Convergence zones for Type I migration: an inward shift for multiple planet systems

¹ Univ. Bordeaux, LAB, UMR 5804, 33270 Floirac, France
e-mail: christophe.cossou@u-bordeaux1.fr
² CNRS, LAB, UMR 5804, 33270 Floirac, France

Received: 5 December 2012
Accepted: 7 February 2013

Abstract

Earth-mass planets embedded in gaseous protoplanetary disks undergo Type I orbital migration. In radiative disks an additional component of the corotation torque scaling with the entropy gradient across the horseshoe region can counteract the general inward migration, Type I migration can then be directed either inward or outward depending on the local disk properties. Thus, special locations exist in the disk toward which planets migrate in a convergent way. Here we present N-body simulations of the convergent migration of systems of low-mass (M = 1−10M_⊕) planets. We show that planets do not actually converge in convergence zones. Rather, they become trapped in chains of mean motion resonances. This causes the planets’ eccentricities to increase to high enough values to affect the structure of the horseshoe region and weaken the positive corotation torque. The zero-torque equilibrium point of the resonant chain of planets is determined by the sum of the attenuated corotation torques and unattenuated differential Lindblad torques acting on each planet. The effective convergence zone is shifted inward. Systems with several planets can experience stochastic migration as a whole due to continuous perturbations from planets entering and leaving resonances.