Mass-ratio distribution of contact binary stars

When the mass ratio of a contact binary system drops below the critical value $q_\mathrm{min}$, the binary undergoes the tidal Darwin instability, leading to a rapid merger and observable brightening. So far, the minimum mass ratio has not been experimentally measured on a sufficiently large population of contact binary stars, because the determination of the mass ratio of a single contact binary typically requires spectroscopy. However, it is possible to infer the mass-ratio distribution of an entire population of contact binaries simply 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 Gaia EDR3 and estimates of effective temperature. Each candidate is assigned a probability of being a contact binary of either early or late type. Altogether, our sample includes about $300$ late-type and $340$ early-type contact-binary candidates with probabilities higher than $50\%$. We model the mass ratio distribution as a power law with a cut off at $q_\mathrm{min}$, and obtain the posterior distributions for the parameters. Our preliminary results constrain $q_\mathrm{min}$ to between $0.05$ and $0.1$ for late-type contact binaries with periods longer than $0.3$ days. For binaries with shorter periods, we find $q_\mathrm{min}$ between $0.15$ and $0.3$, but the sample is small. For early type contact binary stars with periods shorter than $1$ day, we find $q_\mathrm{min}≤0.07$. These results are broadly compatible with theoretical predictions. In addition, our method can be easily extended to large samples of contact binaries from TESS and other space-based surveys, and we expect that $q_\mathrm{min}$ obtained from these samples might put some constraints on tidal-interaction models of close stellar binaries.