 26.2 n ψi =Xlikxk, (1) ψ1p 0.624 −0.890 −0.331 0.782 1.903 47.6 k=1 ψ2p 0.619 0.100 0.873 −0.011 1.155 28.9 where l are the coefficients of the transformation. The ik propertiesofthetransformation aresuch,thattheeigenval- uesλ ofthematrix<ψ ψ >arethevariancesofthedatain i i j distanceoftheSuntothegalactic centre).Thestraight ap- thedirectionoftheprincipalcomponent.Thecorresponding plication of PCAleads totheidentificationof twoprincipal eigenvectorsarethenusedtobuildthenewlinearcombina- components shown in Table 2. tions from the initial parameters. By convention, the first Thefirstprincipalcomponentψ gathersmorethan50%of principal component corresponds to the largest eigenvalue. 1 thevariance.Itscoefficientsareanindication forthedegree As a consequence, the first principal component is a mini- of dependence it has to the original parameters. It appears mum distance fit to a line in the space of the original pa- from the first component that the clusters occupy a three- rameters. The same holds for a possible second, third and dimensional sub-space inside the four-dimensional parame- so on principal component. ters space: a sort of strongly elongated cigar whose main axis is almost parallel to the age axis. Therefore, the old open clusters in Table 1 form a one-parameter family. 2.2.3 Principal Components The projections of the first principal component on the In our case the original space of parameters is four- six planes are: ([Fe/H]–t ), (z–t ), (R–t ), ([Fe/H]–z), 9 9 9 dimensional. The parameters are the age, the metallicity, ([Fe/H]–R), and (z–R). They correspond approximately thez-coordinateandtheradialdistanceRfromthegalactic totheusual regression fits between these pairs of variables. centre (R is computed with R⊙=8.5 kpc, where R⊙ is the The results are shown in Fig. 3. On the galactic disc age-metallicity relation 5 0.50 2000 16.0 0.25 14.0 0.00 1500 -0.25 12.0 1000 -0.50 10.0 -0.75 500 8.0 -1.00 6.0 0 0.0 4.0 8.0 0.0 4.0 8.0 0.0 4.0 8.0 age (Gyr) age (Gyr) age (Gyr) 0.50 0.50 2000 0.25 0.25 0.00 0.00 1500 -0.25 -0.25 1000 -0.50 -0.50 -0.75 -0.75 500 -1.00 -1.00 0 0 1000 2000 5.0 10.0 15.0 5.0 10.0 15.0 z (pc) R (kpc) R (kpc) Figure4.RelationbetweenthefundamentalparametersofthesampleofopenclustersfromPiattietal.(1995),seeSects.2.2.2&2.2.3. Solidlinesaretheprojectionsofthefirstprincipalcomponent: ([Fe/H]–t9),(z–t9),(R–t9),([Fe/H]–z),([Fe/H]–R),and(z–R). A similar analysis is made for the P95ea data set. To 2.3 Stellar population synthesis be representative, a clusters sample has to be well dis- tributed in age, metallicity and position. Their sample in- Thestellar population synthesistechniqueisused togener- cludes 62 clusters with homogeneous metallicities, derived atesyntheticHertzsprung-Russelldiagrams(HRDs)fromei- fromDDOphotometry.Theotherparametersarenonhomo- therstellarevolutionarytracksorisochrones.Itisapowerful geneous, because only one metal-poor cluster (NGC 2243) tool tostudyresolved stellar populations. Theevolutionary with z>1kpc above the galactic plane is included and in phases of a star are linked to each other through libraries addition they did not consider NGC 6791, an old, metal- with stellar evolutionary tracks. The ratio of the number rich cluster with z=1kpc. Moreover, about half of the ofstarsbetweendifferentphasesisdirectlyrelated withthe sample (37 clusters) is younger than 1 Gyr and located at relativeevolutionarytimescale.Thistechniquehasbeenap- z=100 pc. Therefore, homogeneity in age and position is plied mainly to the analysis of stellar aggregates (Aparicio not necessarily guaranteed in their cluster sample. In the et al. 1990, Carraro et al. 1993, Aparicio & Gallart 1995, PCA analysis we follow for consistency P95ea and do not Tosi et al. 1991, Vallenari et al. 1992). consider NGC 6791 and Lo 807. The latter cluster is ex- The so-called HRD galactic software telescope (HRD- cluded, because it lacks an age estimate. Concerning Ru GST) is developed to study the stellar populations in our 46 one has to keep in mind that Carraro&Patat (1995) Galaxy (Ng 1994, Ng et al. 1995). The basis is formed demonstratedthatthisislikelynotanopencluster.Finally, by the latest evolutionary tracks calculated by the Padova the orbits calculated by P95ea are based on an out-of-date group (Bertelli et al. 1994 and references cited therein). A Galaxy model (see for instance Allen&Santillan 1993) and smooth metallicity coverage is obtained through interpola- inadditiontheydidnotcorrectthevelocitycomponentsfor tionbetweenthesetsoftracksfromlow(Z=0.0004)tohigh Galactic differential rotation (Carraro&Chiosi 1994b). (Z=0.10) metallicity. Figure 5 shows a schematic diagram Theresults(ψ1p,ψ2p)ofthePCAareshowninTable2, of the HRD-GST, see also Ng (1994) and Ng et al. (1995) and the projection of the first component shown in Fig. 4 for additional details. areinthesamesixplanesasinFig.3.Thelowereigenvalue SyntheticCMDaregeneratedwithagalacticmodeland and variance of thefirst principal component for theP95ea ought to be comparable with those obtained from observa- samplewithrespecttooursampleisanindicationthattheir tions. The distribution of the stars along the line of sight dataset is less homogeneous. isacomplex mixtureofpopulations.Theages, metallicities and spatial distributions of the stars from different populations contain a wealth of information about the structure, 6 G. Carraro et al. because it is a trace of theprogressive storage of heavyele- mentsin thestar-forming local interstellar medium. Most numerical or analytical chemical evolution models for the Solar Neighbourhood and for the galactic disc (Matteucci&Fran¸cois 1989; Tosi 1988; Prantzos&Aubert 1995; Ferrini et al. 1992, 1994; Pagel&Tautvaisiene 1995; Timmes et al. 1995; Chiappini&Matteucci 1997; Portinari et al. 1997; and references cited in those papers) follow the evolution of chemical abundances for a mixture of stars and gas, which is assumed to be chemically homogeneous in space. The disc is divided into concentric rings, each of which is treated as a homogeneous region. Therefore, such models are aimed at reproducing average features. Many physical inputs of chemical models are rather poorly known and assumptions need to be made about the star formation rate (SFR),theinitial mass function (IMF), theinfall time-scale,andsoforth.Thesequantitiesareusu- allyparameterizedandthencalibratedonobservationalcon- straints.ThepredictedAMRfortheSolarNeighbourhoodis sensitivetotheadoptedSFR,infalltime-scaleandIMF.All chemicalmodelsarebasicallyabletoreproducetheobserved average AMR (see, for instance, Fig. 7). As already mentioned in Sect. 2.1, recent studies of the AMR indicate the Figure 5. Schematic diagram of the HRD-GST. Input for the presence of a significant scatter with respect to theaverage stellar population synthesis engine is the Padova library of stel- trend. The scatter in metallicity for a given age is compa- lar evolutionary tracks. The luminosities and effective tempera- rable to the overall average increase of metallicity from the tureforeachsyntheticstarofarbitrarymetallicityisthentrans- earlyphasesofdiscevolutiontothepresenttime(Edv93ea). formedtoanabsolutemagnitudeinaphotometricpassbandwith As a result, the average AMR no longer represents a tight the method outlined by Bressan et al. (1994) and Charlot et al. constraint forchemical evolutionmodels; thenewchallenge (1996). A synthetic HRD is generated, after specification of the lies now in reproducing the dispersion of the data, rather stellarluminosityfunctionthroughtheinitialmassfunction,the than the average correlation. More complex chemical mod- star formation rate and the age & metallicity range. Synthetic elsarethereforerequired,whichshouldincludemechanisms starsfromthosediagramsarethen‘observed’and‘detected’with inducing the observed scatter. We briefly summarize here the galactic model, through a Monte-Carlo technique. In this various mechanisms that have been suggested. model the densitydistributionof each galactic component along the line of sight is specified. This results in a synthetic CMD of a)Diffusionofstellarorbits allowsstarstomoveawayfrom thefieldofinterest.ThesyntheticCMDoughttobecomparable their birth-places due to scattering by molecular clouds, withtheobservedCMD,whenarealisticsetofinputparameters by density waves in the disc or by infalling satellite galax- isused.Ifthereisamarginalagreementthenchecktheinputfor ies. This phenomenon is revealed by the observed relation eachstepoftheHRD-GST. between the age and the velocity dispersion of disc stars (Wielen 1977, Wielen et al. 1992). Diffusion of stars from different birth-places into nearby orbits results in a spread formation and evolution of ourGalaxy. of metallicities with respect to the expected “local” metal- TheprimarygoaloftheHRD-GSTistodeterminetheinter- licity for a given age; Fran¸cois&Matteucci (1993) discuss stellar extinction along the line of sight and to obtain con- this effect in the framework of chemical evolution models. straintsonthegalacticstructureandontheage–metallicity Edv93ea derived accurate kinematical data and explored of the different stellar populations distinguished in our the influence of stellar orbits on the scatter in the AMR: Galaxy. The results obtained thus far have been reported thescatterremainslarge, evenforsub-sampleswith similar in various papers (Bertelli et al. 1995, 1996; Ng et al. orbitalproperties.Thismightbeanindicationthatanother 1995–1997). The disc is described by a mixture of sub- mechanism is required to explain the scatter, but the argu- populations, each with its specific scale height and metal- ment is still controversial (see Wielen et al. 1996). licity, respectively increasing and decreasing with age. The b) Non-instantaneous mixing of stellar nucleosynthe- star formation of metal poor stars in thegalactic disc com- sis products in the surrounding gas allows for self- mencedaround16–13Gyrago(Ng1994,Ngetal.1997).We enrichment in molecular clouds and for local inhomo- adopted13Gyrforthispaper.Figure7showstheAMRob- geneities (Malinie et al. 1993). Pilyugin&Edmunds (1996) tainedwiththeHRD-GSTtogetherwithdatafrom starsin and van den Hoek&de Jong (1997) combined self- theSolar Neighbourhoodand thelinepredictedbyachem- enrichment due to sequential star formation with episodic ical evolution model. infall of relatively metal-poor gas, triggering star formation on time-scales shorter than the time mixing takes to smear out chemical inhomogeneities. Both sequential star forma- 2.4 Chemical evolution models tionandinfallareobservedtotakeplaceintheSolarNeigh- TheAMRfornearbystarsisastandardconstraintformod- bourhood,buteachmechanisminitselfturnsouttobeinsuf- elling the chemical evolution of the Solar Neighbourhood, ficienttomatchobservationalevidences;ontheotherhand, On the galactic disc age-metallicity relation 7 good agreement is found when both processes are allowed Table 3.Radialgradientwithdifferentage-binning. to operate together. c)Differentgalacticsub-structures(halo,thickdisc,thindisc Agebin(Gyr) Binpopulation d[Fe/H] (dex/kpc) and bulge), each with its own AMR, might overlap in the dR Solar Vicinity. Pardi et al. (1994) followed the parallel evo- t<2 18 −0.064±0.013 lution of halo, thick disc and thin disc with different evo- 2≤t<4 7 −0.113±0.018 lutionary rates, and the resulting mixture of stars shows a 4≤t<6 6 −0.118±0.026 t≥6 6 −0.079±0.033 scatterintheAMR;butitislowerthantheoneobservedin theSolarNeighbourhood.Mostofall,thisexplanationisnot t<3 21 −0.068±0.012 appealing, because only a low contribution from the thick 3≤t<6 10 −0.135±0.016 discandhalopopulationisexpectedintheSolarNeighbour- t≥6 6 −0.079±0.033 hood from star counts analysis. In fact, the expected ratio of metal-poor disc stars with respect to other disc stars is t<4 25 −0.086±0.009 about0.9%andtheratioofhalo/disc≃1/1500(Ng1994,Ng t≥4 12 −0.096±0.024 etal.1997),resultingin2metal-poorthickdiscstarsandno t<5 29 −0.088±0.009 halostarsamongtheEdv93eaFandGstars.Thepredicted t≥5 8 −0.061±0.029 number of stars explains the deficiency of metal-poor stars in Fig. 7. In addition, the expected absence of halo stars is global 37 −0.085±0.008 consistent with the disc kinematics of most of the F and G stars in the sample. The observed scatter should therefore be intrinsic to the disc and not related to the overlap with Mu¨ller (1994), Raiteri et al. (1996), Carraro et al. (1997), other galactic components. andSamland et al. (1997). Althougharbitrary assumptions Therefore, new chemical models need to include the are still needed about the SFR, such models can follow in- possibility of a more complex and composite evolution of fall and gasexchanges amongdifferent galactic regions self- the galactic disc than usually conceived; this in turn adds consistently, reducing the number of free parameters and new, uncertain parameters in the discussion of the chemi- giving a more physical picture of the formation and evolu- cal history of the disc. As correctly underlined by van den tion of theGalaxy. Hoek (1997) and van den Hoek&de Jong (1997), new ob- servationalandtheoreticalconstraintsareneededtodiscern between thedifferent processes. Apart from theproblem related with thescatter in the 3 DISCUSSION AMR, all chemical models are able to reproduce the main WenowcontinuewithacomparisonoftheAMRsdiscussed observational constraints of the Solar Neighbourhood, in in the previous section. We first deal with the radial and spiteofthedifferentparameterization andassumptions.On vertical metallicity gradients observed in the disc, then we thecontrary,differencesappearwhenextendingthestudyto proceed with adiscussion ofthevariousAMRsand eventu- thewhole disc. Inparticular, differentpredictions are given ally suggest some improvements. abouttheevolutionofradialabundancegradientswithtime, although all models are tuned to reproduce the present ra- dialgradientsofoxygenandotherelements.Tosi(1996) di- 3.1 Metallicity gradients rectly compares models from different authors and outlines To make a meaningful comparison between AMRs deduced thatinsomemodelsthepresentnegativegradientisrapidly from different samples, they ought to be in or rescaled to establishedandthenremainsratherunaltered,insomeother the same frame of reference. Positional dependency, due to models it reaches first a steeper value than currently ob- locallydifferentchemicalevolutionhistories,shouldbetaken served and flattens out afterwards, and yet in othermodels intoaccount.But,whencorrectingforit,onehastoconsider a positive gradient is initially established, which then de- that the gradients in different age ranges need not be the creases andeventually turnstonegativevalues. Infact, the same, therefore stars or clusters with different ages are not temporalbehaviourofthegradientbasicallydependsonthe necessarily expected to trace thesame metallicity gradient. competitionbetweenmetalenrichmentbystellarejectaand dilution by infalling metal-poor gas, i.e. on the SFR/infall ratio,at differentgalacto-centric radiiandatdifferentages. 3.1.1 The radial abundance gradient SinceboththeSFRandtheinfallratearepoorlyknowndue totheuncertaintiesintherelated physicalprocesses, differ- The local AMR from Edv93ea, binned with respect to age entassumptionscanresultindifferentpredictionsaboutthe and radial distance, shows a radial dependence of [Fe/H] evolution of the gradient, though all the models can repro- afteracorrection oftheradialdistancefororbitaldiffusion. duce the present situation. An observational determination The radial gradient seems to be shallower or absent for the of the radial gradient at different galactic ages would be a oldest stars, but, within the uncertainties inherent in the strong constraint in discriminating between different chem- correction for orbital diffusion and the large scatter in the ical models (see Sect. 3.1.1). AMR, the data might also be consistent with a gradient ToexplainthescatterinthelocalAMRandtodescribe independentof age. theevolutionofthewholediscinamoreconsistentway,new A radial metallicity gradient for open clusters was first codeswithmorerealisticinputphysicsarerequired.Astart found by Janes (1979) and then confirmed by CC94a and is made with the chemo-dynamical models of Steinmetz & Friel (1995). Open clusters are a much better tracer of the 8 G. Carraro et al. Figure6.Radialabundancegradientsforoursample of open clusters binned in different age ranges. The dashed line (panels a–e) shows the average gradient (−0.09dexkpc−1)asdeterminedfromalltheclusters fromTable1.Thesolidlinesinpanels a–dshow the gradientsdeterminedforthecorrespondingageranges (−0.06, −0.11, −0.12, and −0.08 dex kpc−1, respectively). radial gradient than nearby stars, both because they span for the different age-binning are listed in Table 3. In panels alargerrangeofgalacto-centric distancesandbecausethey b–d thegradient of panel a is included for comparison. arenotaffectedsignificantlybyorbitaldiffusion.Indeed,or- Note that for the determination of the radial gradient bit calculations haveshown that open clusters donot move both CC94a and P95ea did not properly consider separate farawayfromtheirbirth-places(Carraro&Chiosi1994b).A agegroups.ButtheP95eadatasetisbasicallyayoungsam- radialgradient isalso tracedbyHII-regions,B-stars, plane- ple(t<1Gyr)andtheirradialgradientof−0.07dexkpc−1 tary nebulæ (PNæ) and so forth. reflects in fact thepresent day gradient. B-stars and HII-regions, due to their short lifetimes, Table 3 displays the effects of different age-binning on are tracers of the present day radial gradient (of oxygen the derived radial gradients; indicated errors are standard abundance).Thesetwodifferentpopulationsseemedtolead deviations.Beforecommentingtheoutcome,acaveathasto to controversial results: the gradient traced by B-stars was be stressed: the number of objects involved in this analysis much more shallow (even flat) than the gradient traced isrelatively low,sostatistically theresultsarenotvery sig- by HII-regions (see Prantzos&Aubert 1995 and references nificant.Theyshowatrend,whichrequiresverificationwith therein). But the latest spectroscopic studies for large ho- a larger sample. mogeneous samples of B-stars indicate a radial gradient By selecting 2–3 Gyr wide age-bins, the results are similar d[O/H] = −0.07 dex kpc−1 (Smartt&Rolleston 1997), in andindicatethatthepresentdaygradientisabitshallower dR agreement with the gradient deduced from HII-regions, so thanthepastone;themiddleepochseemstodisplayasteep- thatnowadaystheformerdiscrepancyappearstobesolved. ening of the gradient. The choice of wider bins (4 Gyr) ba- sically suggests the same: the present day gradient appears As pointed out in Sect.2.4, thepresent radial gradient again to be shallower. On the other hand, choosing a bin provides a constraint for chemical evolution models, but to width of 5 Gyr, we get a different result, probably due to discern between different models one needs to know how a mixing of the present and middle epoch gradients in the thegradient evolved in thepast. Open clusters are an ideal younger age bin. However in this last case the statistics is template for this analysis, since they have well-determined much poorer, because we are left with only 8 clusters older ages, metallicities and galacto-centric distances. than 5 Gyrversus 29 in theyoungerbin. We analyse our homogeneous cluster sample of Ta- For the whole sample we derive an average gradient of ble 1. We divide the sample in age-bins, and for each bin −0.09 dex kpc−1, seeFig.6e; for any age-bin in Table 3 the we derive the gradient by means of a weighted least-square gradient is close to this average value, within the errors. In fit in the [Fe/H] vs R plane (using a version of the code the overall, our sample of clusters seems to show that the by Pagel&Kazlauskas 1992). In the fitting procedure the radialgradienthasnotchangedmuchintime,thoughahint weights are the errors on [Fe/H], also listed in Table 1. A can be seen for a steeper gradient in the past, at interme- similar analysis was performed by Tosi (1995), but with a diate ages. Therefore, chemical models predicting either a smallersample.Ourresultsforthefourage-bins2Gyrwide constant gradient or a slightly steeper negative gradient in are shown in Fig. 6 and the slopes d[Fe/H] of the gradient the past seem to be favoured with respect to models pre- dR On the galactic disc age-metallicity relation 9 dicting a gradient that settles to the current negative value starting from positive initial values. For a detailed comparison of various chemical models, we refer to Fig. 5 of Tosi (1996) and references quoted therein. Unluckily,due to the large scatter and the small number of clusters in the older age-bins, one cannot actually draw a firm conclusion. Thepresenceof ametallicity gradientforopen clusters has been questioned by Twarog et al. (1997), who find no gradient for the clusters in their sample at galacto-centric radiusbelow10kpc.However,theirFig.3bdisplaysthatthe majority of these clusters are located between 7.5–9.5 kpc and have an overall spread of more than 0.2 dex in metallicity. Over a distance range of only 2 kpc our average gradientcorrespondstoametallicitydifferencesmallerthan 0.2dex.Therefore,withinthatdispersionourresultsarenot necessarily at odds with their sample. In addition, Twarog etal.’sclaimthatopenclustersdisplayastepfunctionwith a discontinuity at 10 kpc rather than a gradient in metallicity should be verified by separating in age groups. The Figure7.TheAMRforstarsintheSolarNeighbourhood(open stepfunctioncouldbeaconsequenceofinsufficientdiscrim- stars and circles, Ng&Bertelli 1997), see also Fig. 2 for details ination between thecontribution from different age groups, aboutthesymbolsizeanduncertaintyintheageforthesestars; becausethesampleinsideR=10 kpcisheavilyweightedto- the solid line is the relation obtained for the galactic disc from ward clusters younger than 1 Gyr, while the outer clusters studieswiththeHRD-GST(Ngetal.1996,1997);thedottedline are predominantly older. isthepredictionfromthechemicalevolutionmodelfromPortinari The radial gradient and its age dependence have been etal.(1997), withanadoptedageforthediscof13Gyr. studiedalsobymeansofPNæ.Maciel&Köppen(1994)find anoxygengradientwhosepresentvalueisinagreementwith thatofHII-regions.Itseemsthatthegradienthasremained analyse the vertical trend. But then, there are not enough roughly constant, or maybe it was slightly shallower in the clusters in the bins to reliably constrain the vertical gradi- past. But, unlike open clusters, PNæ haverather uncertain ent. In addition, open clusters form an incomplete sample ages and distances, and their present location might have due to tidal disruption, which is more effective close to the beenspoiledbyorbitaldiffusion.Allthesefactorsintroduce galactic mid-plane. Therefore, clusters at low galactic lati- uncertaintiesinthederivedagedependenceofthegradient. tudes are preferentially destroyed, which might introduce a Consideringtheindicationsfromnearbystars,openclusters bias in thedetermination of the vertical gradient. and PNæ altogether, the most sensible assumption is that Ng et al. (1996) have demonstrated that both the ra- thegradient remained roughly constant in time. dial and the vertical distribution of open clusters contain StarcountswiththeHRD-GSTarenotsensitiveenough information about the scale length and scale height of the to detect a radial gradient within a single-age popula- galacticstellarpopulations.Inthecaseoffieldstars,orbital tion. Indeed, a gradient of −0.21 dex kpc−1 is already in- diffusion is expected to be effective enough to smooth out ducedbydifferencesinscale-lengthsamongagepopulations, a vertical metallicity gradient within a single-age popula- whilewithinasingle-agepopulationtheintrinsicgradientof tion, so that the vertical structure of the disc is dominated −0.09 dex kpc−1 is masked out by the adopted extinction by the different scale heights of different age populations. along theline of sight. Indeed,instarcountstheyoung,metal-richerstarsarecon- fined to regions close to the galactic mid-plane, while the older, metal-poorer stars with a larger scale height domi- 3.1.2 The vertical abundance gradient nateat larger vertical distances from thegalactic plane. As The existence of a vertical metallicity gradient among old aconsequence, in starcountsa vertical metallicity gradient open clusters is controversial. Friel (1995) and CC94a do is due to sampling of different age populations rather than not find evidence for such a gradient, whereas P95ea do reflecting a gradient within a single-age population. find a correlation between [Fe/H] and vertical position. By In star counts, radial and vertical abundancegradients binning the data in z they obtained a gradient equal to are primarily expected due to differences between the scale −0.34 dex kpc−1. Their sample contains only one cluster length and height between different stellar age populations. above1kpc,togetherwith4clustersabove500pc.Inaddi- Since the relative differences in scale length are small with tion they did not consider NGC 6791, which is high above respect to those in scale height, these latter dominate the the plane (1 kpc) and metal-rich. From our sample the re- HRD-GSTstarcountsanalysis.Astrongverticalabundance sultingslopeisshallower:−0.25 dex kpc−1,notstronglyde- gradient in star counts is therefore a hint that insufficient pendentonanyparticularcluster(Fig.3,left-bottompanel). discrimination wasmadeforthedifferentagegroupswithin Howeveracaveat istobestressed,becausetoestimate a data set. A metallicity gradient within an age population the vertical gradient one should disentangle the effects of is a second order effect. vertical,radialandagedependence.Inprinciple,oneshould Almostallopenclustersofagivenagearefoundatdis- first bin the sample in homogeneous sub-samples with re- tances larger than three times the exponential scale length spect to age and galacto-centric distance, and only then andscaleheightforthecorrespondingstellarpopulationsof 10 G. Carraro et al. UsingopenclusterstotracetheAMRhasthemainad- vantagethatclusteragesaremuchmorereliablydetermined than the ages of single field stars, but also the additional problem of the radial and/or vertical dependence of cluster metallicity.Cameron (1985) wasthefirsttoderiveanAMR from open clusters after correcting for the radial gradient, with the aim at cleaning the data from the space dependence.Butauniqueradialcorrection shouldnotbeapplied recklessly to different age groups, due to the possible age- dependence of the radial gradient (Sect. 3.1.1). Unluckily, the age dependence of the radial gradient is poorly con- strainedandanyconfidentcorrectionfortheradialgradient of open clusters is spoiled. Our sample is consistent with a radial gradient which is constant in time, therefore we derive from it the AMR shown in Fig. 8 by correcting for a gradient of −0.09 dex kpc−1, independent of age. Still, one shouldbearinmindthisuncertaintyinthecorrection,when comparingtheAMRofopenclusterswiththelocalAMRof nearby stars. In addition, we did not apply any correction Figure 8.TheAMRforopenclustersfromTable1(filleddots) fortheverticalgradient,sinceitsvalueorevenitsexistence versus the Solar Neighbourhood. The metallicities of the open are not clearly established yet. Figure 8 displays that the clusters are corrected according to the global radial gradient: [Fe/H]corr=[Fe/H]meas −0.09(R⊙−R)(kpc). Included in this AMRs of open clusters and of stars are in good agreement, figureisasuggestedimprovementforthedescriptionoftheAMR both showing a similar trend in the scatter. We also notice with two separate components for the HRD-GST. The adopted that both relations show a lack of scattered points in the age forthe start ofthe formationof the ‘young’ disccomponent metal-rich side in the age range 3–5 Gyr and/or an excess (solid line) is 8.5 Gyr and 16 Gyr for the ‘old’ disc component of relatively metal-rich objects in therange 5–9 Gyr. (long-dashedline). 3.3 The role of the bulge/bar theHRD-GST.Theverticalgradientduetostellarmixesof The up-turn of the metallicity of the open clusters with different ages, computed at the “transition” region toward possibly a peak near t≃8Gyr might be related with the openclusters,is−0.40dexkpc−1.Thisvalueiscomparable formation of the triaxial bar structure. Nget al. (1996) ob- to the one found by P95ea, confirming that their gradient tainedacomparableageandmetallicityrange(t=8–9 Gyr, couldindeedbeduetoinsufficientdiscriminationofdifferent Z=0.005–0.030) for this structure. The bar however does age groups. not explain the presence of metal-rich stars in the Solar The orbits of clusters are less affected by orbital diffu- Neighbourhood,becauseitslocaldensitywithrespecttolo- sion than those of field stars. So, once a vertical gradient cal disc stars is too low. In addition some of the metal-rich for open clusters were established unambiguously, it could stars are older than thebar. provideanimportantclueaboutthediscformation history. At t≃8Gyr, the stars in the Solar Neighbourhood are But, as already stressed, current samples do not give con- metal-richer than expected from the AMR(HRD-GST:disc) clusive indications. and AMR(chemics). The calculations from Samland et al. (1997) suggest that this could be due to pre-enrichment with material originating from typeIISNæfrom thebulge. 3.2 The galactic disc AMR On the other hand, if the ‘bar’ structure formed through a merger event some of the metal-richer stars from the in- Figure 7 shows various AMRsderived from: ner disc or bulge regions could have migrated near to the − stars in the Solar Neighbourhood with the ages from Solar Neighbourhood and settled down there. This could NB98 (open circles and open stars); explain the presence of rather metal-rich clusters and stars − the HRD-GST population synthesis analysis for the between 5 and 9 Gyr. But suitable dynamical models are galactic disc from Ng et al. (1996, 1997; solid line); required(Mihos&Hernquist1996) toexploreandcheckthe − a chemical evolution model from Portinari et al. (1997; merger/capture scenario properly against all the observa- dotted line). tional constraints. The disc AMR obtained from the HRD-GSTis determined from star counts towards the north galactic pole and the galacticcentre.Nocorrectionforradialorverticalgradients 3.4 Improvements isapplied,becausestarcountsarenotsensitivetogradients within single-age populations, see Sect. 3.1.1&3.1.2. For The comparison of the AMRs from various methods sug- t<5Gyr AMR(HRD-GST:disc)≃AMR(chemics).Between gests some improvements. t=5–13 Gyr the metallicity of AMR(chemics) is higher a) The Solar Neighbourhood: a new sample of stars with thanthatofAMR(HRD-GST:disc).Indeed,starcountstend spectroscopic metallicities andreliable agesisdesirable and to follow the metal-poorer trend, which is more populated betterages are needed for t>10Gyr. and has therefore a larger weight. b) Open & globular clusters: the sample of open clusters

On the galactic disc age-metallicity relation

Similar On the galactic disc age-metallicity relation