On the Eccentricity Distribution of Short-Period Single-Planet Systems

TL;DR

This paper introduces a new statistical method called {} analysis for assessing the significance of small orbital eccentricities in short-period exoplanets, and applies it to a sample of 50 systems to understand their eccentricity distribution.

Contribution

The paper develops the {} analysis method combining bootstrap and Bayesian techniques, and uses it to analyze eccentricities and their distribution in short-period single-planet systems.

Findings

{} analysis effectively assesses small eccentricity significance.

Current data insufficient to determine the influence of tidal interactions.

A mixture of analytical distributions models the eccentricity distribution well.

Abstract

We apply standard Markov chain Monte Carlo (MCMC) analysis techniques for 50 short- period, single-planet systems discovered with radial velocity technique. We develop a new method for accessing the significance of a non-zero orbital eccentricity, namely {\Gamma} analysis, which combines frequentist bootstrap approach with Bayesian analysis of each simulated data set. We find the eccentricity estimations from {\Gamma} analysis are generally consistent with results from both standard MCMC analysis and previous references. The {\Gamma} method is particular useful for assessing the significance of small eccentricities. Our results suggest that the current sample size is insufficient to draw robust conclusions about the roles of tidal interaction and perturbations in shaping the eccentricity distribution of short-period single-planet systems. We use a Bayesian population analysis to show that a mixture of analytical distributions is a good approximation of the underlying eccentricity distribution. For short-period planets, we find the most probable values of parameters in the analytical functions given the observed eccentricities. These analytical functions can be used in theoretical investigations or as priors for the eccentricity distribution when analyzing short-period planets. As the measurement precision improves and sample size increases, the method can be applied to more complex parametrizations for the underlying distribution of eccentricity for extrasolar planetary systems.