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arXiv · 1206.3462

Bayesian inference for orbital eccentricities

L. B. Lucy
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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.

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L. B. Lucy. 2012-12-31. Bayesian inference for orbital eccentricities. https://doi.org/10.1051/0004-6361%2F201219819

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