A Bayesian Kepler Periodogram Detects a Second Planet in HD 208487

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. 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 $908_{-94}^{81}$d, an eccentricity of $0.38_{-0.20}^{0.26}$, a semi-major axis of $1.80_{-0.08}^{0.09}$ AU and an $M \sin i = 0.46_{-0.13}^{0.05}$ M$_{\rm J}$. The revised parameters of the first planet are period $= 129.8\pm 0.4$d, eccentricity $= 0.21\pm 0.09$, semi-major axis $= 0.492_{-0.002}^{0.001}$ AU and $M \sin i = 0.37_{-0.03}^{0.04}$ M$_{\rm J}$. Particular attention is paid to several methods for calculating the Bayes factor which is used to compare models with different numbers of planets.