Influence of an inner disc on the orbital evolution of massive planets migrating in resonance

¹ Institut für Astronomie & Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany e-mail: crida@tat.physik.uni-tuebingen.de
² Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
³ Department of Astronomy, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary

Received: 20 December 2007
Accepted: 13 February 2008

Abstract

Context. The formation of resonant planet pairs in exoplanetary systems involves planetary migration inside the protoplanetary disc. After a resonant capture, subsequent migration leads to a large increase in planetary eccentricities, if no damping mechanism is applied. This has led to the conclusion that the migration of resonant planetary systems cannot take place across large radial distances, but must be terminated rapidly by disc dissipation.

Aims. We investigate if the presence of an inner disc could supply eccentricity damping to the inner planet, and if this effect could explain observed eccentricities in some planetary systems.

Methods. We compute hydrodynamic simulations of giant planets, in orbits of a given eccentricity about an inner gas disc, and measure the effect of the gas disc on the planetary orbital parameters. We perform detailed long-term calculations of the GJ 876 system. We complete N-body simulations, which include artificial forces on the planets that recreate the effect of the inner and outer discs.

Results. We find that we cannot neglect the influence of the inner disc, and that the disc could explain the observed eccentricities. In particular, we reproduce the orbital parameters of a few systems engaged in 2:1 mean motion resonances: GJ 876, HD 73 526, HD 82 943, and HD 128 311. Analytically, we derive the effect that the inner disc should have on the inner planet to reach a specific orbital configuration, for any given damping effect of the outer disc on the outer planet.

Conclusions. We conclude that an inner disc, even though difficult to model properly in hydrodynamical simulations, should be taken into account because of its damping effect on the eccentricity of the inner planet. By including this effect, we can explain quite naturally the observed orbital elements of the pairs of known resonant exoplanets.