Capture and Escape of Planetary Mean-motion Resonances in Turbulent Discs

TL;DR

This study investigates how turbulence in protoplanetary discs affects the stability of mean-motion resonances during planetary migration, revealing turbulence's role in resonance escape and implications for observed planetary system configurations.

Contribution

It demonstrates that realistic disc turbulence enhances resonance overstability, leading to resonance escape and influencing the final orbital configurations of planet pairs.

Findings

Turbulence increases resonance overstability and escape.

Stable 3:2 resonance is insensitive to viscosity.

Turbulence broadens the parameter space for resonance escape.

Abstract

Mean-motion resonances (MMRs) form through convergent disc migration of planet pairs, which may be disrupted by dynamical instabilities after protoplanetary disc (PPD) dispersal. This scenario is supported by recent analysis of TESS data showing that neighboring planet pairs in younger planetary systems are closer to resonance. To study stability of MMRs during migration, we perform hydrodynamical simulations of migrating planet pairs in PPDs, comparing the effect of laminar viscosity and realistic turbulence. We find stable 3:2 resonance capture for terrestrial planet pairs migrating in a moderately massive PPD, insensitive to a range of laminar viscosity (alpha = 0.001 to 0.1). However, realistic turbulence enhances overstability by sustaining higher equilibrium eccentricities and a positive growth rate in libration amplitude, ultimately leading to resonance escape. The equilibrium eccentricity growth rates decrease as planets migrate into tighter and more stable 4:3 and 5:4 MMRs. Our results suggest that active disc turbulence broadens the parameter space for overstability, causing planet pairs to end up in closer-in orbital separations. Libration within MMR typically lead to deviation from exact period ratio |Delta| \sim 0.5%, which alone is insufficient to produce the typical dispersion of |Delta| \sim 1 to 3% in TESS data, suggesting that post migration dynamical processes are needed to further amplify the offset.