Inferring the eccentricity distribution

Details Inferring the eccentricity distribution Inferring the eccentricity distribution

2010-08-24

arxiv.org/abs/1008.4146v2

The Astrophysical Journal, 725, 2166-2175 (2010)

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

ApJ

Scientific paper

10.1088/0004-637X/725/2/2166

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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