An Integrated Analysis of Radial Velocities in Planet Searches

TL;DR

This paper introduces a Bayesian method for analyzing radial velocity data in planet searches, providing efficient, real-time constraints on orbital parameters and false alarm probabilities, improving upon previous techniques.

Contribution

The authors develop a rapid Bayesian algorithm combining analytic and numerical methods for orbital analysis, including long-term trends, with improved false alarm probability estimates.

Findings

Bayesian false alarm probabilities are higher than frequentist estimates.

The method accurately constrains orbital parameters in real time.

Upper limits for circular orbits extend to eccentric orbits with e<0.5.

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.