Deriving reliable fundamental parameters of PMS-rich star clusters
  affected by differential reddening
  We present an approach that improves the search for reliable astrophysical
parameters (e.g. age, mass, and distance) of differentially-reddened, pre-main
sequence-rich star clusters. It involves simulating conditions related to the
early-cluster phases, in particular the differential and foreground reddenings,
and internal age spread. Given the loose constraints imposed by these factors,
the derivation of parameters based only on photometry may be uncertain,
especially for the poorly-populated clusters. We consider a wide range of
cluster {\em (i)} mass and {\em (ii)} age, and different values of {\em (iii)}
distance modulus, {\em (iv)} differential and {\em (v)} foreground reddenings.
Photometric errors and their relation with magnitude are also taken into
account. We also investigate how the presence of unresolved binaries affect the
derived parameters. For each set of {\em (i)} - {\em (v)} we build the
corresponding model Hess diagram, and compute the root mean squared residual
with respect to the observed Hess diagram. The parameters that produce the
minimum residuals between model and observed Hess diagrams are searched by
exploring the full parameter space of {\em (i)} - {\em (v)} by means of {\em
brute force}, which may be time consuming but efficient. Control tests show
that an adequate convergence is achieved allowing for solutions with residuals
10% higher than the absolute minimum. Compared to a colour-magnitude diagram
containing only single stars, the presence of 100% of unresolved binaries has
little effect on cluster age, foreground and differential reddenings;
significant differences show up in the cluster mass and distance from the Sun.
Our approach shows to be successful in minimising the subjectiveness when
deriving fundamental parameters of young star clusters.
