On the distribution of initial masses of stellar clusters inferred from synthesis models

Abstract

The fundamental properties of stellar clusters, such as the age or the total initial mass in stars, are often inferred from population synthesis models. The predicted properties are then used to constrain the physical mechanisms involved in the formation of such clusters in a variety of environments. Population synthesis models cannot, however, be applied blindy to such systems. We show that synthesis models cannot be used in the usual straightforward way to small-mass clusters (say, M < few times 10**4 Mo). The reason is that the basic hypothesis underlying population synthesis (a fixed proportionality between the number of stars in the different evolutionary phases) is not fulfilled in these clusters due to their small number of stars. This incomplete sampling of the stellar mass function results in a non-gaussian distribution of the mass-luminosity ratio for clusters that share the same evolutionary conditions (age, metallicity and initial stellar mass distribution function). We review some tests that can be carried out a priori to check whether a given cluster can be analysed with the fully-sampled standard population synthesis models, or, on the contrary, a probabilistic framework must be used. This leads to a re-assessment in the estimation of the low-mass tail in the distribution function of initial masses of stellar clusters.