The dynamical stability of W Ursae Majoris-type systems

TL;DR

This paper investigates the stability limits of W UMa-type contact binary systems, suggesting that observed systems are more stable than theoretical predictions due to angular momentum loss mechanisms.

Contribution

It provides a revised dynamical stability limit for W UMa systems considering angular momentum loss, aligning theoretical models with observations.

Findings

W UMa systems with mass ratio q ≤ 0.076 are likely unstable and merge.

Observed systems with q ≈ 0.077 are near the stability limit and may merge.

Angular momentum loss via gravitational waves or magnetic winds explains observed stability.

Abstract

Theoretical study indicates that a contact binary system would merge into a rapidly rotating single star due to tidal instability when the spin angular momentum of the system is more than a third of its orbital angular momentum. Assuming that W UMa contact binary systems rigorously comply with the Roche geometry and the dynamical stability limit is at a contact degree of about 70%, we obtain that W UMa systems might suffer Darwin's instability when their mass ratios are in a region of about 0.076--0.078 and merge into the fast-rotating stars. This suggests that the W UMa systems with mass ratio $q\leq0.076$ can not be observed. Meanwhile, we find that the observed W UMa systems with a mass ratio of about 0.077, corresponding to a contact degree of about 86% would suffer tidal instability and merge into the single fast-rotating stars. This suggests that the dynamical stability limit for the observed W UMa systems is higher than the theoretical value, implying that the observed systems have probably suffered the loss of angular momentum due to gravitational wave radiation (GR) or magnetic stellar wind (MSW).