Observational biases in determining extrasolar planet eccentricities in single-planet systems

TL;DR

This study examines biases in measuring exoplanet eccentricities from radial velocity data, revealing overestimations for nearly circular orbits and providing recommendations for more accurate population analyses.

Contribution

It introduces a mock data approach to identify biases in eccentricity measurements and suggests using the mode of the posterior distribution to reduce bias.

Findings

Eccentricities of nearly circular planets are overestimated by 1-2 times the median uncertainty.

The true fraction of planets with eccentricity below 0.05 is about 38%, higher than previous estimates.

Using the mode of the posterior distribution minimizes bias in population studies.

Abstract

We investigate potential biases in the measurements of exoplanet orbital parameters obtained from radial velocity observations for single-planet systems. We create a mock catalog of radial velocity data, choosing input planet masses, periods, and observing patterns from actual radial velocity surveys and varying input eccentricities. We apply Markov Chain Monte Carlo (MCMC) simulations and compare the resulting orbital parameters to the input values. We find that a combination of the effective signal-to-noise ratio of the data, the maximal gap in phase coverage, and the total number of periods covered by observations is a good predictor of the quality of derived orbit parameters. As eccentricity is positive definite, we find that eccentricities of planets on nearly circular orbits are preferentially overestimated, with typical bias of 1-2 times the median eccentricity uncertainty in a survey (e.g., 0.04 in the Butler et al. 2006 catalog). When performing population analysis, we recommend using the mode of the marginalized posterior eccentricity distribution to minimize potential biases. While the Butler et al. (2006) catalog reports eccentricities below 0.05 for just 17% of single-planet systems, we estimate that the true fraction of e < 0.05 orbits is about f(0.05)=38\pm 9%. For planets with P > 10 days, we find f(0.05)=28\pm 8% versus 10% from Butler et al. (2006). These planets either never acquired a large eccentricity or were circularized following any significant eccentricity excitation.