Deriving physical parameters of unresolved star clusters - III. Application to M 31 PHAT clusters

This study is the third of a series that investigates the degeneracy and stochasticity problems present in the determination of physical parameters such as age, mass, extinction, and metallicity of partially resolved or unresolved star cluster populations situated in external galaxies when using broad-band photometry. This work tests the derivation of parameters of artificial star clusters using models with fixed and free metallicity for the WFC3+ACS photometric system. Then the method is applied to derive parameters of a sample of 203 star clusters in the Andromeda galaxy observed with the HST. Following Papers I \& II, the star cluster parameters are derived using a large grid of stochastic models that are compared to the observed cluster broad-band integrated WFC3+ACS magnitudes. We derive the age, mass, and extinction of the sample of M31 star clusters with one fixed metallicity in agreement with previous studies. Using artificial tests we demonstrate the ability of the WFC3+ACS photometric system to derive the metallicity of star clusters. We show that the metallicity derived using photometry of 36 massive M31 star clusters is in a good agreement with the metallicity previously derived using spectroscopy taken from literature.