Is the common envelope ejection efficiency a function of the binary parameters?

Abstract

We reconstruct the common envelope (CE) phase for the current sample of observed white dwarf-main sequence post-common envelope binaries (PCEBs). We apply multi-regression analysis in order to investigate whether correlations exist between the CE ejection efficiencies, alpha_CE, inferred from the sample, and the binary parameters: white dwarf mass, secondary mass, orbital period at the point the CE commences, or the orbital period immediately after the CE phase. We do this with and without consideration for the internal energy of the progenitor primary giants' envelope. Our fits should pave the first steps towards an observationally motivated recipe for calculating alpha_CE using the binary parameters at the start of the CE phase, which will be useful for population synthesis calculations or models of compact binary evolution. If we do consider the internal energy of the giants' envelope, we find a statistically significant correlation between alpha_CE and the white dwarf mass. If we do not, a correlation is found between alpha_CE and the orbital period at the point the CE phase commences. Furthermore, if the internal energy of the progenitor primary envelope is taken into account, then the CE ejection efficiencies are within the canonical range 0<alpha_CE<=1, although PCEBs with brown dwarf secondaries still require alpha_CE>=1.