Deriving physical parameters of unresolved star clusters. I. Age, mass, and extinction degeneracies

Context. Stochasticity and physical parameter degeneracy problems complicate the derivation of the parameters (age, mass, and extinction) of unresolved star clusters when using broad-band photometry.Aims. We develop a method to simulate stochasticity and degeneracies and to investigate their influence on the accuracy of derived physical parameters. Then we apply it to star cluster samples of M 31 and M 33 galaxies.Methods. Age, mass, and extinction of observed star clusters are derived by comparing their broad-band UBVRI integrated magnitudes to the magnitudes of a large grid of star cluster models with fixed metallicity Z  = 0.008. Masses of stars for a cluster model are randomly sampled from the initial mass function. Models of star clusters from the model grid, which have all of their magnitudes located within 3 observational errors from the magnitudes of the observed cluster, are selected for computing their age, mass, and extinction.Results. In the case of the M 31 galaxy, the extinction range is wide and the age-extinction degeneracy is strong for a fraction of its clusters. Because of a narrower extinction range, the age-extinction degeneracy is weaker for the M 33 clusters. By using artificial cluster sample, we show that age-extinction degeneracy can be reduced significantly if the range of intrinsic extinction within the host galaxy is narrow.