Capture of Planets Into Mean Motion Resonances and the Origins of Extrasolar Orbital Architectures

TL;DR

This paper develops a comprehensive analytical theory for the capture of planets into mean motion resonances during orbital migration, explaining the observed distribution of extrasolar planetary orbits.

Contribution

It introduces a generalized Hamiltonian model for planetary resonances with finite masses and eccentricities, and provides criteria for resonant capture and its probabilities.

Findings

Resonant capture is often unsuccessful for low-mass planets due to disk asymmetries.

The observed non-resonant orbital distribution of extrasolar planets can be explained by this theory.

The model applies to the evolution of Jupiter and Saturn in the protosolar nebula.

Abstract

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 disks.