Study of protoplanet migration processes in sub-Keplerian conditions through SPH hydrodynamic simulations

Abstract

The interest on exo-planetary systems has been growing for the last years, due to the improvements on the observational techniques used to detect extra-solar planets. According to current theories, protoplanets-disc interaction plays a major role in determining the final masses and orbits of the newly born planets, through the protoplanets migration processes. The formation of giant planets (Jupiter like) in particular should be contextual to their quick migration on a time-scale in the order of 10^5 years. Such a time-scale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have been analysed recently using N-body and/or fluid-dynamics simulations or a mixing of them. An initial Keplerian distribution of the gas particles velocities is a common assumption. But consistent deviations from a perfect Keplerian kinematics, can occur. Both pressure forces and dissipative effects due to shock occurrence in accretion processes, produce a general sub-Keplerian kinematics, even in non viscous fluid dynamics. In this work, inviscid 2D simulations are performed, using the SPH method, to study the migration of one or two protoplanets, to evaluate the effectiveness of the accretion disc in the protoplanet(s) dragging towards the central star, as a function of the mass of the planet(s) and of the disc tangential kinematics. Both sub-Keplerian and Keplerian kinematic conditions are considered. The aim is to develop a parameter study of protoplanetary migration if moderate and consistent deviations from Keplerian kinematics occur.

For single planet systems, migration times of a few orbital periods for Earth-like planets in sub-Keplerian conditions are obtained, while for Jupiter-like planets estimates suggest that about 10^4 orbital periods occur until the orbital size is reduced to about a half of its initial value.

For two-planets systems, results show a quite general radial migration of the two protoplanets towards the inner radial zones of the disc. In sub-Keplerian disc kinematics the time-scale of the whole radial transport is mainly ruled by planet-disc interaction. Gravitational radial oscillations (GRO) of each component of the two-planets system are also observed as expected in systems with two Jovian planets. In the case of one internal Jovian planet and an external Terrestrial planet, a slingshot effect may occur.