Capture and Stability of Resonant Planet Pairs in Turbulent Disk

TL;DR

This paper develops a theoretical framework to understand how turbulence affects the capture and stability of resonant planet pairs in disks, revealing turbulence as a universal destabilizer that promotes escape from resonance.

Contribution

It introduces an analytical criterion for resonance stability in turbulent disks and validates it with N-body simulations, highlighting turbulence's role in destabilizing resonant pairs.

Findings

Turbulence can cause resonance disruption either directly or via temporary capture and escape.

Turbulence lowers the eccentricity damping threshold needed for resonance stability.

Stronger turbulence generally prevents resonance retention regardless of damping strength.

Abstract

We present a theoretical framework for the resonance capture and stability of two-planet systems in turbulent disks. By incorporating stochastic forcing (parameterized by $\kappa$) alongside laminar angular momentum and eccentricity damping timescales ($\tau_{\rm m}, \tau_{e}$), we derive an analytical criterion for the general $j:j-1$ mean motion resonances, and validate it through N-body simulations. The outcome is mapped in $\kappa$-$\tau_{\rm m}/\tau_{e}$ parameter space, revealing two distinct regimes: resonance trapping and turbulence-induced disruption -- which occurs either directly cross or via temporary capture followed by escape through turbulent diffusion. Crucially, our analysis identifies turbulence as a universal destabilizer. It amplifies the intrinsic overstability mechanism: In laminar disks, escape requires $\tau_{\rm m}/\tau_{e}$ to drop below a critical limit due to excessive eccentricity excitation. We demonstrate that turbulent diffusion lowers this limit, demanding stronger damping (larger $\tau_{\rm m}/\tau_{e}$) for stability. Thus, greater turbulence promotes escape, and sufficiently strong diffusion precludes resonance retention irrespective of eccentricity damping.