Monte Carlo Simulations of Metal-Poor Star Clusters

Metal-poor globular clusters (GCs) can provide a probe of the earliest epoch of star formation in the Universe, being the oldest stellar systems observable. In addition, young and intermediate-age low-metallicity GCs are present in external galaxies. Nevertheless, inferring their evolutionary status by using integrated properties may suffer from large \emph{intrinsic} uncertainty caused by the discrete nature of stars in stellar systems, especially in the case of faint objects. In this paper, we evaluate the \emph{intrinsic} uncertainty (due to statistical effects) affecting the integrated colours and mass--to--light ratios as a function of the cluster integrated visual magnitude ($M_V^{tot}$), which represents a quantity directly measured. Our approach is based on Monte Carlo techniques for randomly generating stars distributed according to the cluster's mass function. Integrated colours and mass--to--light ratios in different photometric bands are checked to be in good agreement with the observational values of low-metallicity Galactic clusters. We present integrated colours and mass--to--light ratios as a function of age for different assumptions on the cluster total $V$ magnitude. We find that the emph{intrinsic} uncertainty cannot be neglected. In particular, in models with $M_V^{tot}=-4$ the broad-band colours show an \emph{intrinsic} uncertainty so high as to prevent precise age evaluation of the cluster. Finally, the present predictions are compared with recent results available in the literature, showing in some cases non-negligible differences.