Evolution of planetesimal discs and planets migration

In this paper, we further develop the model for the migration of planets introduced in Del Popolo et al. (9) and extended to time-dependent planetesimal accretion disks in Del Popolo & Ekcsi (10). More precisely, the assumption of Del Popolo & Ekcsi (10) that the surface density in planetesimals is proportional to that of gas is released. Indeed, the evolution of the radial distribution of solids is governed by many processes: gas-solid coupling, coagulation, sedimentation, evaporation/condensation, so that the distribution of planetesimals emerging from a turbulent disk does not necessarily reflect that of gas (e.g., Stepinski & Valageas 39). In order to describe this evolution we use a method developed in Stepinski & Valageas (40) which, using a series of simplifying assumptions, is able to simultaneously follow the evolution of gas and solid particles for up to 10yr. 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 10yr is used to study the migration rate of a giant planet through the migration model introduced in (9). This allows us to investigate the dependence of the migration rate on the disk mass, on its time evolution and on the value of the dimensionless viscosity parameter α. We find that 2 A. Del Popolo, S. Yeşilyurt & N. Ercan in the case of disks having a total mass of 10 − 10M⊙, and 10 −4 < α < 10, planets can migrate inward over a large distance while if Md < 10 M⊙ the planets remain almost at their initial position for α > 10 and only in the case α < 10 the planets move to a minimum value of orbital radius of ≃ 2AU. Moreover, the observed distribution of planets in the period range 0-20 days can be easily obtained from our model. Therefore, dynamical friction between planets and the planetesimal disk provides a good mechanism to explain the properties of observed extra-solar giant planets.