Planets near Meanmotion Resonances
Abstract
The multipleplanet systems discovered by the Kepler mission exhibit the following feature: planet pairs near firstorder meanmotion resonances prefer orbits just outside the nominal resonance, while avoiding those just inside the resonance. We explore an extremely simple dynamical model for planet formation, in which planets grow in mass at a prescribed rate without orbital migration or dissipation. We develop an analytic version of this model for twoplanet systems in two limiting cases: the planet mass grows quickly or slowly relative to the characteristic resonant libration time. In both cases, the distribution of systems in period ratio develops a characteristic asymmetric peaktrough structure around the resonance, qualitatively similar to that observed in the Kepler sample. We verify this result with numerical integrations of the threebody problem. We show that for the 3 : 2 resonance, where the observed peaktrough structure is strongest, our simple model is consistent with the observations for a range of mean planet masses 20100 M _{⊕}. This predicted mass range is higher—by at least a factor of three—than the range expected from the few Kepler planets with measured masses, but part of this discrepancy could be due to oversimplifications in the dynamical model or uncertainties in the planetary massradius relation.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 2013
 DOI:
 10.1088/0004637X/770/1/24
 arXiv:
 arXiv:1211.5603
 Bibcode:
 2013ApJ...770...24P
 Keywords:

 planetary systems;
 planets and satellites: dynamical evolution and stability;
 planets and satellites: formation;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 16 pages, 9 figures, submitted to ApJ