5 Discussion

Although the assumption of random orbital inclinations seems reasonable, it is at variance with the conclusion of Han et al. (2001) that most of the systems containing exoplanet candidates are seen nearly pole-on. These authors reached this conclusion by trying to extract the astrometric orbit, hence the orbital inclination, from the Hipparcos IAD. Halbwachs et al. (2000) had already cautioned that this approach is doomed to fail for systems with apparent separations on the sky that are below the Hipparcos sensitivity (i.e. 1 mas). In those cases, the solution retrieved from the fit of the IAD residuals is spurious, since the true angular semi-major axis a is simply too small to be seen by Hipparcos. Since Halbwachs et al. (2000) have shown that a actually follows a Rayleigh probability distribution, the fit of the IAD residuals will yield a solution larger than the true value, in fact of the order of the residuals. But since $a \sin i$ is constrained by the spectroscopic orbital elements, the too-large astrometric a value will force i to be close to 0 to match the spectroscopic value of the product $a \sin i$, as convincingly shown by Pourbaix (2001). Hence, this approach gives the impression that all orbits are seen nearly face-on. As an illustrative example, Pourbaix & Arenou (2001) have shown that such an approach leads to a stellar mass for the companion of HD209458 that, on another hand, has been proven to be a 0.69$M_{\rm J}$ planet by the photometric observation of the planet transit in front of the star (Charbonneau et al. 2000).

The Han et al. (2001) result is moreover statistically very unlikely if the orbital planes are oriented at random in space (Pourbaix & Arenou 2001). Han et al. (2001) have tried to justify this unlikely statistical occurrence by invoking biases against high-amplitude orbits in the selection process of the radial-velocity-monitoring samples. To the contrary, the planet-search surveys were specifically devised to avoid such biases, as they aim at finding not only giant planets but also brown dwarfs so as to constrain the substellar secondary mass function of solar-type stars. Furthermore, the Han et al. (2001) argument is totally invalid in the case of volume-limited, statistically well-defined samples like that of the CORALIE planet-search programme in the southern hemisphere (Udry et al. 2000a). This sample has been specifically designed to detect companions of solar-type stars all the way from q=M₂/M₁ = 1 down to $q\leq 0.001$.