Bayesian priors for the eccentricity of transiting planets

Planets on eccentric orbits have a higher geometric probability of transiting their host star. By application of Bayes’ theorem, we reverse this logic to show that the eccentricity distribution of transiting planets is positively biased. Adopting the flexible Beta distribution as the underlying prio...

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Vydáno v:Monthly notices of the Royal Astronomical Society Ročník 444; číslo 3; s. 2263 - 2269
Hlavní autor: Kipping, David M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Oxford University Press 01.11.2014
Témata:
Algorithms
Bayesian analysis
Eccentricity
Logic
Orbits
Planetology
Planets
Probability distribution
Recursive algorithms
Star & galaxy formation
Theorems
Transit
methods: statistical
eclipses
techniques: radial velocities
techniques: photometric
planets and satellites: fundamental parameters
ISSN:0035-8711, 1365-2966
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Shrnutí:Planets on eccentric orbits have a higher geometric probability of transiting their host star. By application of Bayes’ theorem, we reverse this logic to show that the eccentricity distribution of transiting planets is positively biased. Adopting the flexible Beta distribution as the underlying prior for eccentricity, we derive the marginalized transit probability as well as the a priori joint probability distribution of eccentricity and argument of periastron, given that a planet is known to transit. These results allow us to demonstrate that most planet occurrence rate calculations using Kepler data have overestimated the prevalence of planets by ∼10 per cent. Indeed, the true occurrence of planets from transit surveys is fundamentally intractable without a prior assumption for the eccentricity distribution. Further more, we show that previously extracted eccentricity distributions using Kepler data are positively biased. In cases where one wishes to impose an informative eccentricity prior, we provide a recursive algorithm to apply inverse transform sampling of our joint prior probability distribution. Computer code of this algorithm, ECCSAMPLES, is provided to enable the community to sample directly from the prior (availablehere).
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ISSN:0035-8711
1365-2966
DOI:10.1093/mnras/stu1561