Title: Evidence for Two Hot Jupiter Formation Paths,
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.