Extrasolar planet population synthesis III. Formation of planets around stars of different masses

Aims. We extend the models presented by Mordasini and collaborators to the formation of planets orbiting stars of different masses. We discuss the properties of the resulting synthetic planet population in terms of mass, orbit, and metallicity distributions. Methods. The population synthesis calculations that we use are based on the Bernese planet formation model developed by Alibert and collaborators, which self-consistently takes into account planetary growth and migration in an evolving proto-planetary disk. Using this model, we generate synthetic populations of planets by following their growth in a large number of proto-planetary disks, whose properties (mass and lifetime) are selected in a Monte Carlo fashion using probability distributions derived from observations. Results. We show that the scaling of the proto-planetary disk mass with the mass of the central star has a direct and large influence on the properties of the resulting planet population. In particular, the observed paucity of high mass planets orbiting 0.5 M-circle dot stars can be directly explained as resulting from a only slightly steeper than linear scaling. The observed lack of short period planets orbiting 2.0 M-circle dot stars can also be attributed to this scaling but only if associated with a decrease in the mean disk lifetime for stars more massive than 1.5 M-circle dot. Finally, we show that the distribution of minimum mass and semi-major axis of our synthetic planets are statistically comparable with observations.