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This paper continues previous work on the effects of turbulence on meanmotion resonances in extrasolar planetary systems. Turbulence is expected toarise in the disks that form planets, and these fluctuations act to compromiseresonant configurations. This paper extends previous work by considering howinteractions between the planets and possible damping effects imposed by thedisk affect the outcomes. These physical processes are studied using threeapproaches: numerical integrations of the 3-body problem with additionalforcing due to turbulence, model equations that reduce the problem tostochastically driven oscillators, and Fokker-Planck equations that describethe time evolution of an ensemble of systems. With this combined approach, weelucidate the physics of how turbulence can remove extrasolar planetary systemsfrom mean motion resonance. As expected, systems with sufficiently largedamping (dissipation) can maintain resonance, in spite of turbulent forcing. Inthe absence of strong damping, ensembles of these systems exhibit two regimesof behavior, where the fraction of the bound states decreases as a power-law oras an exponential. Both types of behavior can be understood through the modeldeveloped herein. For systems with weak interactions between planets, the modelreduces to a stochastic pendulum, and the fraction of bound states decreases asa power-law. For highly interactive systems, the dynamics are more complicatedand the fraction of bound states decreases exponentially. We show how planetaryinteractions lead to drift terms in the Fokker-Planck equation and account forthis exponential behavior. In addition to clarifying the physical processesinvolved, this paper strengthens the finding that turbulence implies that meanmotions resonances should be rare.

Mean Motion Resonances in Extrasolar Planetary Systems with Turbulence, Interactions, and Damping