A statistical analysis of the extrasolar planets and the low-mass secondaries

We show that the astrometric Hipparcos data of the stars hosting planet candidates are not accurate enough to yield statistically significant orbits. Therefore, the recent suggestion, based on the analysis of the Hipparcos data, that the orbits of the sample of planet candidates are not randomly oriented in space, is not supported by the data. Assuming random orientation, we derive the mass distribution of the planet candidates and shows that it is flat in log M, up to about 10 M-Jup. Furthermore, the mass distribution of the planet candidates is well separated from the mass distribution of the low-mass companions by the 'brown-dwarf desert'. This indicates that we have here two distinct populations, one which we identify as the giant planets and the other as stellar secondaries. We compare the period and eccentricity distributions of the two populations and find them surprisingly similar. The period distributions between 10 and 1650 days are flat in log period, indicating a scale-free formation mechanism in both populations. We further show that the eccentricity distributions are similar - both have a density distribution peak at about 0.2-0.4, with some small differences on both ends of the eccentricity range. We present a toy model to mimic both distributions. The toy model is composed of Gaussian radial and tangential velocity scatters added to a sample of circular Keplerian companions. A scatter of a dissipative nature can mimic the distribution of the eccentricity of the planets, while scatter of a more chaotic nature could mimic the secondary eccentricity distribution. We found a significant paucity of massive giant planets with short orbital periods. The low-frequency of planets is noticeable for masses larger than about 1 M-Jup and periods shorter than 30 days. We point out how, in principle, one can account for this paucity.