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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 systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital resonances by 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 the migration time is comparable to the lifetime of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter, relatively rapid migration regime commensurabilities of high degree such as 8:7 or 11:10 may be formed. However, in any one large-scale migration several different commensurabilities may be formed sequentially, each being associated with significant orbital evolution. We also use a simple analytic theory to develop conditions for first order commensurabilities to be formed. These depend on the degree of the commensurability, the imposed migration and circularization rates, and the planet mass ratios. These conditions are found to be consistent with the results of our simulations.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 42: Extrasolar Planets in Multi-Body Systems: Theory and Observations , 2010 , pp. 333 - 343
Copyright
© EAS, EDP Sciences, 2010

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References

Brouwer, D., & Clemence, G.M., 1961, Methods of Celestial Mechanics (Academic Press, New York)
Gladman, B., 1993, Icarus, 106, 247 CrossRef
Goldreich, P., & Tremaine, S., 1980, ApJ, 241, 425 CrossRef
Kley, W., Peitz, J., & Bryden, G., 2004, A&A, 414, 735
Lee, M.H., & Peale, S.J., 2002, ApJ, 567, 596 CrossRef
Lin, D.N.C., & Papaloizou, J.C.B., 1986, ApJ, 309, 846 CrossRef
Marcy, G.W., Butler, R.P., Fischer, D., et al., 2001, ApJ, 556, 296 CrossRef
Mayor, M., Udry, S., Naef, D., et al., 2004, A&A, 415, 391
Mayor, M., Udry, S., Lovis, C., et al., 2008 [arXiv0806.4587]
McArthur, B.E., Endl, M., Cochran, W.D., et al., 2004, ApJ, 614, L81 CrossRef
Nelson, R.P., & Papaloizou, J.C.B., 2002, MNRAS, 333, 26 CrossRef
Paardekooper, S.-J., & Papaloizou, J.C.B., 2008, A&A, 485, 877
Papaloizou, J.C.B., 2003, Cel. Mech. Dynam. Astron., 87, 53 CrossRef
Papaloizou, J.C.B., & Larwood, J.D., 2000, MNRAS, 315, 823 CrossRef
Papaloizou, J.C.B., & Terquem, C., 2006, Rep. Prog. Phys., 69, 119 CrossRef
Papaloizou, J.C.B., & Szuszkiewicz, E., 2005, MNRAS, 363, 153 CrossRef
Sinclair, A.T., 1975, MNRAS, 171, 59 CrossRef
Snellgrove, M., Papaloizou, J.C.B., & Nelson, R.P., 2001, A&A, 374, 1092