Abstract

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 similar to 1-6 R-circle plus 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 similar to 3 x 10(-5) independent of host type for hosts below 1 M-circle dot. 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-circle dot criterion. The break in q for the microlensing planet population, which mostly probes the region outside the snowline, is similar to 3-10 times higher than that inferred from Kepler. Thus, the most common planet inside the snowline is similar to 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.