Journal Article

An integrated analysis of radial velocities in planet searches

Andrew Cumming and Diana Dragomir

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 401, issue 2, pages 1029-1042
Published in print January 2010 | ISSN: 0035-8711
Published online January 2010 | e-ISSN: 1365-2966 | DOI:
An integrated analysis of radial velocities in planet searches

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We discuss a Bayesian approach to the analysis of radial velocities in planet searches. We use a combination of exact and approximate analytic and numerical techniques to efficiently evaluate χ2 for multiple values of orbital parameters, and to carry out the marginalization integrals for a single planet including the possibility of a long-term trend. The result is a robust algorithm that is rapid enough for use in real-time analysis that outputs constraints on orbital parameters and false-alarm probabilities for the planet and long-term trend. The constraints on parameters and odds ratio that we derive compare well with previous calculations based on Markov Chain Monte Carlo methods, and we compare our results with other techniques for estimating false-alarm probabilities and errors in derived orbital parameters. False-alarm probabilities from the Bayesian analysis are systematically higher than frequentist false-alarm probabilities, due to the different accounting of the number of trials. We show that upper limits on the velocity amplitude derived for circular orbits are a good estimate of the upper limit on the amplitude of eccentric orbits for e≲ 0.5.

Keywords: methods: statistical; binaries: spectroscopic; planetary systems

Journal Article.  10796 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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