A Bayesian periodogram finds evidence for three planets in HD 11964

A Bayesian multiplanet Kepler periodogram has been developed for the analysis of precision radial velocity data. The periodogram employs a parallel tempering Markov chain Monte Carlo algorithm. The HD 11964 data have been re-analysed using 1, 2, 3 and 4 planet models. Assuming that all the models are equally probable a priori, the three planet model is found to be >= 600 times more probable than the next most probable model which is a two planet model. The most probable model exhibits three periods of 38.02(-0.05)(+0.06,) 360(-4)(+4) and 1924(-43)(+44) d, and eccentricities of 0.22(-0.22)(+0.11) 0.63(-0.17)-(+0.34) and 0.05(-0.17)(+0.03), respectively. Assuming the three signals (each one consistent with a Keplerian orbit) are caused by planets, the corresponding limits on planetary mass (M sin i) and semimajor axis are (0.090(-0.14)(+0.15) M-j, 0.253(-0.009)(+0.009) au), (0.21(-0.07)(+0.06) M-j, 1.13(-0.04)(+0.04) au) and (0.77(-0.08)(+0.08) M-J, 3.46(-0.13)(+0.13) au), respectively. The small difference (1.3 sigma) between the 360-d period and one year suggests that it might be worth investigating the barycentric correction for the HD 11964 data.