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

## TL;DR

This study uses microlensing data to analyze the occurrence of Kepler exoplanets based on planet-to-star mass ratio, revealing a universal broken power law and highlighting the importance of mass ratio in planet formation.

## Contribution

It demonstrates that the planet-to-star mass ratio follows a universal broken power law across different host types and compares Kepler and microlensing populations to inform planet formation theories.

## Key findings

- The occurrence rate vs q follows a broken power law with a break at ~3 x10^{-5}.
- The break in q for microlensing planets is 3-10 times higher than for Kepler planets.
- The Solar System's planetary mass distribution broadly aligns with the combined Kepler and microlensing mass-ratio functions.

## 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 ~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.