Capture and Stability of Resonant Planet Pairs in Turbulent Disk

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 (${\tau }_{\mathrm{m}},{\tau }_e$), 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 $\kappa$-${\tau }_{\mathrm{m}}/{\tau }_e$ 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 ${\tau }_{\mathrm{m}}/{\tau }_e$ to drop below a critical limit due to excessive eccentricity excitation. We demonstrate that turbulent diffusion lowers this limit, demanding stronger damping (larger ${\tau }_{\mathrm{m}}/{\tau }_e$) for stability. Thus, greater turbulence promotes escape, and sufficiently strong diffusion precludes resonance retention irrespective of eccentricity damping.

10 pages, 9 figures, accepted by A&A