The frequency of brown-dwarf companions in close orbit around Sun-like stars is low compared to the frequency of planetary and stellar companions. There is presently no comprehensive explanation of this lack of brown-dwarf companions.

By combining the orbital solutions obtained from stellar radial-velocity curves and Hipparcos astrometric measurements, we attempt to determine the orbit inclinations and therefore the masses of the orbiting companions. By determining the masses of potential brown-dwarf companions, we improve our knowledge of the companion mass-function.

The radial-velocity solutions revealing potential brown-dwarf companions are obtained for stars from the CORALIE and HARPS planet-search surveys or from the literature. The best Keplerian fit to our radial-velocity measurements is found using the Levenberg-Marquardt method. The spectroscopic elements of the radial-velocity solution constrain the fit to the intermediate astrometric data of the new Hipparcos reduction. The astrometric solution and the orbit inclination are found using non-linear χ²-minimisation on a two-parameter search grid. The statistical confidence of the adopted orbital solution is evaluated based on the distribution-free permutation test.

The discovery of nine new brown-dwarf candidates orbiting stars in the CORALIE and HARPS radial-velocity surveys is reported. New CORALIE radial velocities yielding accurate orbits of six previously-known hosts of potential brown-dwarf companions are presented. Including the literature targets, 33 hosts of potential brown-dwarf companions are examined. Employing innovative methods, we use the new reduction of the Hipparcos data to fully characterise the astrometric orbits of six objects, revealing M-dwarf companions of masses between 90 M_J and 0.52 M_⊙. In addition, the masses of two companions can be restricted to the stellar domain. The companion to HD�137510 is found to be a brown dwarf. At 95% confidence, the companion of HD�190228 is also a brown dwarf. Twenty-three companions remain brown-dwarf candidates. On the basis of the CORALIE planet-search sample, we obtain an upper limit of 0.6% for the frequency of brown-dwarf companions around Sun-like stars. We find that the companion-mass distribution function increases toward the lower end of the brown-dwarf mass range, suggesting that we detect the high-mass tail of the planetary distribution.

Our findings agree with the results of previous similar studies and confirm the pronounced paucity of brown-dwarf companions around Sun-like stars. They are affected by the Hipparcos astrometric precision and mission duration, which limits the minimum detectable companion mass, and some of the remaining candidates are probably brown-dwarf companions.