White dwarf binaries suggest a common envelope efficiency α1/3

Peter Scherbak and Jim Fuller

Submitted on 3 November 2022


Common envelope (CE) evolution, which is crucial in creating short period binaries and associated astrophysical events, can be constrained by reverse modeling of such binaries' formation histories. Through analysis of a sample of well-constrained white dwarf (WD) binaries with low-mass primaries (7 eclipsing double WDs, 2 non-eclipsing double WDs, 1 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 αCE0.20.4 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.


Comment: 20 pages, 15 figures. Accepted by MNRAS

Subjects: Astrophysics - Solar and Stellar Astrophysics; Astrophysics - High Energy Astrophysical Phenomena


The effect of changing the initial hydrogen envelope mass on the cooling behavior of non-flashing WD models with a fixed total mass of $0.35 \, M_\odot$. As the H-mass is reduced, the WD's luminosity (top panel), radius (middle panel), and temperature (bottom panel) all decrease faster. The top (dark blue) curve is a model with residual H-burning and narrowly avoids a burning flash. Below $\approx \! 10^{-7} \, M_\odot$, further reducing H has a diminishing effect on evolution.