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 = 10 ^ { -2 } , only planet pairs with cumulative mass ratios smaller than ( m _ { 1 } + m _ { 2 } ) / M \lesssim 10 ^ { -5 } \sim 3 M _ { \oplus } / M _ { \odot } are susceptible to breaking resonance at semi-major axis of order a \sim 0.1 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 .