2001A&A...379..992J

The present study derives the distribution of secondary masses M₂ for the 67 exoplanets and very low-mass brown-dwarf companions of solar-type stars, known as of April 4, 2001. This distribution is related to the distribution of M₂ sin i through an integral equation of Abel's type. Although a formal solution exists for this equation, it is known to be ill-conditioned, and is thus very sensitive to the statistical noise present in the input M₂ sin i distribution. To overcome this difficulty, we present two robust, independent approaches: (i) the formal solution of the integral equation is numerically computed after performing an optimal smoothing of the input distribution and (ii) the Lucy-Richardson algorithm is used to invert the integral equation. Both approaches give consistent results. The resulting statistical distribution of exoplanet true masses reveals that there is no reason to ascribe the transition between giant planets and brown dwarfs to the threshold mass for deuterium ignition (about 13.6M_J). The M₂ distribution shows instead that most of the objects have M₂≤10M_J, but there is a small tail with a few heavier candidates around 15M_J.