On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets

TL;DR

This paper investigates how dissipative forces influence the orbital evolution of two-planet systems, revealing complex migration behaviors, bifurcations, and potential stationary states depending on the friction law and system parameters.

Contribution

It introduces a detailed analysis of planetary migration under various friction laws within the three-body problem framework, highlighting bifurcations and stable configurations.

Findings

Migration paths depend on the friction law and system parameters.

Bifurcations lead to new stable orbit families at critical points.

Stationary solutions with fixed eccentricities and semimajor axes are possible.

Abstract

We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different laws of friction are considered. The topology of the phase space is essential in understanding the evolution of the system. The topology is determined by the families of stable and unstable periodic orbits, both symmetric and non symmetric. It is along the stable families, or close to them, that the planets migrate when dissipative forces act. At the critical points where the stability along the family changes, there is a bifurcation of a new family of stable periodic orbits and the migration process changes route and follows the new stable family up to large eccentricities or to a chaotic region. We consider both resonant and non resonant planetary systems. The 2/1, 3/1 and 3/2 resonances are studied. The migration to larger or smaller eccentricities depends on the particular law of friction. Also, in some cases the semimajor axes increase and in other cases they are stabilized. For particular laws of friction and for special values of the parameters of the frictional forces, it is possible to have partially stationary solutions, where the eccentricities and the semimajor axes are fixed.