Bayesian re-analysis of the radial velocities of Gliese 581

Aims. The Gliese 581 planetary system has received attention because it has been proposed to host a low-mass planet in its habitable zone. We re-analyse the radial velocity measurements reported to contain six planetary signals to see whether these conclusions remain valid when the analyses are made using Bayesian tools instead of the common periodogram analyses. Methods. We analyse the combined radial velocity data set obtained using the HARPS and HIRES spectrographs using posterior sampling techniques and computation of the posterior probabilities of models with differing numbers of Keplerian signals. We do not fix the orbital eccentricities and stellar jitter to certain values but treat these as free parameters of our statistical models. Hence, we can take the uncertainties of these parameters into account when assessing the number of planetary signals present in the data, the point estimates of all of the model parameters, and the uncertainties of these parameters. Results. We conclude that based on the Bayesian model probabilities and the nature of the posterior densities of the different models, there is evidence in favour of four planets orbiting GJ 581. The HARPS and HIRES data do not imply the conclusion that there are two additional companions orbiting GJ 581. We also revise the orbital parameters of the four companions in the system. Especially, according to our results, the eccentricities of all the companions in the system are consistent with zero