Linghong Lin, Beibei Liu, Fei Dai, Bin Liu, Jiwei Xie, Man Hoi Lee, Haifeng Yang, Shangfei Liu, Ping Chen

We present a theoretical framework for the resonance capture and stability of two-planet systems in turbulent disks. By incorporating stochastic forcing (parameterized by $κ$) alongside laminar angular momentum and eccentricity damping timescales ($τ_{\rm m}, τ_{e}$), 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 $κ$-$τ_{\rm m}/τ_{e}$ 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 $τ_{\rm m}/τ_{e}$ to drop below a critical limit due to excessive eccentricity excitation. We demonstrate that turbulent diffusion lowers this limit, demanding stronger damping (larger $τ_{\rm m}/τ_{e}$) for stability. Thus, greater turbulence promotes escape, and sufficiently strong diffusion precludes resonance retention irrespective of eccentricity damping.