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 ⊕ and periods <100 days, we find that, except for a normalization factor, the occurrence rate versus q can be described by the same broken power law with a break at ∼3 10^-5 independent of host type for hosts below 1 Mo. 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 Mo 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.