Post-common-envelope binaries from SDSS IX: Constraining the common-envelope efficiency

Context. Reconstructing the evolution of post-common-envelope binaries (PCEBs) consisting of a white dwarf and a main-sequence star can constrain current prescriptions of common-envelope (CE) evolution. This potential could so far not be fully exploited due to the small number of known systems and the inhomogeneity of the sample. Recent extensive follow-up observations of white dwarf/main-sequence binaries identified by the Sloan Digital Sky Survey (SDSS) paved the way for a better understanding of CE evolution. Aims. Analyzing the new sample of PCEBs we derive constraints on one of the most important parameters in the field of close compact binary formation, i.e. the CE efficiency alpha. Methods. After reconstructing the post-CE evolution and based on fits to stellar evolution calculations as well as a parametrized energy equation for CE evolution, we determine the possible evolutionary histories of the observed PCEBs. In contrast to most previous attempts we incorporate realistic approximations of the binding energy parameter lambda. Each reconstructed CE history corresponds to a certain value of the mass of the white dwarf progenitor and - more importantly - the CE efficiency alpha. We also reconstruct CE evolution replacing the classical energy equation with a scaled angular momentum equation and compare the results obtained with both algorithms. Results. We find that all PCEBs in our sample can be reconstructed with the energy equation if the internal energy of the envelope is included. Although most individual systems have solutions for a broad range of values for alpha, only for alpha = 0.2-0.3 do we find simultaneous solutions for all PCEBs in our sample. If we adjust alpha to this range of values, the values of the angular momentum parameter gamma cluster in a small range of values. In contrast if we fix gamma to a small range of values that allows us to reconstruct all our systems, the possible ranges of values for alpha remains broad for individual systems. Conclusions. The classical parametrized energy equation seems to be an appropriate prescription of CE evolution and turns out to constrain the outcome of the CE evolution much more than the alternative angular momentum equation. If there is a universal value of the CE efficiency, it should be in the range of alpha = 0.2-0.3. We do not find any indications for a dependence of a on the mass of the secondary star or the final orbital period.