A Bayesian periodogram finds evidence for three planets in 47UrsaeMajoris
Abstract
A Bayesian analysis of 47 Ursae Majoris radial velocity data confirms and refines the properties of two previously reported planets with periods of 1079 and 2325d. The analysis also provides orbital constraints on an additional longperiod planet with a period of ~10000 d. The threeplanet model is found to be 10^{5} times more probable than the next most probable model which is a twoplanet model. The nonlinear model fitting is accomplished with a new hybrid Markov chain Monte Carlo (HMCMC) algorithm which incorporates parallel tempering, simulated annealing and genetic crossover operations. Each of these features facilitate the detection of a global minimum in χ^{2}. By combining all three, the HMCMC greatly increases the probability of realizing this goal. When applied to the Kepler problem, it acts as a powerful multiplanet Kepler periodogram.
The measured periods are 1078 +/ 2d, 2391^{+100}_{87}d and 14002^{+4018}_{5095}d, and the corresponding eccentricities are 0.032 +/ 0.014,0.098^{+.047}_{.096} and 0.16^{+.09}_{.16}. The results favour loweccentricity orbits for all three. Assuming the three signals (each one consistent with a Keplerian orbit) are caused by planets, the corresponding limits on planetary mass (M sini) and semimajor axis are (2.53^{+.07}_{.06}M_{J},2.10 +/ 0.02au), (0.54 +/ 0.07 M_{J},3.6 +/ 0.1au) and (1.6^{+0.3}_{0.5}M_{J},11.6^{+2.1}_{2.9}au), respectively. Based on a threeplanet model, the remaining unaccounted for noise (stellar jitter) is 5.7ms^{1}.
The velocities of model fit residuals were randomized in multiple trials and processed using a oneplanet version of the HMCMC Kepler periodogram. In this situation, periodogram peaks are purely the result of the effective noise. The orbits corresponding to these noiseinduced periodogram peaks exhibit a welldefined strong statistical bias towards high eccentricity. We have characterized this eccentricity bias and designed a correction filter that can be used as an alternate prior for eccentricity to enhance the detection of planetary orbits of low or moderate eccentricity.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 April 2010
 DOI:
 10.1111/j.13652966.2009.16233.x
 arXiv:
 arXiv:1003.5549
 Bibcode:
 2010MNRAS.403..731G
 Keywords:

 methods: numerical;
 methods: statistical;
 techniques: radial velocities;
 stars: individual: 47UrsaeMajoris;
 planetary systems;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 Mon. Not. R. Astron. Soc. 403, 731, 2010, The definitive version is available at www.blackwellsynergy.com