Bayesian inference for orbital eccentricities

TL;DR

This paper develops Bayesian methods to estimate orbital eccentricities of spectroscopic binaries, providing credible intervals that adapt to measurement thresholds and incorporate physical priors, improving the interpretation of near-circular orbits.

Contribution

It introduces a Bayesian framework for deriving posterior density intervals for eccentricities, including a revised Lucy-Sweeney test, with validation through sampling experiments.

Findings

HPDI's provide upper limits for e below detection threshold

Incorporating tidal dissipation prior refines eccentricity estimates

Sampling confirms the validity of the Bayesian intervals

Abstract

Highest posterior density intervals (HPDI's) are derived for the true eccentricities of spectroscopic binaries with measured values e ~ 0. These yield upper limits when e is below the detection threshold e_th and seamlessly transform to upper and lower bounds when e > e_th. In the main text, HPDI's are computed with an informative eccentricity prior representing orbital decay due to tidal dissipation. In an appendix, the corresponding HPDI's are computed with a uniform prior and are the basis for a revised version of the Lucy-Sweeney test, with the previous outcome e = 0 now replaced by an upper limit. Sampling experiments with known prior confirm the validity of the HPDI's.