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Population Synthesis Studies of Close Binary Systems Using a Variable Common Envelope Efficiency Parameter: I. Dependence upon Secondary Mass

We perform population synthesis calculations of present-day post common envelope binaries (PCEBs) and zero-age cataclysmic variables (ZACVs) using a common envelope efficiency parameter, alphaCE, that is a function of secondary mass, Ms. We investigate three basic possibilities: (1) a standard constant alphaCE prescription, with alphaCE = 1.0, 0.6, 0.3, 0.2, 0.1 and 0.05, to provide a baseline for comparison, (2) a power law dependence, alphaCE = (Ms)^n, with n = 0.5, 1.0 and 2.0, and (3) a dependence in which alphaCE approaches1 for large secondary masses and alphaCE = 0 below some assumed cutoff mass, alphaCE = 1 - Mcut/Ms, where Mcut is the cutoff mass and is equal to 0.0375, 0.075 and 0.15 solar mass. For each population, we compute orbital period, orbital separation, white dwarf mass and secondary mass distributions. We find that if alphaCE is less than ~0.2 in our constant alphaCE sequence, the predicted present-day ZACV population is significantly modified compared with our standard model (alphaCE = 1.0). In our variable alphaCE sequences for ZACVs, we find that for models in which alphaCE decreases very rapidly for small secondary masses, the orbital period distribution below the period gap differs significantly from our standard model. These differences are most evident in our power law sequence model with n = 2 and in our cutoff mass sequence model with Mcut = 0.15 solar mass. In these two models, the fraction of CVs forming with orbital periods below the gap is reduced significantly, the fraction forming in the gap is increased significantly, and both the short-period peak and the minimum period in the ZACV orbital period distribution shift to considerably longer orbital periods compared with our standard model.