Mass-ratio distribution of contact binary stars
Milan Pešta, Ondřej Pejcha
Abstract
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 q min . 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 q min . We find q min = 0.087 −0.015 +0.024 for late-type contact binaries with periods longer than 0.3 days. For late-type binaries with shorter periods, we find q min = 0.246 −0.046 +0.029 , but the sample is small. For early-type contact binary stars with periods shorter than one day, we obtain q min = 0.030 −0.022 +0.018 . These results indicate a dependence of q min 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.