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 Markov chain Monte Carlo (MCMC) algorithm which is capable of efficiently exploring a multiplanet 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 semimajor axis of 1.87-(0.13)(0.14) au and an M sin i = 0.45(-0.13)(+0.11) M-J. The revised parameters of the first planet are period = 129.8 +/- 0.4 d, eccentricity = 0.20 +/- 0.09, semimajor axis = 0.51 +/- 0.02 au and M sin i = 0.41 +/- 0.05 M-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.