Inferring the eccentricity distribution

David W. Hogg, Adam D. Myers, Jo Bovy

    Research output: Contribution to journalArticle

    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, distances, or photometric redshifts-so long as the measurements have been communicated as a likelihood function or a posterior sampling.

    Original languageEnglish (US)
    Pages (from-to)2166-2175
    Number of pages10
    JournalAstrophysical Journal
    Volume725
    Issue number2
    DOIs
    StatePublished - Dec 20 2010

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    Keywords

    • Binaries: general
    • Methods: data analysis
    • Methods: statistical
    • Planetary systems
    • Planets and satellites: fundamental parameters
    • Stars: kinematics and dynamics

    ASJC Scopus subject areas

    • Astronomy and Astrophysics
    • Space and Planetary Science

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