The determination of the age of Globular Clusters: a statistical approach

Abstract

We present a statistical approach for determining the age of Globular Clusters (GCs) that allows estimating the age derived from CMDs more accurately than the conventional methods of the isochrone fitting. We measure how closely a set of synthetic CMDs constructed from different evolutionary models resemble the observed ones by determining the likelihood using Saha and Chi-square statistics. The model which best matches the observational data, of a set of plausible ones, is the one with the highest value of the estimator. We apply this method to a set of three different evolutionary models presented by three different authors. Each of theses sets consists again of many different models of various chemical abundances, ages, input physics and there alike. We subsequently derive the age of GCs NGC 6397, M92 and M3. With a confidence level of 99%, we find that the best estimate of the age is 14.0 Gyrs within the range of 13.8 to 14.4 Gyrs for NGC 6397, 14.75 Gyrs within the range of 14.50 to 15.40 Gyrs for M92, and 16.0 Gyrs within the range of 15.9 to 16.3 Gyrs for M3.