SIMBAD references

We perform population synthesis calculations of present-day post-CE binaries (PCEBs) and zero-age cataclysmic variables (ZACVs) using a common envelope (CE) efficiency parameter, α_CE, that is a function of secondary mass, M_s. We investigate three basic possibilities: (1) a standard constant α_CEprescription, with α_CE ranging from 0.05 to 1.0, to provide a baseline for comparison; (2) a power-law dependence, α_CE=(M_s)ⁿ, with n=0.5, 1.0, and 2.0; and (3) a dependence in which α_CEapproaches 1 for large M_s and α_CE=0 below some assumed cutoff mass, α_CE=1-M_cut/M_s, where M_cut=0.0375, 0.075, and 0.15 M_☉. We find that if α_CE≲0.2 in our constant α_CEsequence, the predicted present-day ZACV population is significantly modified compared with our standard model (α_CE=1.0). All prior population synthesis calculations of the formation of CVs only considered values of α_CE≥0.3 and found that their model populations were not strongly dependent upon the value of α_CE. Our results indicate that a much wider range of values for α_CE, including very low values, must be considered in order for a dependence to be seen. In our variable α_CE sequences for ZACVs, we find that for models in which α_CE decreases very rapidly for small M_s, the orbital period distribution below the period gap differs significantly from our standard model. In particular, the fraction of CVs forming with P<2 hr is reduced significantly, the fraction forming in the gap is increased significantly, and both the short-period peak and the minimum period shift to considerably longer periods compared with our standard model. We suggest that the observed scarcity of CVs with P<77 minutes may possibly provide evidence that progenitor binaries with M_s≲0.10 M_☉ are unable to avoid merger within the CE. We also suggest that if α_CE decreases rapidly for small M_s, it is possible that the lower edge of the period gap could be, in part, an imprint of the ZACV population.