Capture and Stability of Resonant Planet Pairs in Turbulent Disk

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.