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

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 alpha(CE) 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 alpha(CE). Assuming He-core WDs with progenitors of 0.9-2.0 M-circle dot, we find alpha(CE) similar to 0.2-0.4 is consistent with each system we model. Significantly higher values of alpha(CE) 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.

Automated summary

This study estimates the CE energy efficiency alpha(CE) needed to unbind the hydrogen envelope through reverse modeling of white dwarf (WD) binaries, finding that alpha(CE) around 0.2-0.4 is consistent with each system studied. By mapping WD models to a grid of red giant progenitor stars, the total envelope binding energies and possible orbital periods at the point CE evolution is initiated are determined, thus constraining alpha(CE) for CE events that produce He-core WDs.