Highly inclined and eccentric massive planets

II. Planet-planet interactions during the disc phase

¹ naXys, Department of Mathematics, University of Namur, 8 Rempart de la Vierge, 5000 Namur, Belgium
e-mail: sotiris.sotiriadis@unamur.be
² Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, 22100 Lund, Sweden
³ Laboratoire Lagrange, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Boulevard de l’Observatoire, CS34220, 06304 Nice Cedex 4, France
⁴ Institut Universitaire de France, 103 Boulevard Saint Michel, 75005 Paris, France

Received: 9 March 2016
Accepted: 26 November 2016

Abstract

Context. Observational evidence indicates that the orbits of extrasolar planets are more various than the circular and coplanar ones of the solar system. Planet-planet interactions during migration in the protoplanetary disc have been invoked to explain the formation of these eccentric and inclined orbits. However, our companion paper (Paper I) on the planet-disc interactions of highly inclined and eccentric massive planets has shown that the damping induced by the disc is significant for a massive planet, leading the planet back to the midplane with its eccentricity possibly increasing over time.

Aims. We aim to investigate the influence of the eccentricity and inclination damping due to planet-disc interactions on the final configurations of the systems, generalizing previous studies on the combined action of the gas disc and planet-planet scattering during the disc phase.

Methods. Instead of the simplistic K-prescription, our N-body simulations adopt the damping formulae for eccentricity and inclination provided by the hydrodynamical simulations of our companion paper. We follow the orbital evolution of 11 000 numerical experiments of three giant planets in the late stage of the gas disc, exploring different initial configurations, planetary mass ratios and disc masses.

Results. The dynamical evolutions of the planetary systems are studied along the simulations, with a particular emphasis on the resonance captures and inclination-growth mechanisms. Most of the systems are found with small inclinations (≤ 10°) at the dispersal of the disc. Even though many systems enter an inclination-type resonance during the migration, the disc usually damps the inclinations on a short timescale. Although the majority of the multiple systems in our simulations are quasi-coplanar, ~5% of them end up with high mutual inclinations (≥ 10°). Half of these highly mutually inclined systems result from two- or three-body mean-motion resonance captures, the other half being produced by orbital instability and/or planet-planet scattering. When considering the long-term evolution over 100 Myr, destabilization of the resonant systems is common, and the percentage of highly mutually inclined systems still evolving in resonance drops to 30%. Finally, the parameters of the final system configurations are in very good agreement with the semi-major axis and eccentricity distributions in the observations, showing that planet-planet interactions during the disc phase could have played an important role in sculpting planetary systems.