Parametrizing the exoplanet eccentricity distribution with the Beta distribution

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${^{+ 0.044}_{- 0.044}}$ and b = 3.03${^{+ 0.17}_{- 0.16}}$. 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 11.6σ and display a signature consistent with the effects of tidal circularization.