标题： 利用开普勒食双星测量每颗M型矮星的M型矮星数量 显示英文标题

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

摘要： 我们测量了开普勒星场中分离的M型矮星的双星状态，其轨道周期范围为1到90天。 开普勒的测光精度以及对恒星目标长达3个月至4年的几乎连续监测，使其在此时间段内对于掩食双星的检测效率几乎达到了完全覆盖，并适用于所有半径比。 我们的研究采用了一种类似于从行星凌星推断行星出现率的统计框架。 明显的简化之处在于掩食双星具有显著提高的检测效率，这一效率主要受限于它们发生掩食的几何概率。 对于开普勒任务观测到的M型矮星样本，掩食双星的比例表明每颗看似单星的M型矮星都可能有 $0.11 ^{+0.02} _{-0.04}$ 颗紧密的伴星。 我们测量的双星状态高于通过径向速度技术推断出的紧密双星出现率的先前估计值，大约高出2$\sigma$ 倍。 本研究首次利用高精度凌星系外行星巡天任务探测到的掩食双星来推断双星统计学信息。 将此统计框架应用于未来凌星巡天任务发现的掩食双星，将有助于更好地约束短周期M$+$M 双星的发生率，以及其它光谱类型恒星的双星测量。 显示英文摘要

摘要： 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.