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1983Apj...264..206J the Astrophysical Journal, 264:206-214 The Astrophysical Journal, 264:206-214, 1983 January 1 © 1983. The American Astronomical Society. All rights reserved. Printed in U.S.A. 1983ApJ...264..206J THE AGES AND COMPOSITIONS OF OLD CLUSTERS Kenneth Janes Boston University AND Pierre Demarque Yale University Observatory Received 1982 February 1 ; accepted 1982 June 21 ABSTRACT From published color-magnitude diagrams of 23 globular and open clusters we have measured the mean color index or absolute magnitude at various points along the principal sequences. By relating these quantities to the analogous parameters derived from theoretical isochrones it is possible to solve simultaneously for age, heavy-element abundance, and helium abundance. This analysis leads us to conclude that there is no correlation of globular cluster age with composition and that the oldest open clusters are about one-half the age of the globular clusters. Although the substantial observational and theoretical uncertainties prevent a conclusive statement, the evidence suggests that the open clusters have a higher helium abundance than the globular clusters, that the globulars have an age of about 16.6 ± 0.5 Gyr, and that the metal-rich clusters 47 Tue and M71 have [Fe/H] ~ —0.9. Changes in the metallicity scale or mixing length could substantially alter these values. Nevertheless, globular cluster ages as young as 10 Gyr would require large corrections and would yield cluster properties inconsistent with observation. If the Hubble constant is as large as 100 km s~1 Mpc" \ then fundamental changes in stellar evolution theory are required. Subject headings : clusters : globular — clusters : open — cosmology — stars : abundances — stars : evolution — stars : interiors I. INTRODUCTION which can be compared directly with the same quantities Recently Carney (1980) and Demarque (1980) have measured from the theoretical diagrams, simultaneous made estimates of the ages of globular clusters, and both age and composition estimates can be made and their find that there is a substantial range in their ages reliability estimated. A somewhat similar approach has correlated with metallicity, a result which would cause been used by Twarog and Anthony-Twarog (1981) to difficulties for galactic formation theories in which the study the ages and metallicities of open clusters; their globular clusters formed in a rapidly collapsing proto- results are, in general, consistent with those found here. galaxy. In addition, their age estimates are substantially larger than the age of the universe if the Hubble II. PARAMETERIZATION OF ISOCHRONES constant is as large as if = 95 km s_1 Mpc-1 Ciardullo and Demarque (1977, hereafter CD7) (Aaronson et al 1980). Furthermore, although Carney published an extensive grid of theoretical isochrones and Demarque used somewhat different procedures, both which they later transformed into the Mv-(B—V) plane their methods required that the composition of a cluster (Ciardullo and Demarque 1979, hereafter CD9). These must be specified in order to derive its age, but can, in principle, be compared directly with observed Pilachowski, Snedon, and Canterna (1980) and Cohen color-magnitude diagrams, and in order to facilitate this (1980) have concluded that the “metal-rich” globular comparison we have reduced each isochrone to a set of clusters are not as metal rich as had been thought values of color and absolute magnitude at various points previously. A decrease in metallicity would dramatically along the sequence. Specifically, we measured the (B—V) increase the estimated ages of the metal-rich clusters, color index at the main-sequence turnoff and at absolute thereby removing the correlation of age with metallicity magnitudes 0, 4-1, 4-2, 4-6 and the absolute magnitude (but leaving the conflict with a large Hubble constant). at the turnoff and at the inflection point between the The usual approach for comparing color-magnitude turnoff and the base of the giant branch. diagrams of clusters with theoretical isochrones requires The values of these parameters were measured from not only an assumption as to the cluster’s composition originals of the figures in CD9 for isochrones with but also a somewhat subjective judgment of the best fit. Z = 0.04,0.01,0.004,0.001,0.0004, and 0.0001 ; Y = 0.20 The purpose of this paper is to show that, by reducing and 0.30; and age = 2, 5, 10, 15, and 20 or 22 Gyr. the information in a C-M diagram to a few numerical The color index parameters (B—V)0, (B—V)u and quantities (such as the main-sequence turnoff color or the (B—V)2, which represent the giant branch, were plotted color of the giant branch at some absolute magnitude) versus heavy-element abundance (Z) and smooth curves 206 © American Astronomical Society • Provided by the NASA Astrophysics Data System 1983ApJ...264..206J Fig. 1.—The giant branch color index (B—V)0, from the Ciardullo and Demarque (1979) isochrones measured at Mv = 0, plotted vs. heavy-element abundance, log Z, for isochrones of 2, 5, 10, 15, and 20 Gyr. (left) Helium abundance, Y = 0.2. (right) Y = 0.3. Fig. 2.—The giant branch color index (B—V)u measured as in Fig. 1 but at Mv = 1, plotted vs. log Z Fig. 3.—The giant branch color index (B—V)2, measured as in Fig. 1 but at Mv = 2, plotted vs. log Z © American Astronomical Society • Provided by the NASA Astrophysics Data System 208 JANES AND DEMARQUE Vol. 264 were drawn to represent the color versus Z sequence at each of the five ages and for both values of Y (Figs. 1-3). 1983ApJ...264..206J The turnoff parameters (B—V)t, Mvt, and Mvi were plotted versus log (age) for the various values of Z (Figs. 4-6). Finally, the main-sequence parameter (B—V)6 was plotted versus Y at various values of Z (Fig. 7). Figures 1-7 permit one to make a simultaneous estimate of Z, Y, and age for any cluster if its color- magnitude diagram has been parameterized in the same fashion as the isochrones. The giant branch parameters are affected by Z and only slightly by age or Y, the turnoff parameters are affected both by age and Z, and the main sequence parameter is affected by Y and Z. Thus, one can make a rough estimate of a cluster’s age and helium abundance, find Z from Figures 1-3, then refine the age estimates from Figures 4-6, and, if necessary, return to Figures 1-3 for another iteration. Figure 7 can be used to estimate the assumed helium abundance, but, since main-sequence photometry of high quality is required to obtain meaningful results, it is generally necessary to assume a helium abundance. If the observed C-M diagrams and the isochrones are taken at face value, this method leads to a simultaneous solution for Y, Z, and age. Unfortunately, the substantial Fig. 4.—The main-sequence turnoff color index (B—V)t from the Ciardullo and Demarque (1979) isochrones plotted vs. log (age) for heavy-element abundances Z, as shown, and for helium abundance Y = 0.2 (top) and Y = 0.3 (bottom). Fig. 5.—Same as Fig. 4 for the turn-off absolute magnitude Mvt vs. log (age) Fig. 6.—Same as Fig. 4 for the absolute magnitude at the inflection point between the turnoff and the base of the giant branch Mvi © American Astronomical Society • Provided by the NASA Astrophysics Data System No. 1, 1983 OLD CLUSTERS 209 Other theoretical uncertainties are more difficult to evaluate quantitatively. They include uncertainties in the 1983ApJ...264..206J transformation from the Mv-TQff plane to the Mv-(B—V) plane that depend on the model atmospheres and bolometric corrections used (see CD9) and a certain amount of inconsistency and circularity that also results from altering a to force a good fit between old open clusters and models with appropriate parameters. Thus, in an absolute sense, the uncertainties in the values of the relations in Figures 1-7 are substantial. Never- theless, for the sake of comparison of one cluster with another, it is important to recognize that the effects of corrections to the models are such that, if a correction reduces the derived age of a cluster, it will tend to increase its metallicity. It is this fact which permits some constraints to be put on the range of reasonable cluster properties in § IV. III. PARAMETERIZATION OF COLOR-MAGNITUDE DIAGRAMS A relatively small number of color-magnitude Fig. 7.—The main-sequence color index (B—V)6 from the Ciardullo and Demarque (1979) isochrones vs. the helium abundance diagrams have been published which go as faint as the Y for various values of Z, as shown. main-sequence turnoff. Furthermore, the data are far from uniform both with respect to quality and in coverage of the C-M diagram; there are hints of theoretical and observational uncertainties are poten- systematic errors in some of the photometry, possibly tially overwhelming. On the theoretical side it is not affecting the shapes of the diagrams in some cases possible to try all possible combinations of parameters, and introducing scale errors in others, and not all of the but some numerical experiments indicate the extent of distances and reddenings are well known. In spite of some of the uncertainties. these difficulties, we made no attempt to make any The CD9 isochrones are all based on models with corrections to the published photometry in order to solar abundance ratios, but nonsolar ratios are widely avoid introducing any bias in the analysis. Table 1 suspected for globular clusters, and plausible alterations summarizes the available cluster data for globular and in abundance ratios could substantially affect the results. old open clusters.
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