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arXiv · 1008.4146

Inferring the eccentricity distribution

David W. Hogg·Adam D. Myers·Jo Bovy
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Abstract

Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual-star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementation of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision--other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, parallaxes, or photometric redshifts--so long as the measurements have been communicated as a likelihood function or a posterior sampling.

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David W. Hogg, Adam D. Myers, Jo Bovy. 2010-09-25. Inferring the eccentricity distribution. https://doi.org/10.1088/0004-637x%2F725%2F2%2F2166

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