Low mass planet migration in magnetically torqued dead zones - II. Flow-locked and runaway migration, and a torque prescription

TL;DR

This paper investigates low mass planet migration in magnetically influenced protoplanetary discs, identifying distinct migration regimes, including flow-locked and runaway migration, and develops models and prescriptions for these phenomena.

Contribution

It introduces a comprehensive analysis of migration regimes in laminar, magnetically torqued discs, including new models for fast migration and torque prescriptions for planet formation simulations.

Findings

Four migration regimes identified, including flow-locked and runaway migration.

Torque and migration reversals caused by magnetic stresses and surface density bifurcation.

Developed analytical and phenomenological models for fast and steady migration.

Abstract

We examine the migration of low mass planets in laminar protoplanetary discs, threaded by large scale magnetic fields in the dead zone that drive radial gas flows. As shown in Paper I, a dynamical corotation torque arises due to the flow-induced asymmetric distortion of the corotation region and the evolving vortensity contrast between the librating horseshoe material and background disc flow. Using simulations of laminar torqued discs containing migrating planets, we demonstrate the existence of the four distinct migration regimes predicted in Paper I. In two regimes, the migration is approximately locked to the inward or outward radial gas flow, and in the other regimes the planet undergoes outward runaway migration that eventually settles to fast steady migration. In addition, we demonstrate torque and migration reversals induced by midplane magnetic stresses, with a bifurcation dependent on the disc surface density. We develop a model for fast migration, and show why the outward runaway saturates to a steady speed, and examine phenomenologically its termination due to changing local disc conditions. We also develop an analytical model for the corotation torque at late times that includes viscosity, for application to discs that sustain modest turbulence. Finally, we use the simulation results to develop torque prescriptions for inclusion in population synthesis models of planet formation.