Kepler Cycle 1 Observations of Low-mass Stars: New Eclipsing Binaries, Single Star Rotation Rates, and the Nature and Frequency of Starspots

We have analyzed Kepler light curves for 849 stars with T _eff <= 5200 K from our Cycle 1 Guest Observer program. We identify six new eclipsing binaries, one of which has an orbital period of 29.91 days and two of which are probably W UMa variables. In addition, we identify a candidate "warm Jupiter" exoplanet. We further examine a subset of 670 sources for variability. Of these objects, 265 stars clearly show periodic variability that we assign to rotation of the low-mass star. At the photometric precision level provided by Kepler, 251 of our objects showed no evidence for variability. We were unable to determine periods for 154 variable objects. We find that 79% of stars with T _eff <= 5200 K are variable. The rotation periods we derive for the periodic variables span the range 0.31 days <= P _rot <= 126.5 days. A considerable number of stars with rotation periods similar to the solar value show activity levels that are 100 times higher than the Sun. This is consistent with results for solar-like field stars. As has been found in previous studies, stars with shorter rotation periods generally exhibit larger modulations. This trend flattens beyond P _rot = 25 days, demonstrating that even long-period binaries may still have components with high levels of activity and investigating whether the masses and radii of the stellar components in these systems are consistent with stellar models could remain problematic. Surprisingly, our modeling of the light curves suggests that the active regions on these cool stars are either preferentially located near the rotational poles, or that there are two spot groups located at lower latitudes, but in opposing hemispheres.