Deriving physical parameters of unresolved star clusters III.
  Application to M31 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.
