Type I Planet Migration in a Magnetized Disk. II. Effect of Vertical Angular Momentum Transport

TL;DR

This paper investigates how large-scale magnetic fields in protoplanetary disks influence Type I planet migration, revealing that combined vertical and azimuthal magnetic components can significantly accelerate inward migration.

Contribution

It introduces a new model of disk-planet interaction considering vertical angular momentum transport via magnetic fields, showing enhanced inward migration effects not seen in previous models.

Findings

A subthermal vertical magnetic field slightly reduces torque compared to 2D models.

A combined vertical and azimuthal magnetic field greatly accelerates inward migration.

The dominant torque contributions add coherently from both sides of the planet.

Abstract

We study the effects of a large-scale, ordered magnetic field in protoplanetary disks on Type I planet migration using a linear perturbation analysis in the ideal-MHD limit. We focus on wind-driving disks, in which a magnetic torque $\propto B_{0z} \partial B_{0\varphi}/\partial z$ (where $B_{0z}$ and $B_{0\varphi}$ are the equilibrium vertical and azimuthal field components) induces vertical angular momentum transport. We derive the governing differential equation for the disk response and identify its resonances and turning points. For a disk containing a slightly subthermal, pure-$B_{0z}$ field, the total 3D torque is close to its value in the 2D limit but remains lower than the hydrodynamic torque. In contrast with the 2D pure-$B_{0\varphi}$ field model considered by Terquem (2003), inward migration is not reduced in this case when the field amplitude decreases with radius. The presence of a subdominant $B_{0\varphi}$ component whose amplitude increases from zero at $z=0$ has little effect on the torque when acting alone, but in conjunction with a $B_{0z}$ component it gives rise to a strong torque that speeds up the inward migration by a factor $\gtrsim 200$. This factor could, however, be reduced in a real disk by dissipation and magnetic diffusivity effects. Unlike all previously studied disk migration models, in the $B_{0z}+\partial B_{0\varphi}/\partial z$ case the dominant contributions to the torque add with the same sign from the two sides of the planet. We attribute this behavior to a new mode of interaction wherein a planet moves inward by plugging into the disk's underlying angular momentum transport mechanism.