Accounting for Stochastic Fluctuations when Analysing Integrated Light of Star Clusters. I: First Systematics

Star clusters are studied widely both as benchmarks for stellar evolution models and in their own right. Cluster age and mass distributions within galaxies are probes of star formation histories, and of cluster formation and disruption processes. The vast majority of clusters in the Universe is small, and it is well known that the integrated fluxes and colors have broad probability distributions, due to small numbers of bright stars. This paper goes beyond the description of predicted probability distributions, and presents results of the analysis of cluster energy distributions in an explicitly stochastic context. The method developed is Bayesian. It provides posterior probability distributions in the age-mass-extinction space, using multi-wavelength photometric observations and a large collection of Monte-Carlo simulations of clusters of finite stellar masses. Both UBVI and UBVIK datasets are considered, and the study conducted in this paper is restricted to the solar metallicity. We first reassess and explain errors arising from the use of standard analysis methods, which are based on continuous population synthesis models: systematic errors on ages and random errors on masses are large, while systematic errors on masses tend to be smaller. The age-mass distributions obtained after analysis of a synthetic sample are very similar to those found for real galaxies in the literature. The Bayesian approach on the other hand, is very successful in recovering the input ages and masses. Taking stochastic effects into account is important, more important for instance than the choice of adding or removing near-IR data in many cases. We found no immediately obvious reason to reject priors inspired by previous (standard) analyses of cluster populations in galaxies, i.e. cluster distributions that scale with mass as M^-2 and are uniform on a logarithmic age scale.