Bayesian priors for the eccentricity of transiting planets

TL;DR

This paper demonstrates that the eccentricity distribution of transiting planets is positively biased and introduces a Bayesian framework with a Beta prior to correct this bias, impacting planet occurrence rate estimates.

Contribution

The authors derive a Bayesian model for eccentricity priors, quantify the bias in transit-based planet occurrence rates, and provide a sampling algorithm with code for the community.

Findings

Transit probability is positively biased by eccentricity.

Most Kepler planet occurrence rates are overestimated by ~10%.

Provided a recursive sampling algorithm for eccentricity priors.

Abstract

Planets on eccentric orbits have a higher geometric probability of transiting their host star. By application of Bayes' theorem, we reverse this logic to show that the eccentricity distribution of transiting planets is positively biased. Adopting the flexible Beta distribution as the underlying prior for eccentricity, we derive the marginalized transit probability as well as the a-priori joint probability distribution of eccentricity and argument of periastron, given that a planet is known to transit. These results allow to demonstrate that most planet occurrence rate calculations using Kepler data have overestimated the prevalence of planets by ~10%. Indeed, the true occurrence of planets from transit surveys is fundamentally intractable without a prior assumption for the eccentricity distribution. Further more, we show that previously extracted eccentricity distributions using Kepler data are positively biased. In cases where one wishes to impose an informative eccentricity prior, we provide a recursive algorithm to apply inverse transform sampling of our joint prior probability distribution. Computer code of this algorithm, ECCSAMPLES, is provided to enable the community to sample directly from the prior.