A Bayesian Kepler Periodogram detects a second planet in HD 208487

Abstract

An automatic Bayesian Kepler periodogram has been developed for identifying and characterizing multiple planetary orbits in precision radial velocity data. The periodogram is powered by a parallel tempering MCMC algorithm which is capable of efficiently exploring a multi-planet model parameter space. The periodogram employs an alternative method for converting the time of an observation to true anomaly that enables it to handle much larger data sets without a significant increase in computation time. Improvements in the periodogram and further tests using data from HD 208487 have resulted in the detection of a second planet with a period of $909_{-92}^{82}$d, an eccentricity of $0.37_{-0.20}^{0.26}$, a semi-major axis of $1.87_{-0.14}^{0.13}$ AU and an $M \sin i = 0.45_{-0.11}^{0.13}$ M$_{\rm J}$. The revised parameters of the first planet are period $= 129.8\pm 0.4$d, eccentricity $= 0.20\pm 0.09$, semi-major axis $= 0.51\pm0.02$ AU and $M \sin i = 0.41\pm0.05$ M$_{\rm J}$. Particular attention is paid to several methods for calculating the model marginal likelihood which is used to compare the probabilities of models with different numbers of planets.