On the galactic disc age-metallicity relation

12 Pages·0.34 MB·English

by  G. Carraro

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,[email protected]
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, here-
after 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 popula-
tions 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 mod-
els 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 men-
tioned 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, respec-
tively).
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 compar-
ison 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 me-
tallicity. 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 metal-
licity 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&K¨oppen(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 depen-
dence.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 de-
rive 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