The HARPS search for southern extra-solar planets XXXII. Only 4 planets in the Gl~581 system

The Gl 581 planetary system has generated wide interest, because its 4 planets include both the lowest mass planet known around a main sequence star other than the Sun and the first super-Earth planet in the habitable zone of its star. A recent paper announced the possible discovery of two additional super-Earth planets in that system, one of which would be in the middle of the habitable zone of Gl 581. The statistical significance of those two discoveries has, however, been questioned. We have obtained 121 new radial velocity measurements of Gl 581 with the HARPS spectrograph on the ESO 3.6 m telescope, and analyse those together with our previous 119 measurements of that star to examine these potential additional planets. We find that neither is likely to exist with their proposed parameters. We also obtained photometric observations with the 2.5 m Isaac Newton Telescope during a potential transit of the inner planet, Gl 581e, which had a 5% geometric transit probability. Those observations exclude transits for planet densities under 4 times the Earth density within -0.2 sigma to +2.7 sigma of the predicted transit center.