On the Eccentricity Distribution of Exoplanets from Radial Velocity Surveys

TL;DR

This study examines biases in orbital parameter estimation from radial velocity data, revealing that low signal-to-noise ratios lead to overestimated eccentricities and suggesting the true distribution of exoplanet eccentricities may be more circular than observed.

Contribution

It demonstrates that biases in Keplerian fits affect eccentricity estimates, especially in low signal-to-noise conditions, impacting interpretations of exoplanet orbital distributions.

Findings

Fitted eccentricities are systematically overestimated at low SNR.

Detection efficiency decreases mildly with increasing eccentricity.

Biases in fits lead to underestimation of low-eccentricity exoplanets.

Abstract

We investigate the estimation of orbital parameters by least-$\chi^2$ Keplerian fits to radial velocity (RV) data using synthetic data sets. We find that while the fitted period is fairly accurate, the best-fit eccentricity and $M_p\sin i$ are systematically biased upward from the true values for low signal-to-noise ratio $K/\sigma\lesssim 3$ and moderate number of observations $N_{\rm obs}\lesssim 60$, leading to a suppression of the number of nearly circular orbits. Assuming intrinsic distributions of orbital parameters, we generate a large number of mock RV data sets and study the selection effect on the eccentricity distribution. We find the overall detection efficiency only mildly decreases with eccentricity. This is because although high eccentricity orbits are more difficult to sample, they also have larger RV amplitudes for fixed planet mass and orbital semi-major axis. Thus the primary source of uncertainties in the eccentricity distribution comes from biases in Keplerian fits to detections with low-amplitude and/or small $N_{\rm obs}$, rather than from selection effects. Our results suggest that the abundance of low-eccentricity exoplanets may be underestimated in the current sample and we urge caution in interpreting the eccentricity distributions of low-amplitude detections in future RV samples.