  We considered the formation of detached white dwarf main-sequence star (WDMS)
binaries through seven evolutionary channels subdivided according to the
evolutionary process that gives rise to the formation of the white dwarf or its
helium-star progenitor: dynamically stable Roche-lobe overflow (Algol-type
evolution), dynamically unstable Roche-lobe overflow (common-envelope
evolution), or stellar winds (single star evolution). We examine the
sensitivity of the population to changes in the amount of mass lost from the
system during stable Roche-lobe overflow, the common-envelope ejection
efficiency, and the initial mass ratio or initial secondary mass distribution.
In the case of a flat initial mass ratio distribution, the local space density
of WDMS binaries is of the order of 10^{-3}/pc^3. This number decreases to
10^{-4}/pc^3 when the initial mass ratio distribution is approximately
proportional to the inverse of the initial mass ratio. More than 75% of the
WDMS binary population stems from wide systems in which both components evolve
as if they were single stars. The remaining part of the population is dominated
by systems in which the white dwarf is formed in a common-envelope phase. The
birthrate of WDMS binaries forming through a common-envelope phase is about 10
times larger than the birthrate of WDMS binaries forming through a stable
Roche-lobe overflow phase. The ratio of the number of helium white dwarf
systems to the number of carbon/oxygen or oxygen/neon/magnesium white dwarf
systems derived from large samples of observed WDMS binaries by, e.g., future
planet-search missions such as SuperWASP, COROT, and Kepler may furthermore
constrain the common-envelope ejection efficiency.

Astrophysics