Evolution of planetesimal discs and planetary migration

Abstract

In this paper, we further develop the model for the migration of planets introduced by Del Popolo, Gambera & Ercan and extended to time-dependent planetesimal accretion discs by Del Popolo & Eksi. More precisely, the assumption of Del Popolo & Eksi that the surface density in planetesimals is proportional to that of the gas was released. Indeed, the evolution of the radial distribution of solids is governed by many processes: gas-solid coupling, co- agulation, sedimentation, evaporation/condensation, so that the distribution of planetesimals emerging from a turbulent disc does not necessarily reflect that of the gas. In order to describe this evolution we use a method developed by Stepinski & Valageas, which, using a series of simplifying assumptions, is able to simultaneously follow the evolution of gas and solid particles for up to 10 7 yr. This model is based on the premise that the transformation of solids from dust to planetesimals occurs through hierarchical coagulation. Then, the distribution of planetesimals obtained after 10 7 yr is used to study the migration rate of a giant planet through the migration model introduced by Del Popolo, Gambera & Ercan. This allows us to investigate the dependence of the migration rate on the disc mass, on its time evolution and on the value of the dimensionless viscosity parameter α. We find that in the case of discs having a total mass of 10 −3 -10 −1 M� , and 10 −4 10 −3 and only in the case where α< 10 −3 do the planets move to a minimum value of orbital radius of �2 au. Moreover, the observed distribution of planets in the period range 0-20 d can be easily obtained from our model. Therefore, dynamical friction between planets and the plan- etesimal disc provides a good mechanism to explain the properties of observed extrasolar giant planets.