An Analytic Criterion for Turbulent Disruption of Planetary Resonances

Journal Article · Wed Mar 01 04:00:00 EST 2017 · The Astronomical Journal (Online)

DOI:https://doi.org/10.3847/1538-3881/153/3/120· OSTI ID:22863122

Batygin, Konstantin ^[1]

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1. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 (United States)

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 α=10{sup −2}, only planet pairs with cumulative mass ratios smaller than (m{sub 1}+m{sub 2})/M≲10{sup −5}∼3M{sub ⊕}/M{sub ⊙} are susceptible to breaking resonance at semimajor axis of order a∼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.

• OSTI ID: 22863122
• Journal Information: The Astronomical Journal (Online), Journal Name: The Astronomical Journal (Online) Journal Issue: 3 Vol. 153; ISSN 1538-3881
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
CAPTURE
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
FLUCTUATIONS
MASS
PLANETS
PROBABILITY
PROTOPLANETS
RESONANCE
SATELLITES
SOLAR NEBULA
STARS
STOCHASTIC PROCESSES