# Bias and robustness of eccentricity estimates from radial velocity data

## TL;DR

This paper investigates the reliability of eccentricity estimates from radial velocity data, emphasizing the importance of proper noise modeling and convergence checks, and introduces methods to distinguish true planetary signals from artifacts.

## Contribution

It provides a comprehensive analysis of eccentricity estimation robustness, proposing criteria for trustworthy results and methods to detect model inaccuracies in radial velocity data.

## Key findings

- Reliable eccentricity estimates require proper noise modeling and convergence verification.
- Strong peaks in the noise power spectrum can mimic eccentric signals.
- Bayes factors help distinguish true planetary eccentricities from artifacts.

## Abstract

Eccentricity is a parameter of particular interest as it is an informative indicator of the past of planetary systems. It is however not always clear whether the eccentricity fitted on radial velocity data is real or if it is an artefact of an inappropriate modelling. In this work, we address this question in two steps: we first assume that the model used for inference is correct and present interesting features of classical estimators. Secondly, we study whether the eccentricity estimates are to be trusted when the data contain incorrectly modelled signals, such as missed planetary companions, non Gaussian noises, correlated noises with unknown covariance, etc. Our main conclusion is that data analysis via posterior distributions, with a model including a free error term gives reliable results provided two conditions. First, convergence of the numerical methods needs to be ascertained. Secondly, the noise power spectrum should not have a particularly strong peak at the semi period of the planet of interest. As a consequence, it is difficult to determine if the signal of an apparently eccentric planet might be due to another inner companion in 2:1 mean motion resonance. We study the use of Bayes factors to disentangle these cases. Finally, we suggest methods to check if there are hints of an incorrect model in the residuals. We show on simulated data the performance of our methods and comment on the eccentricities of Proxima b and 55 Cnc f.