A quarter century of spectroscopic monitoring of the nearby M dwarf Gl 514. A super-Earth on an eccentric orbit moving in and out of the habitable zone

Context. Statistical analyses based on Kepler data show that most of the early-type M dwarfs host multi-planet systems consisting of Earth- to sub-Neptune-sized planets with orbital periods of up to similar to 250 days, and that at least one such planet is likely located within the habitable zone. M dwarfs are therefore primary targets to search for potentially habitable planets in the solar neighbourhood.Aims. We investigated the presence of planetary companions around the nearby (7.6 pc) and bright (V = 9 mag) early-type M dwarf Gl 514, analysing 540 radial velocities collected over nearly 25 yr with the HIRES, HARPS, and CARMENES spectrographs.Methods. The data are affected by time-correlated signals at the level of 2-3 m s(-1 )due to stellar activity, which we filtered out, testing three different models based on Gaussian process regression. As a sanity cross-check, we repeated the analyses using HARPS radial velocities extracted with three different algorithms. We used HIRES radial velocities and Hipparcos-Gaia astrometry to put constraints on the presence of long-period companions, and we analysed TESS photometric data.Results. We find strong evidence that Gl 514 hosts a super-Earth on a likely eccentric orbit, residing in the conservative habitable zone for nearly 34% of its orbital period. The planet Gl 514 b has minimum mass m(b) sin i(b) = 5.2 +/- 0.9 M-circle plus, orbital period P-b = 140.43 +/- 0.41 days, and eccentricity e(b) = 0.45(-0.14)(-0.15). No evidence for transits is found in the TESS light curve. There is no evidence for a longer period companion in the radial velocities and, based on astrometry, we can rule out a similar to 0.2 M-Jup planet at a distance of similar to 3-10 astronomical units, and massive giant planets and brown dwarfs out to several tens of astronomical units. We discuss the possible presence of a second low-mass companion at a shorter distance from the host than Gl 514 b.Conclusions. Gl 514 b represents an interesting science case for studying the habitability of planets on eccentric orbits. We advocate for additional spectroscopic follow-up to get more accurate and precise planetary parameters. Further follow-up is also needed to investigate the presence of additional planetary signals of less than 1 m s(-1).