Abstract

Context. 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 consider the effects of the observational selection biases of the samples used to compare with the theoretical simulations. Aims. 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. Methods. 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 the selection criteria and all the known observational biases into account. Results. 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 find that our simulations correctly reproduce the properties of the observed distribution of WD+MS PCEBs. In particular, we find that once the observational biases are carefully considered, 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 the observational data better. We also find that systems with He-core WDs are over-represented in the observed sample, because of selection effects. Conclusions. Although our study represents an important step forward in modeling the population of WD+MS PCEBs, the still scarce observational data preclude deriving a precise value of the several free parameters used to compute the CE phase without ambiguity or ascertaining which the correct IMRD might be.