Exploring the brown dwarf desert with Hipparcos

The orbital elements of 11 spectroscopic binaries with brown dwarf candidat es (M-2 sin i between 0.01 and 0.08 M-circle dot) are combined with the Hip parcos observations in order to derive astrometric orbits. Estimations of t he masses of the secondary components are thus calculated. It appears that 5 secondary masses are more than 2 sigma(M2) above the limit of 0.08 M-circ le dot and are therefore not brown dwarfs. 2 other stars are still discarde d at the 1 sigma(M2) level, 1 brown dwarf is accepted with a low confidence , and we are finally left with 3 viable candidates which must be studied by other means. A statistical approach is developed, based on the relation between the semi -major axes of the photocentric orbit, a(0), their errors, sigma(a0), and t he frequency distribution of the mass ratios, q. It is investigated whether the set of values of a(0) and sigma(a0) obtained for the sample is compati ble with different frequency distributions of q. It is concluded that a min imum actually exists for M-2 between about 0.01 and 0.1 M-circle dot for co mpanions of solar-type stars. This feature could correspond to the transiti on between giant planets and stellar companions. Due to the relatively larg e frequency of single brown dwarfs found recently in open clusters, it is c oncluded that the distribution of the masses of the secondary components in binary systems does not correspond to the IMF: at least for masses below t he hydrogen-ignition limit.