Mass-ratio distribution of contact binary stars

TL;DR

This study infers the mass-ratio distribution of contact binary stars using light curve data and Bayesian analysis, revealing minimum mass ratios that depend on star type and period, consistent with theoretical models.

Contribution

It introduces a novel method to estimate mass-ratio distributions of contact binaries from light curves, bypassing the need for spectroscopy, and provides new empirical measurements of q_min.

Findings

q_min for late-type binaries > 0.087

q_min for early-type binaries ≈ 0.030

Method applicable to future large surveys

Abstract

The mass ratio $q$ of a contact binary star evolves due to mass transfer, magnetic braking, and thermal relaxation oscillations to small values until it crosses a critical threshold $q_\text{min}$. When that happens, the binary undergoes the tidal Darwin instability, leading to a rapid coalescence of the components and observable brightening of the system. So far, the distribution of $q$ has not been measured on a sufficiently large population of contact binary stars, because the determination of $q$ for a single contact binary usually requires spectroscopy. But as was shown previously, it is possible to infer the mass-ratio distribution of the entire population of contact binaries from the observed distribution of their light curve amplitudes. Employing Bayesian inference, we obtain a sample of contact binary candidates from the Kepler Eclipsing Binary Catalog combined with data from Gaia and estimates of effective temperatures. We assign to each candidate a probability of being a contact binary of either late or early type. Overall, our sample includes about 300 late-type and 200 early-type contact binary candidates. We model the amplitude distribution assuming that mass ratios are described by a power law with an exponent $b$ and a cut off at $q_\text{min}$. We find $q_\text{min}=0.087^{+0.024}_{-0.015}$ for late-type contact binaries with periods longer than 0.3 days. For late-type binaries with shorter periods, we find $q_\text{min}=0.246^{+0.029}_{-0.046}$, but the sample is small. For early type contact binary stars with periods shorter than 1 day, we obtain $q_\text{min}=0.030^{+0.018}_{-0.022}$. These results indicate a dependence of $q_\text{min}$ on the structure of the components and are broadly compatible with previous theoretical predictions. Our method can be easily extended to large samples of contact binaries from TESS and other space-based surveys.