The detection and characterisation of 54 massive companions with the SOPHIE spectrograph -- 7 new brown dwarfs and constraints on the BD desert

Context. Brown-dwarfs (BD) are substellar objects with masses intermediate between planets and stars within about 13-80 MJ. While isolated brown-dwarfs are most likely produced by gravitational collapse in molecular clouds down to masses of a few MJ, a nonnegligible fraction of low-mass companions might be formed through the planet formation channel in protoplanetary disks. The upper mass limit of objects formed within disks is still observationnally unknown, the main reason being the strong dearth of BD companions at orbital periods shorter than 10 years, a.k.a. the brown-dwarf desert. Aims. We aim at determining the best statistics of secondary companions within the 10-100 MJup range within ∼10 au from the primary star, while minimising observational bias. This can help determining the mass limit separating planet-formed from star-formed browndwarfs. Moreover, the exact shape of the BD desert in a mass-period space is still underdetermined, and can strongly constrain the companion-star interactions mechanisms at work in close binary systems at small mass ratio. Methods. We made an extensive use of the radial velocity (RV) surveys of FGK stars below 60 pc distance to the Sun and in the northern hemisphere performed with the SOPHIE spectrograph at Observatoire de Haute-Provence. We derived the Keplerian solutions of the RV variations of 54 sources. Public astrometric data of the Hipparcos and Gaia missions allowed deriving direct astrometric solution of orbital motion and constraining the mass of the companion for most sources. We introduce GASTON, a new method to derive inclination combining RVs Keplerian and astrometric excess noise from Gaia DR1. Results. We report the discovery of 12 new BD candidates. For 5 of them, additional astrometric data led to revise their mass in the M-dwarf regime. Among the 7 remaining objects, 4 are confirmed BD companions, and 3 others are likely also in this mass regime. Moreover, we report the detection of 42 objects in the M-dwarf mass regime 90 MJ–0.52 M . The resulting M sin i-P distribution of BD candidates shows a clear drop in the detection rate below 80-day orbital period. Above that limit, the BD desert reveals rather wet, with a uniform distribution of the M sin i. We derive a minimum BD-detection frequency around Solar-like stars of 2.0±0.5%.