Monte Carlo simulations of post-common-envelope white dwarf + main
  sequence binaries: comparison with the SDSS DR7 observed sample
  Detached white dwarf + main sequence (WD+MS) systems represent the simplest
population of post-common envelope binaries (PCEBs). Since the ensemble
properties of this population carries important information about the
characteristics of the common-envelope (CE) phase, it deserves close scrutiny.
However, most population synthesis studies do not fully take into account the
effects of the observational selection biases of the samples used to compare
with the theoretical simulations. Here we present the results of a set of
detailed Monte Carlo simulations of the population of WD+MS binaries in the
Sloan Digital Sky Survey (SDSS) Data Release 7. We used up-to-date stellar
evolutionary models, a complete treatment of the Roche lobe overflow episode,
and a full implementation of the orbital evolution of the binary systems.
Moreover, in our treatment we took into account the selection criteria and all
the known observational biases. Our population synthesis study allowed us to
make a meaningful comparison with the available observational data. In
particular, we examined the CE efficiency, the possible contribution of
internal energy, and the initial mass ratio distribution (IMRD) of the binary
systems. We found that our simulations correctly reproduce the properties of
the observed distribution of WD+MS PCEBs. In particular, we found that once the
observational biases are carefully taken into account, the distribution of
orbital periods and of masses of the WD and MS stars can be correctly
reproduced for several choices of the free parameters and different IMRDs,
although models in which a moderate fraction (<=10%) of the internal energy is
used to eject the CE and in which a low value of CE efficiency is used (<=0.3)
seem to fit better the observational data. We also found that systems with
He-core WDs are over-represented in the observed sample, due to selection
effects.
