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Three body resonances in close orbiting planetary systems: tidal dissipation and orbital evolution

Published online by Cambridge University Press:  14 May 2014

John C. B. Papaloizou
John C. B. Papaloizou*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK e-mail: jcbp2@damtp.cam.ac.uk
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Abstract

We study the orbital evolution of a three-planet system with masses in the super-Earth regime resulting from the action of tides on the planets induced by the central star which cause orbital circularization. We consider systems either in or near to a three-body commensurability for which adjacent pairs of planets are in a first-order commensurability. We develop a simple analytic solution, derived from a time averaged set of equations, that describes the expansion of the system away from strict commensurability as a function of time, once a state where relevant resonant angles undergo small amplitude librations has been attained. We perform numerical simulations that show the attainment of such resonant states focusing on the Kepler 60 system. The results of the simulations confirm many of the scalings predicted by the appropriate analytic solution. We go on to indicate how the results can be applied to put constraints on the amount of tidal dissipation that has occurred in the system. For example, if the system has been in a librating state since its formation, we find that its present period ratios imply an upper limit on the time average of 1/Q′, With Q′ being the tidal dissipation parameter. On the other hand if a librating state has not been attained, a lower upper bound applies.

Keywords

planet formationplanetary systemsresonancestidal interactions
Type
Research Article
Information
International Journal of Astrobiology , Volume 14 , Issue 2: SPECIAL ISSUE: EXOPLANET , April 2015 , pp. 291 - 304
Copyright
Copyright © Cambridge University Press 2014 

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