Abstract. The G0 V star HD 166435 has been observed by the fiber-fed spectrograph ELODIE as one of the targets in the large extra-solar planet survey that we are conducting at the Observatory of Haute-Provence. We detected coherent, low-amplitude, radial-velocity variations with a period of 3.7987 days, suggesting a possible close-in planetary companion. Subsequently, we initiated a series of high-precision photometric observations to search for possible planetary transits and an additional series of Ca II H and K observations to measure the level of surface magnetic activity and to look for possible rotational modulation. Surprisingly, we found the star to be photometrically variable and magnetically active. A detailed study of the phase stability of the radial-velocity signal revealed that the radial-velocity variability remains coherent only for durations of about 30 days. Analysis of the time variation of the spectroscopic line profiles using line bisectors revealed a correlation between radial velocity and line-bisector orientation. All of these observations, along with a one-quarter cycle phase shift between the photometric and the radial-velocity variations, are well explained by the presence of dark photospheric spots on HD 166435. We conclude that the radial-velocity variations are not due to gravitational interaction with an orbiting planet but, instead, originate from line-profile changes stemming from star spots on the surface of the star. The quasi-coherence of the radial-velocity signal over more than two years, which allowed a fair fit with a binary model, makes the stability of this star unusual among other active stars. It suggests a stable magnetic field orientation where spots are always generated at about the same location on the surface of the star.

Context. Searching for planets around stars with different masses probes the outcome of planetary formation for different initial conditions. The low-mass M dwarfs are also the most frequent stars in our Galaxy and potentially therefore, the most frequent planet hosts. Aims. This drives observations of a sample of 102 southern nearby M dwarfs, using a fraction of our guaranteed time on the ESO/HARPS spectrograph. We observed 460 hours and gathered 1965 precise (∼ 1 − 3 m/s) radial velocities, spanning the period from Feb. 11th, 2003 to Apr. 1st 2009. Methods. This paper makes available the sample's time series, presents their precision and variability. We apply systematic searches for long-term trends, periodic signals and Keplerian orbits (from 1 to 4 planets). We analyze the subset of stars with detected signals and apply several diagnostics to discriminate whether the observed Doppler shifts are caused by stellar surface inhomogeneities or by the radial pull of orbiting planets. To prepare for the statistical view of our survey we also compute the limits on possible unseen signals, and derive a first estimate of the frequency of planets orbiting M dwarfs. Results. We recover the planetary signals corresponding to 9 planets already announced by our group (Gl 176 b, Gl 581 b, c, d & e, Gl 674 b, Gl 433 b, Gl 667C b and Gl 667C c). We present radial velocities that confirm GJ 849 hosts a Jupiter-mass planet, plus a long-term radial-velocity variation. We also present RVs that precise the planetary mass and period of Gl 832b. We detect longterm RV changes for Gl 367, Gl 680 and Gl 880 betraying yet unknown long-period companions. We identify candidate signals in the radial-velocity time series of 11 other M dwarfs. Spectral diagnostics and/or photometric observations demonstrate however that they are most probably caused by stellar surface inhomogeneities. Finally, we find our survey sensitive to few Earth-mass planets for periods up to several hundred days. We derive a first estimate of the occurrence of M-dwarf planets as a function of their minimum mass and orbital period. In particular, we find that giant planets (m sin i = 100 − 1, 000 M ⊕ ) have a low frequency (e.g. f 1% for P = 1 − 10 d and f = 0.02 +0.03 −0.01 for P = 10 − 100 d), whereas super-Earths (m sin i = 1 − 10 M ⊕ ) are likely very abundant ( f = 0.36 +0.25 −0.10 for P = 1 − 10 d and f = 0.35 +0.45 −0.11 for P = 10 − 100 d). We also obtained η ⊕ = 0.41 +0.54 −0.13 , the frequency of habitable planets orbiting M dwarfs (1 ≤ m sin i ≤ 10 M ⊕ ). For the first time, η ⊕ is a direct measure and not a number extrapolated from the statistic of more massive and/or shorter-period planets.