Parametrizing the exoplanet eccentricity distribution with the Beta distribution

TL;DR

This paper demonstrates that the Beta distribution effectively models the eccentricity distribution of exoplanets, providing a flexible, proper prior, and reveals differences between short- and long-period planets with high statistical confidence.

Contribution

It introduces the Beta distribution as a parametric model for exoplanet eccentricities and applies Bayesian analysis to confirm its suitability over other models.

Findings

Beta distribution fits 396 exoplanet eccentricities well

Beta distribution is 3.7 times more likely than alternative models

Distinct eccentricity distributions for short- and long-period planets

Abstract

It is suggested that the distribution of orbital eccentricities for extrasolar planets is well-described by the Beta distribution. Several properties of the Beta distribution make it a powerful tool for this purpose. For example, the Beta distribution can reproduce a diverse range of probability density functions (PDFs) using just two shape parameters (a and b). We argue that this makes it ideal for serving as a parametric model in Bayesian comparative population analysis. The Beta distribution is also uniquely defined over the interval zero to unity, meaning that it can serve as a proper prior for eccentricity when analysing the observations of bound extrasolar planets. Using nested sampling, we find that the distribution of eccentricities for 396 exoplanets detected through radial velocity with high signal-to-noise is well-described by a Beta distribution with parameters a = 0.867+/-0.044 and b = 3.03+/-0.17. The Beta distribution is shown to be 3.7 times more likely to represent the underlying distribution of exoplanet eccentricities than the next best model: a Rayleigh + exponential distribution. The same data are also used in an example population comparison utilizing the Beta distribution, where we find that the short- and long-period planets are described by distinct Beta distributions at a confidence of 11.6 sigma and display a signature consistent with the effects of tidal circularization.