On the orbital evolution of a pair of giant planets in mean motion resonance

TL;DR

This study uses numerical simulations to explore how pairs of giant planets in protoplanetary discs can form and maintain mean motion resonances, revealing the influence of disc mass and planet size on their orbital evolution.

Contribution

It provides new insights into the formation and evolution of resonant giant planet pairs through detailed 2D and 3D simulations considering various disc masses and planetary parameters.

Findings

Low-mass discs can produce inward migrating 2:1 resonant pairs.

Larger mass planets can reach 3:1 resonance, matching observations.

Passing through 2:1 resonance often leads to unstable configurations and scattering.

Abstract

Pairs of extrasolar giant planets in a mean motion commensurability are common with 2:1 resonance occurring most frequently. Disc-planet interaction provides a mechanism for their origin. However, the time scale on which this could operate in particular cases is unclear. We perform 2D and 3D numerical simulations of pairs of giant planets in a protoplanetary disc as they form and maintain a mean motion commensurability. We consider systems with current parameters similar to those of HD 155358, 24 Sextantis and HD 60532, and disc models of varying mass, decreasing mass corresponding to increasing age. For the lowest mass discs, systems with planets in the Jovian mass range migrate inwards maintaining a 2:1 commensurability. Systems with the inner planet currently at around 1 au from the central star could have originated at a few au and migrated inwards on a time scale comparable to protoplanetary disc lifetimes. Systems of larger mass planets such as HD 60532 attain 3:1 resonance as observed. For a given mass accretion rate, results are insensitive to the disc model for the range of viscosity prescriptions adopted, there being good agreement between 2D and 3D simulations. However, in a higher mass disc a pair of Jovian mass planets passes through 2:1 resonance before attaining a temporary phase lasting a few thousand orbits in an unstable 5:3 resonance prior to undergoing a scattering. Thus finding systems in this commensurability is unlikely.