The W-Function Applied to the Age of Globular Clusters

Abstract

We present a statistical approach for estimating the age of GlobularClusters by measurement of the likelihood between the observed clustersequences in the Colour-Magnitude Diagram and the synthetic clustersequences computed from stellar evolutionary models. In the conventionalisochrone fitting procedure, the age is estimated in a subjective way.Here, we calculate the degree of likelihood by applying a modernstatistical estimator, the Saha estimator W, and the interval ofconfidence from {χ}^2 statistics. We apply this approach to sets ofthree different evolutionary models. Each of these sets consists ofdifferent chemical abundances, ages, input physics, etc. Based on ourapproach, we estimate the age of NGC 6397, M92 and M3. With a confidencelevel of 99%, we find that the best estimate of the age is 14.0 Gyrwithin the range of 13.8 to 14.4 Gyr for NGC 6397, 14.75 Gyr within therange of 14.50 to 15.40 Gyr for M92, and 16.0 Gyr within the range of15.9 to 16.3 Gyr for M3.