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

Davis, P. J.; Kolb, U. and Knigge, C. (2012). Is the common envelope ejection efficiency a function of the binary parameters? Monthly Notices of the Royal Astronomical Society, 419(1) pp. 287–303.

DOI: https://doi.org/10.1111/j.1365-2966.2011.19690.x

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 multiregression analysis in order to investigate whether correlations exist between the CE ejection efficiencies, α_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 α_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 α_CE and the white dwarf mass. If we do not, a correlation is found between α_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 < α_CE ≤ 1, although PCEBs with brown dwarf secondaries still require α_CE≳1.

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