Population synthesis of cataclysmic variable star: I. A new methodology and initial study on the post common-envelope stage.

We report the results of our population synthesis for post common-envelope binaries by following the evolution of each system in detail. Our main focus is a comparison with the white dwarf mass distribution of post common-envelope systems from the Sloan Digital Sky Survey. We employ a Monte Carlo method to choose the initial parameters of the progenitors (primary mass, mass ratio and orbital period). Then the evolution of the progenitor binary system is followed up to the onset of the common-envelope phase, which usually occurs near the tip of the giant branch or asymptotic giant branch. An approximate post-Helium flash evolution for primary masses ${\leq}2.25 \mathrm{M_{\odot}}$ is included. The binary parameters before and after common-envelope phase are calculated using the energy budget argument. In this paper we address the case of α=1.0, which is the commonly adopted value to calculate the common-envelope ejection. We consider a hydrogen-exhausted core to define the core mass of the primary (white dwarf mass, M) at the onset of common envelope phase. To obtain the present-day M distributions, we assumed a constant star formation rate. The distribution resulting from our population synthesis shows a double peak profile for M, similar to previous population syntheses and recent observational data. Our present synthesis result could not reproduce the location of the low and high mass peaks from the observations, but shows how a future synthesis can be made to produce an M distribution which is closer to observational data. [ABSTRACT FROM AUTHOR]