A Universal Break in the Planet-to-Star Mass-Ratio Function of Kepler MKG stars

We follow the microlensing approach and quantify the occurrence of Kepler exoplanets as a function of planet-to-star mass ratio, q, rather than planet radius or mass. For planets with radii ~1-6 R_earth and periods <100 days, we find that, except for a normalization factor, the occurrence rate vs q can be described by the same broken power law with a break at ~3 x10^{-5} independent of host type for hosts below 1 M_sun. These findings indicate that the planet-to-star mass ratio is a more fundamental quantity in planet formation than planet mass. We then compare our results to those from microlensing for which the overwhelming majority satisfies the M_host<1 M_sun criterion. The break in q for the microlensing planet population, which mostly probes the region outside the snowline, is 3-10 times higher than that inferred from Kepler. Thus, the most common planet inside the snowline is ~3-10 times less massive than the one outside. With rocky planets interior to gaseous planets, the Solar System broadly follows the combined mass-ratio function inferred from Kepler and microlensing. However, the exoplanet population has a less extreme radial distribution of planetary masses than the Solar System. Establishing whether the mass-ratio function beyond the snowline is also host type independent will be crucial to build a comprehensive theory of planet formation.