Abstract

The Kepler spacecraft has discovered a large number of planets with up to one-year periods and down to terrestrial sizes. While the majority of the target stars are main-sequence dwarfs of spectral type F, G, and K, Kepler covers stars with effective temperatures as low as 2500 K, which corresponds to M stars. These cooler stars allow characterization of small planets near the habitable zone, yet it is not clear if this population is representative of that around FGK stars. In this paper, we calculate the occurrence of planets around stars of different spectral types as a function of planet radius and distance from the star and show that they are significantly different from each other. We further identify two trends. First, the occurrence of Earth-to Neptune-sized planets (1-4 R-circle plus) is successively higher toward later spectral types at all orbital periods probed by Kepler; planets around M stars occur twice as frequently as around G stars, and thrice as frequently as around F stars. Second, a drop in planet occurrence is evident at all spectral types inward of a similar to 10 day orbital period, with a plateau further out. By assigning to each spectral type a median stellar mass, we show that the distance from the star where this drop occurs is stellar mass dependent, and scales with semi-major axis as the cube root of stellar mass. By comparing different mechanisms of planet formation, trapping, and destruction, we find that this scaling best matches the location of the pre-main-sequence co-rotation radius, indicating efficient trapping of migrating planets or planetary building blocks close to the star. These results demonstrate the stellar-mass dependence of the planet population, both in terms of occurrence rate and of orbital distribution. The prominent stellar-mass dependence of the inner boundary of the planet population shows that the formation or migration of planets is sensitive to the stellar parameters.