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We apply population synthesis techniques to calculate the present‐day population of post‐common envelope binaries (PCEBs) for a range of theoretical models describing the common envelope (CE) phase. Adopting the canonical energy budget approach, we consider models where the ejection efficiency αCE is either a constant or a function of the secondary mass. We obtain the envelope binding energy from detailed stellar models of the progenitor primary, with and without the thermal and ionization energy, but we also test a commonly used analytical scaling. We also employ the alternative angular momentum budget approach, known as the γ‐algorithm. We find that a constant, global value of αCE≳ 0.1 can adequately account for the observed population of PCEBs with late spectral‐type secondaries. However, this prescription fails to reproduce IK Pegasi (IK Peg), which has a secondary with spectral type A8. We can account for IK Peg if we include thermal and ionization energy of the giant's envelope, or if we use the γ‐algorithm. However, the γ‐algorithm predicts local space densities that are 1 to 2 orders of magnitude greater than estimates from observations. In contrast, the canonical energy budget prescription with an initial mass ratio distribution that favours unequal initial mass ratios (n(qi) ∝q−0.99i) gives a local space density which is in good agreement with observations, and best reproduces the observed distribution of PCEBs. Finally, all models fail to reproduce the sharp decline for orbital periods, Porb≳ 1 d in the orbital period distribution of observed PCEBs, even if we take into account selection effects against systems with long orbital periods and early spectral‐type secondaries.

Context. The complexity of the common-envelope phase and of magnetic stellar wind braking currently limits our understanding of close binary evolution. Because of their intrinsically simple structure, observational population studies of white dwarf plus main sequence (WDMS) binaries can potentially test theoretical models and constrain their parameters. Aims. The Sloan Digital Sky Survey (SDSS) has provided a large and homogeneously selected sample of WDMS binaries, which we characterise in terms of orbital and stellar parameters. Methods. We have obtained radial velocity information for 385 WDMS binaries from follow-up spectroscopy and for an additional 861 systems from the SDSS subspectra. Radial velocity variations identify 191 of these WDMS binaries as post common-envelope binaries (PCEBs). Orbital periods of 58 PCEBs were subsequently measured, predominantly from time-resolved spectroscopy, bringing the total number of SDSS PCEBs with orbital parameters to 79. Observational biases inherent to this PCEB sample were evaluated through extensive Monte Carlo simulations. Results. We find that 21-24% of all SDSS WDMS binaries have undergone common-envelope evolution, which is in good agreement with published binary population models and high-resolution HST imaging of WDMS binaries unresolved from the ground. The bias-corrected orbital period distribution of PCEBs ranges from 1.9 h to 4.3 d and approximately follows a normal distribution in log(P orb ), peaking at ∼10.3 h. There is no observational evidence for a significant population of PCEBs with periods in the range of days to weeks. Conclusions. The large and homogeneous sample of SDSS WDMS binaries provides the means to test fundamental predictions of binary population models, hence to observationally constrain the evolution of all close compact binaries.

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