Rotation, activity, and stellar obliquities in a large uniform sample of Kepler solar analogs

In this study, we undertook a deep photometric examination of a narrowly-defined sample of solar analogs in the Kepler field, with the goals of producing a uniform and statistically meaningful sample of such stars, comparing the properties of planet hosts to those of the general stellar population, and examining the behavior of rotation and photometric activity among stars with similar overall physical parameters. We successfully derived photometric activity indicators and rotation periods for 95 planet hosts (Kepler objects of interest [KOIs]) and 954 solar analogs without detected planets; 573 of these rotation periods are reported here for the first time. Rotation periods average roughly 20 d, but the distribution has a wide dispersion, with a tail extending to P > 35 d which appears to be inconsistent with published gyrochronological relations. We observed a weak rotation-activity relation for stars with rotation periods less than about 12 d; for slower rotators, the relation is dominated by scatter. However, we are able to state that the solar activity level derived from Virgo data is consistent with the majority of stars with similar rotation periods in our sample. Finally, our KOI sample is consistently approximately 0.3 dex more variable than our non-KOIs; we ascribe the difference to a selection effect due to low orbital obliquity in the planet-hosting stars and derive a mean obliquity for our sample of χ = 6+5°-6, similar to that seen in the solar system