Photometric Amplitude Distribution of Stellar Rotation of Kepler KOIs-Indication for Spin-Orbit Alignment of Cool Stars and High Obliquity for Hot Stars

The observed amplitude of the rotational photometric modulation of a star with spots should depend on the inclination of its rotational axis relative to our line of sight. Therefore, the distribution of observed rotational amplitudes of a large sample of stars depends on the distribution of their projected axes of rotation. Thus, comparison of the stellar rotational amplitudes of the Kepler KOIs with those of Kepler single stars can provide a measure to indirectly infer the properties of the spin-orbit obliquity of Kepler planets. We apply this technique to the large samples of 993 KOIs and 33,614 single Kepler stars in temperature range of 3500-6500 K. We find with high significance that the amplitudes of cool KOIs are larger, on the order of 10%, than those of the single stars. In contrast, the amplitudes of hot KOIs are systematically lower. After correcting for an observational bias, we estimate that the amplitudes of the hot KOIs are smaller than the single stars by about the same factor of 10%. The border line between the relatively larger and smaller amplitudes, relative to the amplitudes of the single stars, occurs at about 6000K. Our results suggest that the cool stars have their planets aligned with their stellar rotation, while the planets around hot stars have large obliquities, consistent with the findings of Winn et al. (2010) and Albrecht et al. (2012). We show that the low obliquity of the planets around cool stars extends up to at least 50 days, a feature that is not expected in the framework of a model that assumes the low obliquity is due to planet-star tidal realignment.