Type I Planet Migration in a Magnetized Disk

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

Authors:

Bans et al

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 ∝B0z∂B0φ/∂z (where B0z and B0φ 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-B0z 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-B0φ 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 B0φ component whose amplitude increases from zero at z=0 has little effect on the torque when acting alone, but in conjunction with a B0z component it gives rise to a strong torque that speeds up the inward migration by a factor ≳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 B0z+∂B0φ/∂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.