White dwarf binaries suggest a common envelope efficiency α ∼ 1/3

Abstract

ABSTRACT Common envelope (CE) evolution, which is crucial in creating short-period binaries and associated astrophysical events, can be constrained by reverse modelling of such binaries’ formation histories. Through analysis of a sample of well-constrained white dwarf (WD) binaries with low-mass primaries (seven eclipsing double WDs, two non-eclipsing double WDs, one WD-brown dwarf), we estimate the CE energy efficiency αCE needed to unbind the hydrogen envelope. We use grids of He- and CO-core WD models to determine the masses and cooling ages that match each primary WD’s radius and temperature. Assuming gravitational wave-driven orbital decay, we then calculate the associated ranges in post-CE orbital period. By mapping WD models to a grid of red giant progenitor stars, we determine the total envelope binding energies and possible orbital periods at the point CE evolution is initiated, thereby constraining αCE. Assuming He-core WDs with progenitors of 0.9–2.0 M⊙, we find αCE ∼ 0.2–0.4 is consistent with each system we model. Significantly higher values of αCE are required for higher mass progenitors and for CO-core WDs, so these scenarios are deemed unlikely. Our values are mostly consistent with previous studies of post-CE WD binaries, and they suggest a nearly constant and low envelope ejection efficiency for CE events that produce He-core WDs.