Mass-ratio distribution of contact binary stars

The mass ratio q of a contact binary star evolves through mass transfer, magnetic braking, and thermal relaxation oscillations to low values until it crosses a critical threshold qmin. When this occurs, the binary undergoes the tidal Darwin instability, leading to a rapid coalescence of the components and to an observable brightening of the system. The distribution of q has not been measured on a sufficiently large population of contact binary stars so far because determining q for a single contact binary usually requires spectroscopy. As was shown previously, however, 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 obtained a sample of contact binary candidates from the Kepler Eclipsing Binary Catalog combined with data from Gaia and estimates of effective temperatures. We assigned a probability of being a contact binary of either late or early type to each candidate. Overall, our sample includes about 300 late-type and 200 early-type contact binary candidates. We modeled the amplitude distribution assuming that mass ratios are described by a power law with an exponent b and a cutoff at qmin. We find $ q_{\mathrm{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_{\mathrm{min}}=0.246^{+0.029}_{-0.046} $, but the sample is small. For early-type contact binary stars with periods shorter than one day, we obtain $ q_{\mathrm{min}}=0.030^{+0.018}_{-0.022} $. These results indicate a dependence of qmin on the structure of the components, and they are broadly compatible with previous theoretical predictions. We do not find any clear trends in b. Our method can easily be extended to large samples of contact binaries from TESS and other space-based surveys