2005A&A...436..363D

We use the model for the migration of planets introduced in Del Popolo et al. (2003MNRAS.339..556D) to calculate the observed mass and semimajor axis distribution of extra-solar planets. The assumption that the surface density in planetesimals is proportional to that of gas is relaxed, and in order to describe disc evolution we use a method which, using a series of simplifying assumptions, is able to simultaneously follow the evolution of gas and solid particles for up to 10⁷yr. The distribution of planetesimals obtained after 10⁷yr is used to study the migration rate of a giant planet through the model described in the present paper. The disk and migration models are used to calculate the distribution of planets as function of mass and semimajor axis. The results show that the model can give a reasonable prediction of planets' semi-major axes and mass distribution. In particular there is a pile-up of planets at a ≃0.05AU, a minimum near 0.3AU, indicating a paucity of planets at that distance, and a rise for semi-major axes larger than 0.3AU, out to 3AU. The semi-major axis distribution shows that the more massive planets (typically, masses larger than 4M_J) form preferentially in the outer regions and do not migrate much. Intermediate-mass objects migrate more easily whatever the distance at which they form, and that the lighter planets (masses from sub-Saturnian to Jovian) migrate easily.