Monte Carlo simulations of metal-poor star clusters

Context. Metal-poor globular clusters (GCs) can provide a probe of the earliest epoch of star formation in the Universe, being the oldest observable stellar systems. 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 intrinsic uncertainty caused by the discrete nature of stars in stellar systems, especially in the case of faint objects. Aims. In this paper, we evaluate the intrinsic uncertainty ( due to statistical effects) affecting the integrated colours and mass-to-light ratios as a function of the cluster's integrated visual magnitude (M-V(tot)), which represents a directly measured quantity. We investigate the case of metal-poor, single-burst stellar populations with age from a few million years to a likely upper value for the Galactic globular cluster ages (similar to 15 Gyr). Methods. Our approach is based on Monte Carlo techniques for randomly generating stars distributed according to the cluster's mass function. Results. Integrated colours and mass-to-light ratios in different photometric bands are checked for good agreement with the observational values of low-metallicity Galactic clusters; the effect of different assumptions on the horizontal branch (HB) morphology is shown to be irrelevant, at least for the photometric bands explored here. 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 intrinsic uncertainty cannot be neglected. In particular, in models with M-V(tot) V = -4 the broad-band colours show an intrinsic uncertainty high enough to prevent the precise age of the cluster from being evaluated. The effects of different assumptions on the initial mass function and on the minimum mass for which carbon burning is ignited for both integrated colours and mass-to-light ratios are also analysed. Finally, the present predictions are compared with recent results available in the literature, showing non-negligible differences in some cases.