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Published August 11, 2015 | Published + Submitted
Journal Article Open

Capture of planets into mean-motion resonances and the origins of extrasolar orbital architectures


The early stages of dynamical evolution of planetary systems are often shaped by dissipative processes that drive orbital migration. In multi-planet systems, convergent amassing of orbits inevitably leads to encounters with rational period ratios, which may result in establishment of mean-motion resonances. The success or failure of resonant capture yields exceedingly different subsequent evolutions, and thus plays a central role in determining the ensuing orbital architecture of planetary systems. In this work, we employ an integrable Hamiltonian formalism for first order planetary resonances that allows both secondary bodies to have finite masses and eccentricities, and construct a comprehensive theory for resonant capture. Particularly, we derive conditions under which orbital evolution lies within the adiabatic regime, and provide a generalized criterion for guaranteed resonant locking as well as a procedure for calculating capture probabilities when capture is not certain. Subsequently, we utilize the developed analytical model to examine the evolution of Jupiter and Saturn within the protosolar nebula, and investigate the origins of the dominantly non-resonant orbital distribution of sub-Jovian extrasolar planets. Our calculations show that the commonly observed extrasolar orbital structure can be understood if planet pairs encounter mean-motion commensurabilities on slightly eccentric (e ~ 0.02) orbits. Accordingly, we speculate that resonant capture among low-mass planets is typically rendered unsuccessful due to subtle axial asymmetries inherent to the global structure of protoplanetary discs.

Additional Information

© 2015 The Author. Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2015 May 7. Received 2015 May 6. In original form 2015 April 3. First published online June 13, 2015. I am thankful to Katherine Deck, Chris Spalding, Peter Goldreich, Greg Laughlin, Heather Knutson, Geoff Blake, Renu Malhotra and Mike Brown for inspirational conversations, as well as to Alessandro Morbidelli, whose careful review of the manuscript and insightful suggestions led to a substantial improvement of the paper.

Attached Files

Submitted - 1505.01778v1.pdf

Published - MNRAS-2015-Batygin-2589-609.pdf


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August 22, 2023
August 22, 2023