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Periodic radial velocity variations in the nearby M-dwarf star Gl411 arereported, based on measurements with the SOPHIE spectrograph. Current data donot allow us to distinguish between a 12.95-day period and its one-day alias at1.08 days, but favour the former slightly. The velocity variation has anamplitude of 1.6 m/s, making this the lowest-amplitude signal detected withSOPHIE up to now. We have performed a detailed analysis of the significance ofthe signal and its origin, including extensive simulations with bothuncorrelated and correlated noise, representing the signal induced by stellaractivity. The signal is significantly detected, and the results from all testspoint to its planetary origin. Additionally, the presence of an additionalacceleration in the velocity time series is suggested by the current data. Onthe other hand, a previously reported signal with a period of 9.9 days,detected in HIRES velocities of this star, is not recovered in the SOPHIE data.An independent analysis of the HIRES dataset also fails to unveil the 9.9-daysignal.  If the 12.95-day period is the real one, the amplitude of the signal detectedwith SOPHIE implies the presence of a planet, called Gl411 b, with a minimummass of around three Earth masses, orbiting its star at a distance of 0.079 AU.The planet receives about 3.5 times the insolation received by Earth, whichimplies an equilibrium temperature between 255 K and 350 K, and makes it toohot to be in the habitable zone. At a distance of only 2.5 pc, Gl411 b, is thethird closest low-mass planet detected to date. Its proximity to Earth willpermit probing its atmosphere with a combination of high-contrast imaging andhigh-dispersion spectroscopy in the next decade.

The SOPHIE search for northern extrasolar planets. XIV. A temperate ($T_\mathrm{eq}\sim 300$ K) super-earth around the nearby star Gliese 411