Bayesian inference for orbital eccentricities

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