The Metal Contents of Milky Way Globular ClustersAuthor(s): Graeme H. SmithSource: Publications of the Astronomical Society of the Pacific, Vol. 112, No. 767 (January2000), pp. 12-17Published by: The University of Chicago Press on behalf of the Astronomical Society of the PacificStable URL: http://www.jstor.org/stable/10.1086/316498 .

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PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 112 :12È17, 2000 January2000. The Astronomical Society of the PaciÐc. All rights reserved. Printed in U.S.A.(

The Metal Contents of Milky Way Globular ClustersGRAEME H. SMITH

University of California Observatories/Lick Observatory, University of California, Santa Cruz, CA 95064 ; graeme=ucolick.org

Received 1999 July 2 ; accepted 1999 September 8

ABSTRACT. Globular clusters in the Milky Way contain total masses of heavy elements ranging from afew solar masses to as great as 104 Given that a massive star of greater than 40 can produce inM

_. M

_excess of 12 of heavy elements, it is possible that at least some globular clusters contain the metals fromM

_only a very small number of supernovae, although many clusters contain a sufficiently large mass of metalsthat the contribution from 10 to 200 or more supernovae is required. More than one supernova event wouldbe needed within an initially metal-free cloud to raise the heavy-element abundance to a level greater than[A/H]\ [1.8 dex. Many halo Ðeld stars have metallicities much lower than this. It is possible that suchstars formed from cold primeval clouds with masses in excess of 2] 106 that were self-enriched by onlyM

_one or two supernovae.

The metallicity distribution of Milky Way globular clusters shows some features that may vary withcluster mass. By binning clusters into integrated-magnitude groups of less than [8.0, [8.0 to [6.5,M

V,tand greater than [6.5, it is shown that the percentage of clusters with metallicities [A/H][ [1.0 increaseswith decreasing cluster mass. In addition to this trend, the occurrence of intermediate metallicities with[A/H]\ [1.0^ 0.2 is mainly restricted to globular clusters fainter than It is possible thatM

V,t\[8.0.some of these intermediate-metallicity clusters formed during an era in the Galactic halo that favored theproduction of lower mass systems.

1. INTRODUCTION

One characteristic of the globular cluster system of theMilky Way (MW) which has received much attention onaccount of the information that it can provide about galaxyformation and chemical enrichment is the heavy-elementabundance distribution or ““ metallicity ÏÏ distribution (e.g.,Hartwick 1976 ; Searle & Zinn 1978 ; Zinn 1985 ; Laird et al.1988 ; Ryan & Norris 1991). For example, a well-documented feature of the MW globular cluster metallicitydistribution is that it is bimodal (e.g., Freeman & Norris1981), a property which has been discussed in detail by Zinn(1985), Armandro† & Zinn (1988), and Armandro† (1989)as being attributable to the presence of two relatively dis-tinct groups of globular clusters within the Galaxy : a halogroup and a disk group. A component of the globularcluster population associated with the Galactic bulge hasalso been identiÐed (Minniti 1995).

By contrast, less attention has been devoted to the totalmetal contents of globular clusters (GCs). The low metalabundances of many GCs result in their total heavy-elementcontents being quite low, and the number of supernovaewhich contributed metals to clusters such as M92 was poss-ibly very small (Cohen 1979). In this paper we use informa-tion on the metallicities and heavy-element contents ofMilky Way globular clusters to develop some inferences

about the degree to which heavy elements from massivestars were diluted within the interstellar medium of theearly gaseous Galactic halo. In addition, we investigate thepossibility that the Milky Way GC metallicity distributionmay have some subtle features that vary with cluster mass.

2. THE METAL CONTENTS OF MILKY WAYGLOBULAR CLUSTERS

The metallicity of a globular cluster star would have beendetermined by two factors : (1) the number of massive starsthat had previously contributed metals to the gas fromwhich the globular cluster eventually formed, and (2) theextent to which these metals had been diluted with ambientmaterial at the time of cluster formation. The Ðrst of these,the number of massive stars needed to produce the metalcontent of a globular cluster, can be estimated from thetotal mass of metals within the cluster combined with theo-retical calculations of the metal productions of massivestars. In turn, the total heavy-element contents of MWglobular clusters can be calculated from the cluster inte-grated magnitude and metallicity.

Values of the total absolute magnitude and metal-MV,t

licities [A/H] of Milky Way globular clusters were obtainedfrom the Catalogue of Milky Way Globular Cluster Param-eters, maintained by W. E. Harris, which contains a com-

12

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5

10

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25

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0

5

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-2 -1 0-2

-4

-6

-8

-10

[A/H]

METAL CONTENTS OF MILKY WAY GCs 13

FIG. 1.ÈMetallicity distribution of Milky Way globular clustersderived from the Harris GC Catalogue.

pilation of properties of Milky Way GCs (hereafter HarrisGC Catalogue).1 The version of the catalog used in thispaper is that dated 1999 June 22. The reader is referred tothe paper by Harris (1996) for a discussion of this com-pilation.

The metallicity distribution for 145 clusters in the HarrisGC Catalogue is shown in Figure 1. A metallicity bimodal-ity is clearly evident, with peaks near [A/H]\ [1.5 and[0.5, in good accord with the conclusions of Armandro† &Zinn (1988). A plot of cluster integrated absolute magnitude

versus metallicity from the Harris GC Catalogue isMV,t

shown in Figure 2. There is no obvious correlation betweenthe plotted quantities. The accepted interpretation of thislack of correlation is that (most) globular clusters are notself-enriched systems, but rather their metal abundanceswere established by chemical enrichment events within thehalo prior to their formation.

The total absolute magnitude of a cluster can be con-verted to a total mass using the relationM

c

log10 (Mc/M

_)\ 2.42[ 0.4M

V,t (1)

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ1 See W. E. Harris, Catalogue of Milky Way Globular Cluster Param-

eters (1999 June 22), which is located at http ://physun.physics.mcmaster.ca/Globular.html.

FIG. 2.ÈPlot of the total absolute visual magnitude vs. metallicityMV,t

[A/H] for globular clusters of the Milky Way. The data were obtainedfrom the Harris GC Catalogue.

if a mass-to-light ratio of is adopted (followingM/LV

\ 3.0Cherno† & Djorgovski 1989). In addition, the mass ofheavy elements within a cluster of mass isM

ZM

c

log10 (MZ/M

_) \ log (M

c/M

_) ] [A/H][ 1.77 , (2)

where a solar heavy-element mass fraction of isZ_

\ 0.017adopted. Equations (1) and (2) can be combined to give

log10 (MZ/M

_) \ 0.65] [A/H][ 0.4M

V,t . (3)

This equation has been used to plot lines of constant inMZ

Figure 3, which is otherwise identical to Figure 2. Each lineis labeled by the corresponding value of in units of solarM

Zmasses. The total metal contents of MW globular clustersrange over 4 orders of magnitude : 1.0 \ (M

Z/M

_)\ 104.

The mass of heavy elements ejected by a star ofmz,s (M

_)

mass is taken from Woosley & Weaver (1986) to bems(M

_)

mz,s \ 0.4m

s[ 4.2 . (4)

A star of mass is capable of ejecting in excess ofms[ 40 M

_12 of heavy elements. In the case of most globularM

_

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-2 -1 0-2

-4

-6

-8

-10

[A/H]

1 10 100

10e3 10e4

14 SMITH

FIG. 3.ÈDuplicate of Fig. 2 onto which has been added loci of constantcluster metal content (straight lines) ; each line is labeled with the corre-sponding total mass of metals in a cluster (in solar mass units).

clusters the total metal content is much greater than this,and on the order of 10 to 200 or more supernovae areneeded to account for the metal content of many GCs.However, there are some globular clustersÈin the lower leftof Figure 3Èwhose metal contents are comparable to theoutput of only a few supernovae. Figure 3 indicates thatthere are nine GCs containing a total mass of metals com-parable to or less than 10 In addition, a substantialM

_.

fraction of GCs contain less than 100 of heavy ele-M_

ments. These relatively low metal contents raise the possi-bility that the regions within the halo clouds from which atleast some MW globular clusters formed had been enrichedby only a small number of massive stars.

3. DILUTION OF METALS IN GLOBULARCLUSTER PROGENITOR CLOUDS

As noted above, the metallicity in the gas from which aglobular cluster formed would have depended not only onthe number of supernovae that released metals into it butalso on the degree to which supernova ejecta had beendiluted throughout this gas. The low metal contents of some

GCs lead us to consider the metallicity that could be pro-duced within a gas cloud by a single massive star whichejects heavy elements via a supernova explosion. A varia-tion of this problem has been addressed by Brown, Burkert,& Truran (1991) for the case of multiple supernovae withina cloud, whose ejecta are assumed to combine to producean expanding supershell. A very simpliÐed calculation ispresented here which considers the metal enrichment pro-duced by a single star exploding as a supernova within aninitially metal-free cloud of gas. It is assumed that themetals ejected by such a star are transported outwardwithin an expanding supernova shell which sweeps upmaterial from the ambient medium. During the advancedstages in the expansion of this shell, the mass of ambient gasthat has been incorporated into the shell will greatly exceedthe mass of material ejected by the star. We assume that theejected metals become distributed homogeneously through-out the swept-up shell. Suppose that a star of initial mass m

sejects a total mass of material in a supernova explosion,mejof which a mass is in the form of heavy elements. At them

z,stime that the supernova shell ceases to expand at the con-clusion of the momentum-driven phase (the snowplowphase), the velocity of the shell will have become equal tothe mean particle speed within the ambient medium Ifv

a.

the total mass of ambient gas which has been swept up atthis time is then the momentum-driven phase of super-M

A,

nova shell expansion will cease when

MA

\ mejvexpva

, (5)

where is equal to the initial expansion speed of thevexpsupernova ejecta. If the mass of metals has becomem

z,suniformly distributed throughout the swept-up mass atM

Athe time of the cessation of the snowplow phase,2 thisswept-up material will be enriched to a metal abundance of

Combining this result with equation (5), andZ1\ mz,s/MA

.setting givesm

z,s \ bmej,

Z1 \ bva

vexp. (6)

Typical values of b can be estimated from equation (4) ;b \ 0.25 (^0.05) seems to be a fairly representative valuefor stars of mass An initial expansion speed ofm

s[ 20 M

_.

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ2 This assumption is idealistic. Observations of young supernova rem-

nants such as Cas A show spatial inhomogeneities in the heavy elementsejected by the progenitor star (e.g., Chevalier & Kirshner 1978 ; Lamb1978). However, Shigeyama & Tsujimoto (1998) note that as the remnantexpands, various instabilities such as Rayleigh-Taylor instability (e.g.,Draine & McKee 1993) will serve to mix the ejecta with the swept-upambient material. The assumption that the ejected metals are distributedhomogeneously throughout the swept-up ambient gas is at least consistentwith the chemical homogeneity of globular clusters in heavy elements suchas Fe (as reviewed, for example, by Stetson 1993).

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METAL CONTENTS OF MILKY WAY GCs 15

km s~1 is adopted, this being the maximum ejectavej\ 104speed listed for Type II supernovae by Weiler & Sramek(1988), as well as the speed typically observed near super-nova maximum (Raymond 1984). In addition, theories ofshock breakout from massive stars undergoing supernovaexplosions indicate speeds of this order (e.g., Bethe 1996).Further supposing that km s~1, such as may prevailv

a\ 10

within a 104 K halo protocloud that has been heated by theactivity of massive stars, gives which isZ1\ 2.5] 10~4,equivalent to a logarithmic abundance relative to the Sun of[A/H]\ [1.83 for This gives a metallicityZ

_\ 0.017.

that is typical of the lowest abundance globular clusters ofthe Galactic halo.3 If, instead, a supernova event occurswithin a very cold cloud for which km s~1, the super-v

a\ 1

nova shell will expand much farther during the snowplowphase, with the result that the ejected metals will be distrib-uted throughout a more massive shell of ambient gas ; theresultant metallicity of the material within the shell will be

which corresponds to [A/H]\ [2.8.Z1\ 2.5] 10~5,This is B0.5 dex lower than the heavy-element abundancesof the most metal-poor globular clusters, but metallicitiesthis low, and lower, are found among the halo Ðeld stars(e.g., Bond 1980 ; Beers, Preston, & Shectman 1992).

An implication of these calculations is that if globularclusters formed within primeval halo clouds, i.e., clouds ofzero metallicity, that self-enriched themselves to the clustermetallicity via supernovae activity, then the degree of dilu-tion of metals must have been no greater than that obtain-ing within a single supernova remnant shell at the cessationof the moment-driven phase. To produce a metallicitygreater than [A/H]\ [1.8 may require that individualsupernova shells were not able expand to the completion ofthe snowplow phase, possibly because of encounteringother such shells. Alternatively, if shell expansion was notinhibited, it would be required that the ambient medium beprocessed through several supernova shells at di†erenttimes. In either case it is inferred that multiple supernovaevents would be necessary within a primeval cloud toaccount for an abundance of [A/H][ [1.8. This conclu-sion is in accord with the observation, noted above, that themetal contents of many globular clusters (Fig. 3) are suffi-ciently great as to require the contribution of a substantialnumber of supernovae. However, it might seem unrealisticto invoke primeval clouds as the progenitors of globularclusters on account of the high level of supernova activity.

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ3 In cases where the initial ejecta speed is smaller than 104 km s~1,vexp

the dilution of supernova material will not be as great at the end of thesnowplow phase. For example, a range of speeds of D2000È9000 km s~1 isobserved among the fast-moving knots of the young Galactic supernovaremnant Cas A (van den Bergh 1971 ; Bell 1977). If is taken to be in thisvexprange, then the corresponding values of [A/H] would be [1.8 to [1.1 for

km s~1. Such a metallicity range is less than that among globularva\ 10

clusters in the halo of the Galaxy.

The alternative is to assume that the progenitor clouds ofglobular clusters were not primeval, i.e., were not of zerometal abundance, but rather were built up from gas thathad been enriched in metals during prior episodes of starformation. This alternative provides a natural explanationfor the lack of correlation between mass and metallicityamong the Milky Way GCs as noted above.

By contrast, the lowest metallicity Ðeld stars in the halomay have formed within very cold clouds in which thedensity of supernovae was low, such that there was littleprobability prior to the end of the momentum-conservingexpansion phase that an individual supernova shell wouldoverlap other metal-enriched shells. In particular, it is pos-sible that the most metal-poor Ðeld stars may have beenformed within self-enriched primeval clouds. A lower limitto the mass of such clouds can be had by assuming that theyexperienced metal enrichment by only one supernova. Atotal of 10 of metals, such as might be ejected from aM

_single massive star during the formation of the halo, wouldhave to be diluted within a total mass of 1.9 ] 106 ofM

_metal-free gas in order to produce an average metallicity of[A/H]\ [3.5 (an abundance which is characteristic of anumber of stars discovered by Beers et al. 1992). This can becompared to the amount of ambient material that would beswept up by a supernova shell. If a star ejects a mass of

at an initial ejecta speed of km s~1mej\ 20 M_

vexp\ 104in a supernova explosion, the mass swept up into the shellby the end of the snowplow phase, as calculated from equa-tion (5), will be for a warm ambientM

A\ 2 ] 104 M

_medium with km s~1 and for av

a\ 10 M

A\ 2 ] 105 M

_medium with km s~1. Even in a quiescent medium,v

a\ 1

this calculation indicates that the heavy elements from asingle supernova must have been diluted within an amountof ambient metal-free gas that is greater than the massswept up at the end of the snowplow phase if the lowestmetallicities found among metal-poor halo Ðeld stars are tobe explained.4 It is possible therefore that the most metal-poor Ðeld stars in the halo formed from cold primevalclouds of mass in excess of 2] 106 that experiencedM

_only one or two supernovae. In such quiescent clouds themetal output of a single supernova could have becomediluted with a mass of material greater than that swept upat the conclusion of the snowplow phase, resulting in metal-licities of [A/H]\ [3.5 dex or lower. This inferred scarcityof supernovae among the Ðrst sites of low-mass star forma-tion in the halo is in accord with the arguments of Audouze

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ4 Equation (2) of Shigeyama & Tsujimoto (1998) indicates values of M

Athat are about 2.2È4.3 times higher than those calculated here if a super-nova of energy ergs and ambient media of density n \ 10 cm~3E0\ 1051and to 1 km s~1 are considered. Even with such increased dilutionv

a\ 10

of the supernova ejecta at the end of the snowplow phase, further dilutionwith the ambient interstellar medium is still needed to produce the lowestmetallicities found among halo Ðeld stars.

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[A/H]

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16 SMITH

& Silk (1995) and Shigeyama & Tsujimoto (1998). It is alsoin accord with the observations of signiÐcant star-to-stardi†erences in heavy-element abundance ratios among themost metal-poor halo Ðeld giants (McWilliam et al. 1995).As McWilliam et al. (1995) suggest, such di†erences couldbe produced by stochastic Ñuctuations in the small numbersof supernovae that enriched the gas from which such starsformed.

The young halo probably lost most of the heavy elementsproduced by its massive stars, with only a fraction of thesemetals actually being incorporated into low-mass halo Ðeldor GC stars. A generation of stars which produced a mass

of heavy elements will also form a mass of long-MZ

MZ/y

lived stars and stellar remnants, where y is the yield (Searle& Sargent 1972). For a globular cluster of mass andM

cheavy-element mass fraction Z, the mass of long-lived starsand remnants associated with the formation of the metalcontent of this cluster is

Mr\ZM

cy

\ 10*A@H+McZ

_y

.

The ratio of this mass to the cluster mass is Mr/M

c\

since for a Salpeter-like10*A@H+Z_/y B 10*A@H+, Z

_B y

stellar mass function (Smith & McClure 1987). For haloglobular cluster metallicities with [A/H] of [2.3 to [1.0,

ranges from 1/200 to 1/10. The small values of thisMr/M

cratio indicate that most of the heavy elements manufacturedby stars in the halo were not incorporated into subsequenthalo star formation, but were instead lost from the halo atsome stage in its evolution. In the chemical evolution modelfor the halo formulated by Hartwick (1976), which employsthe instantaneous recycling approximation, the loss ofmetals from the halo occurs contemporaneously with starformation.

4. A POSSIBLE MASS DEPENDENCE IN THEMETALLICITY DISTRIBUTION OF MILKY WAY

GLOBULAR CLUSTERS?

Although it appears from Figure 2 that there is a lack ofcorrelation between integrated magnitude and metallicityamong MW globular clusters, a couple of additional obser-vations serve to add a caveat to this conclusion. The rangeof metallicities among the most massive GCs with totalmagnitudes (i.e., masses ofM

V,t\ [8.0 log10 Mc/M

_[

5.62 for is comparable to that among lessM/LV

\ 3.0)massive GCs. However, among such high-mass GCs there isa relative deÐciency of objects with metallicities of[0.8[ [A/H][ [1.2, and there are no clusters withmetallicities [ 0.8[ [A/H][ [1.0. By contrast, a

FIG. 4.È[A/H] metallicity distributions for Milky Way globular clus-ters of three di†erent absolute magnitude groups : M

V,t \ [8.0,and The cluster metallicity data were[ 8.0¹M

V,t ¹ [6.5, MV,t [[6.5.

taken from the Harris GC Catalogue.

number of lower mass GCs have such intermediate metal-licities, particularly those with absolute magnitudes in therange Figure 4 shows the metallicity[ 6.5º M

V,tº [8.0.distributions for globular clusters in three di†erent absolutemagnitude groups : high-mass clusters with M

V,t\ [8.0,intermediate-mass clusters with and[ 6.5º M

V,tº [8.0,low-mass clusters with With decreasingM

V,t [[6.5.cluster mass there is a trend toward a greater percentage ofobjects with [A/H][ [1.0. In the three magnitude groupscited above the fraction of GCs with [A/H][ [1.0 is 0.19,0.33, and 0.40, respectively. Metallicities of greater thanone-tenth solar are therefore more frequent among lowermass MW globular clusters than among higher masssystems.5 In addition, although a bimodality can be dis-cerned in the metallicity distributions of all three groups ofGCs, there is less of a gap at intermediate metallicities( [ 0.8[ [A/H][ [1.2) among the intermediate-mass

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ5 The MW open clusters may represent the most extreme expression of

this trend.

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METAL CONTENTS OF MILKY WAY GCs 17

clusters. The fraction of clusters having metallicities rangingfrom [0.80 to [1.19 dex is 0.054, 0.14, and 0.12 for theabove mass groups. Intermediate metallicities are thereforeless common among high-mass clusters than(M

V,t\[8.0)among GCs of lower mass.

The data in Figure 4 suggest the intriguing possibilitythat the metallicity distribution of the MW globular clustersmay exhibit some subtle variation with cluster mass.Perhaps some of the lower mass clusters formed toward theend of the star formation epoch in the Galactic halo whenthe metal abundance in the interstellar medium of the halohad risen to [A/H]D [1.0. As a result of the infall of muchof the proto-Galaxy into the disk, the formation of lowermass but higher metallicity GCs might have been favoredtoward the conclusion of the cluster formation epoch in thehalo. A substantial population of low-mass moderate-metallicity globular clusters may have formed in the halo ;however, many of these may have been subsequently dis-rupted by a variety of processes such as stellar mass loss,evaporation, and tidal shocking accompanying passages ofthe clusters through the Galactic disk or bulge (Fall & Rees1977 ; Applegate 1986 ; Aguilar, Hut, & Ostriker 1988 ;Cherno† & Weinberg 1990 ; Oh & Lin 1992 ; Gnedin &Ostriker 1997). Such disruptive processes may have alteredthe globular cluster metallicity distribution if there hadbeen any initial dependence on cluster mass.

Although such a scenario may be interesting, it must becautioned that the statistical signiÐcance of the trends seenin Figure 4 is only marginal. Particularly when consideringclusters in the narrow metallicity range [ 1.2\[A/H]\ [0.8, the number of objects is small. A two-sidedKolmogorov-Smirnov (K-S) test (made using the routineKSTWO in the IDL Astronomy Library) yielded a 24%probability that the metallicity distributions of the high-mass and intermediate-mass GCs were drawn from thesame parent distribution. Similarly, the K-S test indicated a21% probability that the high- and low-mass cluster metal-licity distributions were drawn from the same parent.Hence, despite the trends noted above, the null hypothesisthat globular clusters of di†erent masses have the samemetallicity distribution cannot be ruled out at a high level ofprobability. Improved data on the metallicities of low-massclusters could help to clarify this issue ; many of these low-mass clusters are relatively distant and/or poorly studiedand so the errors in the metallicity data are likely to besigniÐcant.

The author wishes to acknowledge valuable conversa-tions with Andreas Burkert. We thank William Harris andan anonymous referee for useful comments on earlier ver-sions of this manuscript, and Lee Rottler for running theIDL KSTWO routine.

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