  This paper continues previous work on the effects of turbulence on mean
motion resonances in extrasolar planetary systems. Turbulence is expected to
arise in the disks that form planets, and these fluctuations act to compromise
resonant configurations. This paper extends previous work by considering how
interactions between the planets and possible damping effects imposed by the
disk affect the outcomes. These physical processes are studied using three
approaches: numerical integrations of the 3-body problem with additional
forcing due to turbulence, model equations that reduce the problem to
stochastically driven oscillators, and Fokker-Planck equations that describe
the time evolution of an ensemble of systems. With this combined approach, we
elucidate the physics of how turbulence can remove extrasolar planetary systems
from mean motion resonance. As expected, systems with sufficiently large
damping (dissipation) can maintain resonance, in spite of turbulent forcing. In
the absence of strong damping, ensembles of these systems exhibit two regimes
of behavior, where the fraction of the bound states decreases as a power-law or
as an exponential. Both types of behavior can be understood through the model
developed herein. For systems with weak interactions between planets, the model
reduces to a stochastic pendulum, and the fraction of bound states decreases as
a power-law. For highly interactive systems, the dynamics are more complicated
and the fraction of bound states decreases exponentially. We show how planetary
interactions lead to drift terms in the Fokker-Planck equation and account for
this exponential behavior. In addition to clarifying the physical processes
involved, this paper strengthens the finding that turbulence implies that mean
motions resonances should be rare.
