Bayesian inference for orbital eccentricities

Astrophysics Group, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, UK
e-mail: l.lucy@imperial.ac.uk

Received: 14 June 2012
Accepted: 21 December 2012

Abstract

Highest posterior density intervals (HPDIs) are derived for the true eccentricities ε 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, 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 ε = 0 now replaced by an upper limit ε_U. Sampling experiments with known prior confirm the validity of the HPDIs.