An Integrated Analysis of Radial Velocities in Planet Searches

Abstract

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 chi-squared 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 eccentricities less than about 0.5.

16 pages, 9 figures, to appear in MNRAS

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• A Bayesian Periodogram Finds Evidence for Three Planets in 47 Ursae Majoris
• HADES RV Programme with HARPS-N at TNG XV. Planetary occurrence rates around early-M dwarfs
• Precise radial velocities of giant stars XVI. Planet occurrence rates from the combined analysis of the Lick, EXPRESS, and PPPS giant star surveys
• Connecting substellar and stellar formation. The role of the host star's metallicity
• Mid-to-Late M Dwarfs Lack Jupiter Analogs
• Observing Strategies for the Detection of Jupiter Analogs
• Bayesian Methods for Analysis and Adaptive Scheduling of Exoplanet Observations
• Mutual Occurrence Ratio of Planets. I. New Clues to Reveal Origins of Hot- and Warm-Jupiter from the RV Sample
• Space based microlensing planet searches
• Radial velocity homogeneous analysis of M dwarfs observed with HARPS. II. Detection limits and planetary occurrence statistics
• BEBOP II: Sensitivity to sub-Saturn circumbinary planets using radial-velocities