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

Context. The formation of resonant pairs of planets in exoplanetary systems involves planetary migration in the protoplanetary disc. After a resonant capture, the subsequent migration in this configuration leads to a large increase of planetary eccentricities if no damping mechanism is applied. This has led to the conclusion that the migration of resonant planetary systems cannot occur over large radial distances and has to be terminated sufficiently rapidly through disc dissipation. Aims. In this study, we investigate whether the presence of an inner disc might supply an eccentricity damping of the inner planet, and if this effect could explain the observed eccentricities in some systems. Methods. To investigate the influence of an inner disc, we first compute hydrodynamic simulations of giant planets orbiting with a given eccentricity around an inner gas disc, and measure the effect of the latter on the planetary orbital parameters. We then perform detailed long term calculations of the GJ 876 system. We also run N-body simulations with artificial forces on the planets mimicking the effects of the inner and outer discs. Results. We find that the influence of the inner disc can not be neglected, and that it might be responsible for the observed eccentricities. In particular, we reproduce quite well 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. Finally, we derive analytically the effect that the inner disc should have on the inner planet to reach a specific orbital configuration with a 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 hydro-dynamical 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.