1153-1160, November 1987 AGES of GLOBULAR CLUSTERS

Home , NGC 6352, NGC 6362, NGC 6397, Turnoff point

Publications of the Astronomical Society of the Pacific 99: 1153-1160, November 1987

AGES OF GLOBULAR CLUSTERS

CHARLES J. PETERSON Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211 and Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics 5071 West Saanich Road, Victoria, BC V9A 2Y9, Canada Received 1986 August 11.

ABSTRACT Ages have been calculated for 41 globular clusters for which color-magnitude diagram studies allow a determination of the luminosity difference between the horizontal-branch and the main-sequence turnoff point. The data indicate only weak support for a slight difference in age between clusters in the inner halo and those in the outer halo. No correlation between cluster ages and cluster metallicities is found. Key words: globular clusters-ages

I. Introduction II. The Data Globular cluster color-magnitude diagrams provide Our sample of data is taken from an essentially com- data not only about individual cluster properties, but also plete survey of all modern color-magnitude diagram stud- yield information that may be used to study the structure ies in the standard UBVRl photometric system (Peterson and evolution of the Galaxy and to set a constraint upon its 1986) supplemented by a few studies which have ap- age and the age of the universe. In particular, various peared more recently. Neglecting a number of older studies have been made in recent years to obtain ages for studies in which it is known that observational errors globular clusters (Gratton 1985; Sandage 1986, and refer- affect the fainter end of the magnitude scale, we find there ences cited therein) and to search for an age-galactocen- are approximately 70 studies of 41 clusters to or below the tric radius relationship that would give clues to the nature level of the main-sequence turnoff. For each of these of the collapse of the Galaxy halo. In particular, Gratton clusters we have determined AV(TO —HB), the differ- (1985), from an analysis based on color-magnitude dia- ence in visual magnitude between the main-sequence gram information for 26 clusters, argued that clusters in turnoff and the horizontal-branch level. Wherever possi- the inner halo (fíGC < 15 kpc) are coeval, with a mean age ble, we have taken the horizontal-branch magnitude 3-5 X 109 years older than the clusters of the outer halo V(HB) as the mean magnitude of the horizontal-branch which continued to form during a delayed outer halo stars at the position of the RR Lyrae gap. For clusters with collapse; these results are consistent with the models of very red or very blue horizontal branches, it has been Tinsley and Larson (1978) for the formation of the Galaxy, assumed that the best estimate of this magnitude is equal but contrast with the general consensus that globular to the blue edge of the red horizontal-branch star distri- clusters are of the same age (Sandage 1982a ; Carney 1983; bution or the red edge of the blue horizontal-branch star Burstein 1985). distribution, respectively. For those clusters for which At the present time, published data are now available red horizontal-branch stars have been used, we must note for 15 additional clusters. We have also surveyed the that an additional uncertainty is introduced into our cal- literature to intercompare independent studies of the culations as VandenBerg (1986) has shown their luminosi- same clusters to allow an external estimation of the accu- ties to be dependent on the abundance ratio of the CNO racy of color-magnitude diagram parameters that may be elements to Fe. used for estimation of cluster ages. Our new analysis of The turnoff magnitude V (TO) is defined as the magni- this somewhat larger sample of cluster data does not tude at the bluest position of the main sequence. To be as confirm the strong age-galactocentric radius relation consistent as possible, these values have been deter- found by Gratton. Within the accuracy of our derived mined directly from published color-magnitude diagrams ages and within the assumption that the helium abun- or from tabulated fiducial values for the main sequence. dance is constant, all clusters appear to be approximately Our determinations of AV(TO —HB), are given in coeval. Table I together with the literature references. In Table

1153 © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 1154 CHARLES J. PETERSON

II are given our adopted values of the mean level of the show the distribution of AV(TO —HE). The standard de- horizontal branch V(HB) at the position of the RR Lyrae viation of the distribution is 0.16 magnitude, a value that gap, a value of the extinction E{B—V), and the average is consistent with the expected error in the determination AV(TO —HE) of the values from the individual studies of the magnitude difference. As has been emphasized, for together with the standard deviation of the mean. Ν example, by Smith et al. (1986), the distribution of stars in represents the number of studies used in the determina- a color-magnitude diagram at the position of the main-se- tion of this average. For the metallicity of the clusters, we quence turnoif has a constant {Β —V) color for a luminos- have taken [Fe/H] directly from the study of Pilachowski ity range of approximately 0.5 magnitude in V ; thus, the (1984), with the exceptions of five objects for which we intrinsic ability to determine V(TO) is subject to an error have found [Fe/H] from a new calibration against of 0.1 to 0.2 magnitude. Coupled with the observational (ß-y)0)g and/or AV1.4 = V (red giants at (B-V)o= 1.40) error in determination of V(HE) (which is particularly — V (HE) (Fig. 1). The derivations of the cluster ages t and uncertain for several clusters that have very blue horizon- the galactocentric radial distances RGC are discussed in tal branches), the distribution shown in Figure 2 could Section III. easily be explained solely by measurement error. In Fig- The data at this point already give two indications of the ure 3a we show the same data as a function of metallicity. result that we will obtain in Section III, namely that the As discussed in Section III, the computation of age de- majority of clusters appear to be the same age within the pends somewhat on [Fe/H]. In the figure we have shown uncertainties of the observational error. In Figure 2 we the expected slope of an isochrone which can be seen to

TABLE I References for Color Magnitude Diagrams

Cluster Δν(ΤΟ-ΗΒ) Reference Cluster AV(TO-HB) Reference NGC 104 3.45 Tifft (1963) NGC 5904 3.65 Richer and Fahlman (1987) 3.50 Hesser and Hartwick (1977), NGC 6121 3.18 Alcaino and Liller (1984) Harris, Hesser, and Atwood (1983) 3.6 Richer and Fahlman (1984) 3.75 Cannon (1981) NGC 6171 3.58 Da Costa, Mould, and Ortolani (1984) 3.73 Gratton (1985) 3.75 Sandage and Roques (1984) 3.6 Hesser et al. (1987) NGC 6205 3.4 Sandage (1970) NGC 288 3.8 Samus' and Shugarov (1978) 3.19 Richer and Fahlman (1986) 3.5 Alcaino and Liller (1980c) NGC 6218 3.9 Mironov et al. (1984) 3.8 Harris, Hesser, and Atwood (1983) NGC 6229 3.45 Cohen (1985) 3.5 Buonanno et al. (1984b, 1984c) NGC 6254 3.75 Samus' and Shugarov (1983) 3.8 Olszewski, Canterna, and Harris (1984) NGC 6341 3.45 Sandage and Katem (1983) 3.9 Penny (1984) 3.55 Christian and Heasley (1986) NGC 362 3.55 Gratton (1985) NGC 6352 3.6 Nemec, Hesser, and Ugarte (1981) 3.32 Boite (1987) NGC 6362 3.41 Alcaino and Lüler (1986a) Eridanus 3.5 Ortolani and Gratton (1986) NGC 6397 3.7 Cannon (1974) Reticulum 3.4 Gratton and Ortolani (1987) 3.8 Alcaino and Liller (1980a) NGC 1904 3.44 Gratton and Ortolani (1986) NGC 6535 3.5 Anthony-Twarog and Twarog (1985) 3.85 Heasley, Janes, and Christian (1986) NGC 6656 3.4 Alcaino and Liller (1983) NGC 2298 3.31 Gratton and Ortolani (1986) NGC 6752 3.7 Wesselink (1974) 3.4 Alcaino and Liller (1986b) 3.5 Carney (1979) NGC 2808 3.6 Buonanno et al. (1984a) 3.5 Cannon (1981) 3.55 Gratton and Ortolani (1986) 3.63 Grenon and Blecha (1984) Pal 3 3.5 Ortolani and Gratton (1986) 3.75 Buonanno et al. (1986) NGC 3201 3.33 Alcaino and Liller (1981) 3.72 Penny and Dickens (1986) 3.50 Penny (1984) NGC 6809 3.7 Penny (1984) Pal 4 3.2 Reed and Harris (1986) Pal 11 3.2 Cudworth and Schommer (1984) 3.33 Christian and Heasley (1986) NGC 6838 3.55 Arp and Hartwick (1971) NGC 4590 3.5 Penny (1984) NGC 7006 3.56 Cohen (1985) 3.35 McClure et al. (1987) 3.4 Ortolani (1986) NGC 5053 3.35 Walker, Pike, and McGee (1976) NGC 7078 3.33 Sandage and Katem (1977) NGC 5139 3.5 Da Costa and Villumsen (Í981) 3.33 Fahlman, Richer, and VandenBerg (1985) 3.8 Cannon (1981) 3.7 Harris and Hesser (1987) 3.58 Gratton (1985) NGC 7089 3.25 Samus' and Shugarov (1979) 3.8 Walker (1986) 3.65 Inman and Carney (1982) NGC 5272 3.4 Sandage (1970) NGC 7099 3.6 Piotto et al. (1987) NGC 5466 3.32 Cohen (1985) Pal 12 3.2 Harris and Canterna (1980) 3.6 Nemec and Harris (1987) 3.2 Stetson and Smith (1987) Pal 5 3.34 Ortolani (1985) Pal 13 3.29 Ortolani, Rosino, and Sandage (1985) 3.3 Smith et al. (1986) NGC 7492 3.6 Buonanno et al. (1987)

TABLE II Globular Clusters with Photometry to the Main Sequence TurnofF

Cluster V(HB) E(B-V) AV(TO-HB) Ν [Fe/H] log t Rgc (Note 1) (Note 2) (years) (Kpc) NGC 104 14.05 0.04 3.61 ± 0.06 5 -0.85 10.20 7.8 NGC 288 15.3 0.03 3.72 ± 0.07 6 -1.31 10.27 11.7 NGC 362 15.43 0.04 3.44 ± 0.12 2 -1.06 10.14 9.4 Eridanus 20.2 0.03 3.5 1 -1.1* 10.17 66.1 Reticulum 19.07 0.02 3.4 1 -2.0* 10.17 36.9 NGC 1904 16.15 0.01 3.65 ± 0.20 2 -1.45 10.23 18.6 NGC 2298 16.09 0.08 3.36 ± 0.05 2 -1.66: 10.14 16.3 NGC 2808 16.11 0.22 3.58 ± 0.03 2 -1.09 10.20 10.8 Pal 3 20.55 0.03 3.5 1 -2.1 10.22 72.9 NGC 3201 14.72 0.21 3.41 ± 0.09 2 -1.19 10.13 9.2 Pal 4 20.63 0.02 3.27 ± 0.07 2 -2.15 10.13 102.5 NGC 4590 15.63 0.03 3.42 ± 0.08 2 -2.11 10.19 10.1 NGC 5053 16.63 0.01 3.35 1 -2.15 10.16 16.8 NGC 5139 14.50 0.11 3.67 ± 0.08 4 -1.64 10.28 6.7 NGC 5272 15.66 0.00 3.4 1 -1.43 10.25 12.0 NGC 5466 16.58 0.00 3.46 ± 0.14 2 -1.6 10.18 15.8 Pal 5 17.40 0.03 3.32 ± 0.02 2 -1.16 10.09 16.0 NGC 5904 15.15 0.03 3.65 1 -1.31 10.14 6.4 NGC 6121 13.36 0.39 3.39 ± 0.21 2 -1.23 10.13 6.7 NGC 6171 15.63 0.35 3.67 ± 0.09 2 -0.94 10.23 3.9 NGC 6205 14.85 0.03 3.30 ± 0.11 2 -1.41 10.10 8.5 NGC 6218 14.90 0.17 3.9 1 -1.27 10.31 5.6 NGC 6229 18.08 0.10 3.45 1 -1.25 10.15 25.4 NGC 6254 14.65 0.26 3.75 1 -1.39 10.29 5.1 NGC 6341 15.05 0.02 3.50 ± 0.05 2 -2.05 10.22 9.5 NGC 6352 15.2 0.23 3.6 1 -0.8 10.20 3.8 NGC 6362 15.34 0.10 3.41 1 -0.96 10.12 5.3 NGC 6397 12.95 0.18 3.75 ± 0.05 2 -2.24 10.34 6.4 NGC 6535 15.8 0.36 3.5 1 -1.4* 10.19 4.3 NGC 6656 13.97 0.35 3.4 1 -1.55 10.15 5.8 NGC 6752 13.72 0.04 3.63 ± 0.05 6 -1.23 10.23 5.8 NGC 6809 14.33 0.08 3.7 1 -1.55 10.28 4.6 Pal 11 17.3 0.34 3.2 1 -0.8* 10.02 7.4 NGC 6838 14.41 0.27 3.55 1 -0.79 10.17 7.2 NGC 7006 18.79 0.00 3.48 ± 0.08 2 -1.32 10.17 38.6 NGC 7078 15.83 0.11 3.45 ± 0.12 3 -2.01 10.20 10.2 NGC 7089 16.05 0.06 3.45 ± 0.20 2 -1.48 10.17 10.1 NGC 7099 15.05 0.02 3.6 1 -2.32 10.28 7.2 Pal 12 17.1 0.02 3.2 ±0.0 1 -1.0* 10.03 14.8 Pal 13 17.70 0.00 3.29 1 -1.8 10.11 27.0 NGC 7492 17.63 0.00 3.6 1 -1.34 10.23 19.5

Notes to Table II: 1 Mean is 3.500 ± 0.025 (s.d.m.). 2 Pilachowski (1984) unless otherwise marked with an *, for which [Fe/H] comes from a calibration with ÁV1.4 and/or (B-V)o,i.

-.5 Ί 1 Γ 1 1 1 Γ -.5 ι ι ι ι I I I I I I I I I I I I I I I I I M i I I

o ©o O SgcP o O o o o

-1 o -1 - o o 0 o0 o 0 o o0 o O ODO o S 2 ? S ► » e00 q σ o I-..5 - á -1.5 - o o a* O oo o Pd o 0o o o (Mr® r* o o

-2 oO -2 - O o o o o o o o

-2.5 1 J I I L -2.5 Lj-1- I I I ι ι ι I ' ' I I I I I I I I I I ι ' .5 1.5 .5 1.5 2 2.5 3.5 (B - V)(0ie) AV1.4 — Fig. 1-Calibrations of (Β V)o g and AVI.4 with metallicity [Fe/H]. The color-magnitude diagram parameters come from the survey of Peterson (1986); [Fe/H] values were taken from Pilachowski (1984).

agree well with the overall trend in the data. 41 CLUSTERS III. The Calculation of Cluster Ages The calculation of cluster ages is straightforward and derives from analytical fits to stellar model calculations for both horizontal-branch stars and for stars in the vicinity of the main-sequence turnoif. From horizontal-branch star models (Caloi, Castellani, and Tornambè 1978), Gratton derives for the zero-age brightness level

Mv(ZAHB) = +0.16[Fe/H] + 0.92 (1) where the transformation from theoretical parameters (log Teff, logL/Lo) to observational parameters (V,(ß — V)) has been accomplished by use of the theoretical model atmospheres of Kurucz (1979). As our tabulation of cluster 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 AV(TO - HB) data (Table II) represents a mean magnitude V(HB) for the horizontal-branch and not a zero-age luminosity level, Fig. 2-The distribution of AV(TO —HB) for 37 clusters in which pho- we have corrected equation (1) by 0.05 magnitude for use tometry is available to the main-sequence turnoff magnitude. in both the age calculation and for determination of clus-

τ—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—r 10.4 a b- 10.3 — o o o Oo QQ X 3.5 (oS 10.2 O O o 0o o Η 0 o g 10.1 o o

10 - 3 - (5[AV(T0 - HB)]/ó[Fe/H] -J 1 I I I I I I I I I I I I 1 I I I L 9 g ι I ι ι ι ι I ι ι ι ι I ι ι ι ι I l -2.5 -2 -1.5 -1 .5 1 1.5 2 [Fe/H] (Pilachowski) LOG GALACTOCENTRIC RADIUS (KFC) 10.4 π—ι—ι—I—ι—ι—ι—r π—ι—ι—ι—i—i—ι—r 10.4 d- 10.3 - 10.3

ä 10·2 COÚ 10.2 ?» O O o

§ 10.1 g 10.1

10 - ÓLog t/<5[Fe/H] 10 - 9 10 9 10

9.9 Jl _1 I I L 9.9 -2.5 -2 -1.5 -.5 .5 1 1.5 [Fe/H] (Pilachowski) LOG GALACrrOCENTOC RADIUS (KPC) Fig. 3-(a) AV(TO—HB) as a function of metallicity [Fe/H]. The slope of the theoretical dependency of the magnitude difference on metallicity (Gratton 1985) is shown by the short line, (b) Globular cluster ages as a function of galactocentric radial position. The solid line is the formal least-squares fit to the data, log t = (10.178 ± 0.012) — (0.086 ± 0.040)(log RGC — 1.0). The dashed lines show the one standard deviation variation of the slope of the log t — log fíGC relation, (c) The variation with galactocentric radius of the average age of clusters. The size of the radial binning is shown by the extent of the horizontal line through each of the five averages. The vertical error bar represents one standard deviation of the mean. The number of globular cluster ages represented in each average is indicated at the bottom. The solid line gives the solution and the dashed lines indicate the effect of changing the slope by one standard deviation for the least-squares solution log t = (10.181 ± 0.020) - (0.061 ± 0.048)(log KGc — 1.0). (d) Globular cluster ages versus metallicity. The slope of the theoretical dependency of age upon metallicity is shown (eq. (3) of text). ter distances. Main-sequence turnoff isochrones were which follows from equations (1) and (2). Note that equa- derived by Gratton from the theoretical models of Van- tions (1), (2), and (3) apply only for a fixed helium abun- denBerg (1983): dance ofY = 0.23. The positions of the horizontal branch and the turnoff point are functions of Y ; as Y increases the log t = 0.440Mv(TO) - 0.125[Fe/H] + 8.185 . (2) horizontal branch brightens but the turnoff magnitude To use equation (2) to compute the age t directly intro- becomes fainter. As a consequence, the derived age of a duces additional uncertainty due to the imprecision with cluster depends on Y in the sense that for a given which we know distance moduli. Sandage (1982a) first AV(TO —HB), a helium-rich cluster will be younger than pointed out that by combining the two equations, the age a helium-poor cluster (this is well illustrated in Fig. 2 of can be shown to depend only on the difference in bright- VandenBerg 1987). Thus in agreement with the proce- ness between the turnoff and the horizontal branch. We dure of Gratton, we will determine ages under the explicit thus compute ages from assumption that δ Y = 0 for the globular clusters. Although our calculation of ages follows the derivation log t = 0.440AV(TO —HB) - 0.055[Fe/H] + 8.568 ,(3) given by Gratton (1985), the points of difference between

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 1158 CHARLES J. PETERSON the way in which we have handled the data should be kept IV. Discussion clearly in mind. First, our selection of data depends on an Gratton (1985) concluded that the globular clusters essentially, complete survey of published color-magni- gave evidence for a fast collapse of the inner region of the tude diagram studies, rather than on selection of parame- galactic halo (the mean age of clusters with RGC < 15 kpc ters from a specific reference; thus our initial values of was found to be í = 16.3 ± 0.3 X 109 years) and a slower AV(TO —HE) do differ for a number of clusters. Second, collapse of the outer halo (for which the mean age of we have adopted the metallicity scale of Pilachowski clusters was found tobei=11.6± 1.2 X 109 years), an (1984), noting that this scale is basically the same as that observational result which would be consistent with mod- found by Brodie and Hanes (1986). (The small difference els for the formation of the Galaxy by Tinsley and Larson between their scales translates below into an age differ- (1978). ence of less than 3%. Use of any alternative metallicity The results of the present study, however, do not scale for the globular clusters, such as that of Zinn and confirm the strong radial age gradient found by Gratton. West (1984), Smith (1984), or Straizys (1982), will not In Figure 3b the presence of a significant difference in age significantly change our results.) On the average, the between inner and outer clusters is not readily apparent. Pilachowski and the Gratton metallicity scales are similar, A simple linear least-squares fit through the data yields but there is a large scatter for the individual clusters. There is also an indication that the specific values adopted log í = (10.189 ± 0.012)-(0.044 ± 0.029)(log fíGc-1 ·0) . (4) by Gratton for clusters of intermediate metallicity are 2 The correlation coefficient of the solution is small, r = affected by the systematic, nonlinear error confirmed by 0.054, an indication of the weakness of the formal correlation Brodie and Hanes to be present in the original Zinn (1980) solution. If the data are binned as shown in Figure 3c, we find scale upon which most subsequent studies have relied. a somewhat smaller radial gradient in age Third, unlike Gratton, we have not considered the alternative formulation for horizontal-branch magnitudes log í = (10.194 ± 0.013)-(0.036 ± 0.017)(log fíGc—1.0) _ which derives from study of the period-luminosity-ampli- (r2 = 0.610) . ( ; tude relationship of RR Lyrae variables (Sandage, Katem, At best, only a weak age gradient is present. and Sandage 1981; Sandage 1982a,b). To attempt to re- solve the discrepancy in horizontal-branch magnitudes At the suggestion of the referee who emphasized that obtained by Sandage and colleagues from application of the studies listed in Table I constitute a very inhomoge- pulsational variable theory and those obtained from the neous sample of data, we have tested our result through Caloi et al. models is beyond the scope of this paper. The restriction of the data sample. Elimination of all studies in only direct observational study of the influence of metal- which photometry does not go at least 2 magnitudes licity on the brightnesses of horizontal-branch stars is the below the main-sequence turnoff point and for which work of Butler, Dickens, and Epps (1978) who studied photometric errors at that level appear to be greater than approximately 70 variables in the cluster ω Centauri (see about σΒ y ~ 0.06 yields a restricted data sample of 20 also Gratton, Tornambè, and Ortolani 1986). Butler et al. studies on 17 clusters. For these objects, we find found that [Fe/H] for the cluster variables ranges from log ί = (10.176 ± 0.019)-(0.048 ± 0.056)(log fíGc-1 ·0) ,(6) —2.3 to —0.5, with a marginal brightness gradient of the form ômv/6[Fe/H] ^ 0.1; within observational error, this which is not significantly different than the solution for the gradient is consistent with the metallicity dependence whole sample of data. These data and the linear fit are shown deduced from the Caloi et al. models. Various other in Figure 4. studies have looked at field variables, but no consensus Alternatively, we can ignore any possible radial variation has been reached on the magnitude-metallicity relation in age and consider only the distribution of the values of log t (see the recent reviews by Burki and Meylan 1986; for the 41 clusters. If there is no dependency of age on Jameson 1986). We note, too, that the major effect on galactocentric radius, then the standard deviation of the computation of ages by use of the Sandage relation is only distribution of log t should be accountable on the basis in the age scale with little effect on any age-galactocentric only of observational error. We suggest above that the radius relation (Gratton 1985). The Sandage relation re- standard deviation of 0.15 magnitude in the AV(TO —HB) duces cluster ages by an amount equivalent to At = distribution (Fig. 2) is consistent with the expected mea- 0.069[Fe/H] + 0.028. surement error. Furthermore, the observational error in Ages calculated from equation (3) are given in Table II. [Fe/H] is 0.21 (Pilachowski 1984). From equation (3), we In Figure 3b these ages have been plotted against galacto- would infer therefore that the standard deviation for a centric radius position. Figure 3c shows also the age- calculation of log t for a given cluster has an uncertainty of galactocentric radius relation from binning the clusters 0.07, in excellent agreement with the calculated standard into five radial groups. The age-metallicity relationship of deviation of the distribution of log t of 0.070 for the 41 these clusters is shown in Figure 3d. clusters. The mean age of the 41 clusters is

tions, Zinn argued that the globular clusters form two 10.4 1 1 1 1 1 1 1 1 1 1 \ 1 1 1 1 1 1 r distinct subsystems, a spherically distributed halo group and a disk group with a flatter spatial distribution. Only 10.3 - three of the 41 clusters represented here belong to Zinn's o o - o o disk subsystem; within the statistical error, they are the same age as the whole sample of clusters which supports Zinn's conclusion that the thick disk phase of galaxy formation was short lived. Additional studies of disk clusters, however, would be greatly desirable. o Grateful acknowledgement is made to G. Alcaino, K. o 10 — Gudworth, W. E. Harris, J. N. Heasley, J. E. Hesser, S. Ortolani, and A. J. Penny for providing data about cluster color-magnitude diagram studies in advance of publica- g g I i I I I I ι I I I I I I I ' ' I I I tion. I wish also to thank I. R. King and the Berkeley .5 1 1.5 2 LOG GALACTOCENTRIC RADIUS (KPC) Astronomy Department for their hospitality during a sab- Fig. 4-Globular cluster ages as a function of galactocentric radial posi- batical visit at which time this study was begun, and Jim tion for a restricted sample of "best" observed clusters. The solid line is Hesser and an anonymous referee for useful comments on the formal least-squares fit to the data, log t = (10.176 ± 0.019) - (0.048 a preliminary version of this paper. ± 0.056)(log fíGC — 1.0). The dashed lines show the one standard deviation variation of the slope of the log t — log fíGC relation. REFERENCES Alcaino, G., and Liller, W. 1980a, A. /., 85, 680. (log t) = 10.186 ± 0.011 (sdm) (7) 1980k, A./., 85, 1330. 9 1980c, A./., 85, 1592. or{t) = 15.3 X 10 years. 1981, AJ., 86, 1480. Janes and Demarque (1983) also have considered the 1983, A./., 88, 1330. question of globular cluster ages and metallicities. By 1984, Ap./. Suppl., 56, 19. comparison between theoretical color indices and abso- 1986«, A./., 91, 303. 1986¿>, Astr. Αρ., 161, 61. lute magnitudes at the main-sequence turnofF, at the Anthony-Twarog, B. J., andTwarog, B. A. 1985, Ap. J., 291, 595. subgiant to giant branch transition, and along the giant Arp, H. C., and Hartwick, F. D. A. 1971, Ap. /., 167, 499. branch and observed cluster color-magnitude diagrams, Bolte, M. 1987, Ap./., 315, 469. they obtain an age of í = 16.6 ± 0.5 X 109 for 15 globular Brodie, J. P., and Hanes, D. A. 1986, Ap./., 300, 258. clusters. Furthermore, they found no correlation of clus- Buonanno, R., Corsi, C. E., Ferraro, I., and Fusi Pecci, F. 1987, Asir. Αρ. Suppl, 67, 327. ter age with metallicity, a result that persists for the Buonanno, R., Corsi, C. E., Fusi Pecci, F., and Harris, W. Ε. 1984a, present and substantially larger set of data shown in Fig- A./., 89, 365. ure 3d. Buonanno, R., Corsi, C. E., Fusi Pecci, F., Alcaino, G., and Liller, W. To draw more definite conclusions about the formative 19S4b, Astr. Ap. Suppl, 57, 75. process of the globular cluster system from these data is 1984c. Ap./., 277, 220. Buonanno, R., Corsi, C. E., lannicola, G., and Fusi Pecci, F. 1986, difficult at this time as there does not exist a comprehen- Astr. Αρ., 159, 189. sive theory for the origin of the clusters. In the context of Burki, G., and Meylan, G. 1986, Asir. Αρ., 159, 255. the Tinsley and Larson models for the formation of the Burstein, D. 1985, Pub. A.S.F., 97, 89. Galaxy it may be that the era of cluster formation does not Butler, D., Dickens, R. J., and Epps, E. 1978, Ap. J., 225, 148. coincide with the overall collapse of the inner and outer Caloi, V., Castellani, V., andTornambè, Α. 1978, Astr. Αρ. Suppl, 33, 169. halo, but rather occurred only during an early and a very Cannon, R. D. 1974, M.N.R.A.S., 167, 551. short period during the initial collapse. Of direct interest 1981, M.N.R.A.S., 195, 1. to interpretation of these data is the theoretical work of Carney, B. W. 1979, Α./., 84, 515. Fall and Rees (1986) who have considered the formation 1983, Highlights In Astr., 6, 255. of clusters during the collapse of a protogalaxy. Their Christian, C. Α., and Heasley, J. N. 1986, Ap. /., 303, 216. Cohen, J. G. 1985, A./., 90, 2254. theory is able to explain various properties of clusters, but Gudworth, K., and Schommer, R. 1984, Pub. A.S.P., 96, 786. it is not clear over what time scale cluster formation would Da Costa, G. S., and Villumsen, J. V. 1981, in Astrophysical Parameters occur. It is strongly suggested by the data presented here for Globular Clusters, ed. A. G. D. Philip and D. S. Hayes (Schnec- that cluster formation was a relatively short-lived phe- tady, N.Y.: L. Davis Press), p. 527. nomenon in the early history of the Galaxy. Da Costa, G. 8., Mould, J. R., and Ortolani, 8. 1984, Ap. /., 282, 125. Fahlman, G. G., Richer, Η. B., and VandenBerg, D. A. 1985, Ap. /. Of greater interest, however, would be the estimation Suppl, 58, 225. of ages of Zinn's (1985) disk clusters. On the basis of Fall, S. M., and Rees, M. J. 1986, Αρ. /., 298, 18. metallicities, kinematical properties, and spatial loca- Gratton, R. G. 1985, Astr. Αρ., 147, 169.

Gratton, R. G., and Ortolani, S. 1986, Asir. Αρ. SuppL, 65, 63. Piotto, G., Gapaccioli, M., Ortolani, S., Rosino, L., Alcaino, G., and 1987, Asir. Αρ. SuppL, in press. Liller, W. 1987, A./., 97, 360. Gratton, R. G., Tornambè, Α., and Ortolani, S. 1986, Astr. Αρ., 169, Reed, B. G., and Harris, W. E. 1986, A.J., 91, 81. 111. Richer, Η. B., and Fahlman, G. G. 1984, Ap. /., 277, 227. Grenon, M., and Blecha, A. 1984, in Observational Tests of the Stellar 1986, Ap./., 304, 273. Evolution Theory, ed. A. Maeder and A. Renzini (Dordrecht: D. 1987, Ap./., 316, 360. Reidel), p. 163. Samus', Ν. N., and Shugarov, S. Yu. 1978, Astr. Tsirk, No. 1023. Harris, W. E., and Ganterna, R. 1980, Ap./., 239, 815. 1979, Soviet Astr., 23, 749. Harris, W. E., and Hesser, J. E. 1987, in preparation. 1983, Soviet Astr., 27, 633. Harris, W. E., Hesser, T. E., and Atwood, B. 1983, Pub. A.S.P., 95, Sandage, A. 1970, Ap./., 162, 841. 951. 1982Ö, Αρ. /., 252, 553. Heasley, J. N., Janes, Κ. Α., and Ghristian, G. A. 1986, A.J., 91, 1108. 1982k, Αρ./., 252, 574. Hesser, J. E., and Hartwick, F. D. A. 1977, Ap. J. Suppl., 33, 361. 1986, Ann. Rev. Astr. Αρ., 24, 421. Sandage, Α., and Katem, B. 1977, Ap. /., 215, 62. Hesser, J. E., Harris, W. E., VandenBerg, D. Α., Allwright, J, W. B., 1983, A./., 88, 1146. Shott, P., and Stetson, P. 1987, Pub. A.S.P., 99, 739. Sandage, Α., and Roques, P. 1984, A./., 89, 1166. Inman, R. T., and Garney, B. W. 1982, Bull. A.A.S., 14, 877. Sandage, Α., Katem, B., and Sandage, M. 1981, Ap./. Suppl, 46, 41. Jameson, R. F. 1986, Vistas in Astr., 29, 17. Smith, G. H., McGlure, R. D., Stetson, P. B., Hesser, J. E., and Bell, Janes, Κ. Α., and Demarque, P. 1983, Ap. /., 264, 206. R. A. 1986, A./., 91, 842. Kurucz, R. 1979, Ap. J. Suppl, 40, 1. Smith, H. A. 1984, Ap./., 281, 148. McGlure, R. D., VandenBerg, D. Α., Bell, R. Α., Hesser, J. Ε., and Stetson, P. B., and Smith, G. H. 1987, to be published in Froceeámgs o/ Stetson, P. 1987, A./., 93, 1144. the ESO Workshop on "Stellar Evolution and Dynamics in the Outer Mironov, Α. V., Samus', Ν. N., Shugarov, S. Yu., and Yuferov, A. O. Halo of the Galaxy". 1984, Astr. Tsirk., No. 1313. Straizys, V. 1982, Ap. Space Sei., 81, 179. Nemec, J. M., and Harris, H. G. 1987, Ap./., 316, 172. Tifft, W. G. 1963, M.N.R.A.S., 126, 16. Nemec, J. M., Hesser, J. E., and Ugarte, P. P. 1981, in Astrophysical Tinsley, Β. M., and Larson, R. B. 1978, Ap. /., 221, 554. Parameters for Globular Clusters, ed. A. G. D. Philip and D. S. VandenBerg, D. A. 1983, Ap. /. Suppl, 51 29. Hayes (Schnectady, N.Y. : L. Davis Press), p. 577. 1986, in Production and Distribution of C,N, O Elements, ed. Olszewski, E. W., Ganterna, R., and Harris, W. E. 1984, Ap. /., 281, I. J. Danziger, F. Matteucci, and K. Kjär (Garching bei München: 158. European Southern Observatory), p. 73. Ortolani, S. 1985, private communication. 1987, in Globular Cluster Systems in Galaxies, ed. J. Grindlay 1986, Messenger, No. 36, 23. and A. G. D. Philip (Dordrecht: D. Reidel), in press. Ortolani, S., and Gratton, R. 1986, Mem. della Soc. Astron. Italiana, Walker, A. R. 1986, in Instrumentation and Research Programs for 57, 351. Small Telescopes, ed. J. B. Hearnshaw and P. L. Gottrell (Dor- Ortolani, S., Rosino, L., and Sandage, A. 1985, A./., 90, 473. drecht: D. Reidel), p. 33. Penny, A. J. 1984, in Observational Tests of the Stellar Evolution Walker, M. F., Pike, G. D., and McGee, J. D. 1976, M.N.fí.A.S., 175, Theory, ed. A. Maeder and A. Renzini (Dordrecht: D. Reidel), 525. p. 157. Wesselink, Α. 1974, M.N.fí.A.S., 168, 345. Penny, A. J., and Dickens, R. J. 1986, M.N.fí.A.S., 220, 845. Zinn, R. 1980, Αρ./. Suppl, 42, 19. Peterson, G. J. 1986, Pub. A.S.P., 98, 1258. 1985, Αρ./., 293, 424. Pilachowski, G. A. 1984, Ap. /., 281, 614. Zinn, R., and West, M. J. 1984, Αρ. /. Suppl, 55, 45.