White dwarf eccentricity fluctuation and dissipation by AGB convection

TL;DR

This paper extends the fluctuation-dissipation theory to explain the eccentricities of white dwarf binaries with AGB progenitors, highlighting the role of residual hydrogen envelope mass and common-envelope damping effects.

Contribution

It introduces a new theoretical framework for massive CO white dwarf eccentricities considering AGB evolution and identifies the dominant role of hydrogen envelope mass and common-envelope damping.

Findings

Eccentricity e~3×10^{-3} is nearly independent of white dwarf mass.

Eccentricities are below the theoretical limit, indicating damping during common-envelope phase.

A tight empirical relation e∝P^{3/2} links period and eccentricity for massive white dwarfs.

Abstract

Millisecond pulsars with white dwarf companions have typical eccentricities $e\sim 10^{-6}-10^{-3}$. The eccentricities of helium white dwarfs are explained well by applying the fluctuation-dissipation theorem to convective eddies in their red giant progenitors. We extend this theory to more massive carbon-oxygen (CO) white dwarfs with asymptotic giant branch (AGB) progenitors. Due to the radiation pressure in AGB stars, the dominant factor in determining the remnant white dwarf's eccentricity is the critical residual hydrogen envelope mass $m_{\rm env}$ required to inflate the star to giant proportions. Using a suite of MESA stellar evolution simulations with $\Delta m_{\rm c}=10^{-3}\,{\rm M}_\odot$ core-mass intervals, we resolved the AGB thermal pulses and found that the critical $m_{\rm env}\propto m_{\rm c}^{-6}$. The resulting eccentricity $e\sim 3\times 10^{-3}$ is almost independent of the remnant CO white dwarf's mass $m_{\rm c}$. Nearly all of the measured eccentricities lie below this robust theoretical limit, indicating that the eccentricity is damped during the common-envelope inspiral that follows the unstable Roche-lobe overflow of the AGB star. Specifically, we focused on white dwarfs with median masses $m_{\rm c}>0.6\,{\rm M}_\odot$. These massive white dwarfs begin their inspiral with practically identical orbital periods and eccentricities, eliminating any dependence on the initial conditions. For this sub-sample, we find an empirical relation $e\propto P^{3/2}$ between the final period and eccentricity that is much tighter than previous studies - motivating theoretical work on the eccentricity evolution during the common envelope phase. The eccentricities of lower mass CO white dwarfs may be explained by alternative formation channels.