Measuring the Number of M-Dwarfs per M-Dwarf Using Kepler Eclipsing Binaries

We measure the binarity of detached M-dwarfs in the Kepler field with orbital periods in the range of 1-90 days. Kepler's photometric precision and nearly continuous monitoring of stellar targets over time baselines ranging from 3 months to 4 years make its detection efficiency for eclipsing binaries nearly complete over this period range and for all radius ratios. Our investigation employs a statistical framework akin to that used for inferring planetary occurrence rates from planetary transits. The obvious simplification is that eclipsing binaries have a vastly improved detection efficiency that is limited chiefly by their geometric probabilities to eclipse. For the M-dwarf sample observed by the Kepler Mission, the fractional incidence of eclipsing binaries implies that there are $0.11 ^{+0.02} _{-0.04}$ close stellar companions per apparently single M-dwarf. Our measured binarity is higher than previous inferences of the occurrence rate of close binaries via radial velocity techniques, at roughly the 2$\sigma$ level. This study represents the first use of eclipsing binary detections from a high quality transiting planet mission to infer binary statistics. Application of this statistical framework to the eclipsing binaries discovered by future transit surveys will establish better constraints on short-period M$+$M binary rate, as well as binarity measurements for stars of other spectral types.