# Toward an initial mass function for giant planets

## TL;DR

This paper reconstructs the initial mass distribution of exoplanets by analyzing current eccentricities and using Bayesian methods to account for planets lost through dynamical interactions, revealing that ejected planets are mostly sub-Saturns.

## Contribution

It introduces a Bayesian framework combining simulations and observations to infer the primordial exoplanet mass function, accounting for dynamical ejections and collisions.

## Key findings

- Ejected planets are mainly sub-Saturns.
- Present-day bimodal distribution is not primordial.
- Intermediate-mass planets are preferentially removed by dynamical instability.

## Abstract

The distribution of exoplanet masses is not primordial. After the initial stage of planet formation is complete, the gravitational interactions between planets can lead to the physical collision of two planets, or the ejection of one or more planets from the system. When this occurs, the remaining planets are typically left in more eccentric orbits. Here we use present-day eccentricities of the observed exoplanet population to reconstruct the initial mass function of exoplanets before the onset of dynamical instability. We developed a Bayesian framework that combines data from N-body simulations with present-day observations to compute a probability distribution for the planets that were ejected or collided in the past. Integrating across the exoplanet population, we obtained an estimate of the initial mass function of exoplanets. We find that the ejected planets are primarily sub-Saturn type planets. While the present-day distribution appears to be bimodal, with peaks around $\sim 1 M_{\rm J}$ and $\sim 20 M_\oplus$, this bimodality does not seem to be primordial. Instead, planets around $\sim 60 M_\oplus$ appear to be preferentially removed by dynamical instabilities. Attempts to reproduce exoplanet populations using population synthesis codes should be mindful of the fact that the present population has been depleted of intermediate-mass planets. Future work should explore how the system architecture and multiplicity might alter our results.