A Bayesian Kepler periodogram detects a second planet in HD208487

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 HD208487 have resulted in the detection of a second planet with a period of 909⁸²_-92d, an eccentricity of 0.37^0.26_-0.20, a semimajor axis of 1.87^0.13_-0.14au and an M sini = 0.45^+0.11_-0.13 M_J. The revised parameters of the first planet are period = 129.8 +/- 0.4d, eccentricity = 0.20 +/- 0.09, semimajor axis = 0.51 +/- 0.02au and M sini = 0.41 +/- 0.05M_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.