# Evidence for Two Hot Jupiter Formation Paths

## TL;DR

This study analyzes hot Jupiter formation mechanisms using survey data, finding evidence for two distinct formation paths—disk migration and high-eccentricity migration—based on population distribution modeling.

## Contribution

It introduces a hierarchical Bayesian mixture model to distinguish hot Jupiter populations and provides evidence supporting two separate formation channels.

## Key findings

- Radial velocity and Kepler data fit a single population with a cutoff near 2$a_{Roche}$.
- HAT and WASP data show strong evidence for two distinct populations.
- Approximately 15% of hot Jupiters are consistent with disk migration, while 85% align with high-eccentricity migration.

## Abstract

Disk migration and high-eccentricity migration are two well-studied theories to explain the formation of hot Jupiters. The former predicts that these planets can migrate up until the planet-star Roche separation ($a_{Roche}$) and the latter predicts they will tidally circularize at a minimum distance of 2$a_{Roche}$. Considering long-running radial velocity and transit surveys have identified a couple hundred hot Jupiters to date, we can revisit the classic question of hot Jupiter formation in a data-driven manner. We approach this problem using data from several exoplanet surveys (radial velocity, Kepler, HAT, and WASP) allowing for either a single population or a mixture of populations associated with these formation channels, and applying a hierarchical Bayesian mixture model of truncated power laws of the form $x^{\gamma-1}$ to constrain the population-level parameters of interest (e.g., location of inner edges, $\gamma$, mixture fractions). Within the limitations of our chosen models, we find the current radial velocity and Kepler sample of hot Jupiters can be well explained with a single truncated power law distribution with a lower cutoff near 2$a_{Roche}$, a result that still holds after a decade, and $\gamma=-0.51\pm^{0.19}_{0.20}$. However, the HAT and WASP data show evidence for multiple populations (Bayes factor $\approx 10^{21}$). We find that $15\pm^{9}_{6}\%$ reside in a component consistent with disk migration ($\gamma=-0.04\pm^{0.53}_{1.27}$) and $85\pm^{6}_{9}\%$ in one consistent with high-eccentricity migration ($\gamma=-1.38\pm^{0.32}_{0.47}$). We find no immediately strong connections with some observed host star properties and speculate on how future exoplanet surveys could improve upon hot Jupiter population inference.