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Conditions for the occurrence of mean-motion resonances in a low mass planetary system

Published online by Cambridge University Press:  19 April 2010

K. Goździewski ,
A. Niedzielski ,
J. Schneider ,
J. C.B. Papaloizou  and
E. Szuszkiewicz
J. C.B. Papaloizou
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
E. Szuszkiewicz
Affiliation:
CASA* and Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
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Abstract

The dynamical interactions that occur in newly formed planetary systemsmay reflect the conditions occurring in the protoplanetary diskout of which they formed.With this in mind, we explore the attainment and maintenance of orbital resonancesby migrating planets in the terrestrial mass range. Migration time scales varying between~106 yr and ~103 yr are considered. In the former case, for which themigration time is comparable to the lifetime of the protoplanetary gas disk,a 2:1 resonance may be formed. In the latter, relatively rapid migrationregime commensurabilities of high degree such as 8:7 or 11:10 may be formed.However, in any one large-scale migration several differentcommensurabilities may be formed sequentially, each being associated with significant orbital evolution. We also use a simple analytic theory to develop conditions forfirst order commensurabilities to be formed. These depend on thedegree of the commensurability, the imposed migration and circularization rates,and the planet mass ratios. These conditions are found to be consistent with theresults of our simulations.

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