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An Analytic Criterion for Turbulent Disruption of Planetary Resonances

Batygin, Konstantin and Adams, Fred C. (2017) An Analytic Criterion for Turbulent Disruption of Planetary Resonances. Astronomical Journal, 153 (3). Art. No. 120. ISSN 0004-6256. doi:10.3847/1538-3881/153/3/120.

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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(-2), only planet pairs with cumulative mass ratios smaller than (m_1 + m_2)/M ≾ 10^(-5) ~ 3M⊕/M⊙ 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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Batygin, Konstantin0000-0002-7094-7908
Adams, Fred C.0000-0002-8167-1767
Additional Information:© 2017 The American Astronomical Society. Received 2016 December 23; revised 2017 January 6; accepted 2017 January 16; published 2017 February 20. We would like to thank Juliette Becker, Tony Bloch, Wlad Lyra, and Chris Spalding for useful discussions, as well as the referee, whose insightful report led to a considerable improvement of the manuscript. K.B. acknowledges support from the NSF AAG program AST1517936, and from Caltech. F.C.A. acknowledges support from the NASA Exoplanets Research Program NNX16AB47G, and from the University of Michigan.
Group:Astronomy Department
Funding AgencyGrant Number
University of MichiganUNSPECIFIED
Subject Keywords:planetary systems – planets and satellites: dynamical evolution and stability – planets and satellites: formation
Issue or Number:3
Record Number:CaltechAUTHORS:20170224-093051768
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Official Citation:Konstantin Batygin and Fred C. Adams 2017 AJ 153 120
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74523
Deposited By: Tony Diaz
Deposited On:24 Feb 2017 17:58
Last Modified:11 Nov 2021 05:27

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