1153-1160, November 1987 AGES of GLOBULAR CLUSTERS
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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-se- quence 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.