Bayesian Re-analysis of the Gliese 581 Exoplanet System
  A re-analysis of Gliese 581 HARPS and HIRES precision radial velocity data was carried out with a Bayesian multi-planet Kepler periodogram (from 1 to 6 planets) based on a fusion Markov chain Monte Carlo algorithm. In all cases the analysis included an unknown parameterized stellar jitter noise term. For the HARPS data set the most probable number of planetary signals detected is 5 with a Bayesian false alarm probability of 0.01. These include the $3.1498\pm0.0005$, $5.3687\pm0.0002$, $12.927_{-0.004}^{+0.006}$, and $66.9\pm0.2$d periods reported previously plus a $399_{-16}^{+14}$d period. The orbital eccentricities are $0.0_{-0.0}^{+0.2}$, $0.00_{-0.00}^{+0.02}$, $0.10_{-0.10}^{+0.06}$, $0.33_{-0.10}^{+0.09}$, and $0.02_{-0.02}^{+0.30}$, respectively. The semi-major axis and $M sin i$ of the 5 planets are ($0.0285\pm0.0006$ au, $1.9\pm0.3$M$_{\earth}$), ($0.0406\pm0.0009$ au, $15.7\pm0.7$M$_{\earth}$), ($0.073\pm0.002$ au, $5.3\pm0.4$M$_{\earth}$), ($0.218\pm0.005$ au, $6.7\pm0.8$M$_{\earth}$), and ($0.7\pm0.2$ au, $6.6_{-2.7}^{+2.0}$M$_{\earth}$), respectively. The analysis of the HIRES data set yielded a reliable detection of only the strongest 5.37 and 12.9 day periods. The analysis of the combined HIRES/HARPS data again only reliably detected the 5.37 and 12.9d periods. Detection of 4 planetary signals with periods of 3.15, 5.37, 12.9, and 66.9d was only achieved by including an additional unknown but parameterized Gaussian error term added in quadrature to the HIRES quoted errors. The marginal distribution for the sigma of this additional error term has a well defined peak at $1.8\pm0.4$m s$^{-1}$. It is possible that this additional error arises from unidentified systematic effects. We did not find clear evidence for a fifth planetary signal in the combined HIRES/HARPS data set. 
Philip C. Gregory
astro-ph.SR astro-ph.EP