A Bayesian re-analysis of HD 11964: evidence for three planets

Astronomers searching for the small signals induced by planets inevitably face significant statistical challenges. Bayesian inference has the potential of improving the interpretation of existing observations, the planning of future observations and ultimately inferences concerning the overall population of planets. This paper illustrates how a re-analysis of published radial velocity data sets with a Bayesian multi-planet Kepler periodogram is providing strong evidence for additional planetary candidates. The periodogram is implemented with a Markov chain Monte Carlo (MCMC) algorithm that employs an automated adaptive control system. For HD 11964, the data has been re-analyzed using 1, 2, 3 and 4 planet models. The most probable model exhibits three periods of 38.02'-0.22+0.11', 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'-0.05+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 semi-major axis are (0.090'-0.14+0.15'MJ, 0.253'-0.009+0.009'au), (0.21'-0.07+0.06'MJ, 1.13'-0.04+0.04'au), (0.77'-0.08+0.08'MJ, 3.46'-0.13+0.13'au), respectively.