Title: An Analytic Criterion for Turbulent Disruption of Planetary Resonances,
Abstract: Mean motion commensurabilities in multi-planet systems are an expected
outcome of protoplanetary disk-driven migration, and their relative dearth in
the observational data presents an important challenge to current models of
planet formation and dynamical evolution. One natural mechanism that can lead
to the dissolution of commensurabilities is stochastic orbital forcing, induced
by turbulent density fluctuations within the nebula. While this process is
qualitatively promising, the conditions under which mean motion resonances can
be broken are not well understood. In this work, we derive a simple analytic
criterion that elucidates the relationship among the physical parameters of the
system, and find the conditions necessary to drive planets out of resonance.
Subsequently, we confirm our findings with numerical integrations carried out
in the perturbative regime, as well as direct N-body simulations. Our
calculations suggest that turbulent resonance disruption depends most
sensitively on the planet-star mass ratio. Specifically, for a disk with
properties comparable to the early solar nebula with $\alpha=0.01$, only planet
pairs with cumulative mass ratios smaller than
$(m_1+m_2)/M\lesssim10^{-5}\sim3M_{\oplus}/M_{\odot}$ are susceptible to
breaking resonance at semi-major axis of order $a\sim0.1\,$AU. Although
turbulence can sometimes compromise resonant pairs, an additional mechanism
(such as suppression of resonance capture probability through disk
eccentricity) is required to adequately explain the largely non-resonant
orbital architectures of extrasolar planetary systems.