Planetary mass function and planetary systems

With planets orbiting stars, a planetary mass function should not be seen as a low-mass extension of the stellar mass function, but a proper formalism needs to take care of the fact that the statistical properties of planet populations are linked to the properties of their respective host stars. This can be accounted for by describing planet populations by means of a differential planetary mass-radius-orbit function, which together with the fraction of stars with given properties that are orbited by planets and the stellar mass function allows the derivation of all statistics for any considered sample. These fundamental functions provide a framework for comparing statistics that result from different observing techniques and campaigns which all have their very specific selection procedures and detection efficiencies. Moreover, recent results both from gravitational microlensing campaigns and radial-velocity surveys of stars indicate that planets tend to cluster in systems rather than being the lonely child of their respective parent star. While planetary multiplicity in an observed system becomes obvious with the detection of several planets, its quantitative assessment however comes with the challenge to exclude the presence of further planets. Current exoplanet samples begin to give us first hints at the population statistics, whereas pictures of planet parameter space in its full complexity call for samples that are 2-4 orders of magnitude larger. In order to derive meaningful statistics, however, planet detection campaigns need to be designed in such a way that well-defined fully deterministic target selection, monitoring and detection criteria are applied. The probabilistic nature of gravitational microlensing makes this technique an illustrative example of all the encountered challenges and uncertainties.