This paper reports on the detection of a planetary system with three Super-Earths orbiting HD40307. HD40307 is a K2V metal-deficient star at a distance of only 13 parsec, part of the HARPS GTO high-precision planet-search programme. The three planets on circular orbits have very low minimum masses of respectively 4.2, 6.9 and 9.2 Earth masses and periods of 4.3, 9.6 and 20.5 days. The planet with the shortest period is the lightest planet detected to-date orbiting a main sequence star. The detection of the correspondingly low amplitudes of the induced radial-velocity variations is completely secured by the 135 very high-quality HARPS observations illustrated by the radial-velocity residuals around the 3-Keplerian solution of only 0.85 m/s. Activity and bisector indicators exclude any significant perturbations of stellar intrinsic origin, which supports the planetary interpretation. Contrary to most planet-host stars, HD40307 has a marked sub-solar metallicity ([Fe/H]=-0.31), further supporting the already raised possibility that the occurrence of very light planets might show a different dependence on host stars metallicity compared to the population of gas giant planets. In addition to the 3 planets close to the central star, a small drift of the radial-velocity residuals reveals the presence of another companion in the system the nature of which is still unknown.
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