A new method based on artificial neural network techniques for determining the fraction of binaries in star clusters

We present a new method based on artificial neural networks techniques aimed at determining the fraction of binary systems populating star clusters. We address the problem from a statistical point of view, avoiding the important biases induced by individual binary identification. The idea is to evaluate the percentage of binaries by comparing the distribution of main-sequence stars along the cluster's H-R diagram with the corresponding distribution in a set of synthetic H-R diagrams, in which the percentage of binaries has been changed, and applying the chi(2) minimization method. The chi(2) test is performed using a novel artificial neural network technique published by Garrido, Gaitan, & Serra-Ricart in 1994, which transforms a complicated test in the multidimensional input space to a simple test in a one-dimensional space without losing sensitivity. In this paper, the reliability of the method is analyzed. To this end, observational data were substituted by a sample of synthetic data for which the correct values of model parameters are known in advance. The good behavior of the results presented here suggests that the frequency of binary stars in clusters can be calculated to a precision of about 10% for a typical cluster of a few hundred stars with a relatively large percentage of binaries (around 40%). Therefore, the application of this method to the analysis of real clusters promises to yield accurate information on their global binary star content.