Type I Planet Migration in a Magnetized Disk. I. Effect of Large-Scale Vertical and Azimuthal Field Components

TL;DR

This study investigates how large-scale magnetic fields in protoplanetary disks influence Type I planet migration, revealing that magnetic fields can slow but not reverse inward migration, with 3D effects inducing turbulence.

Contribution

The paper provides a combined numerical and analytical analysis of magnetic field effects on planet migration, emphasizing the importance of 3D dynamics and magnetic field configurations.

Findings

Magnetic fields can slow inward migration by up to a factor of two.

Pure azimuthal magnetic fields do not cause outward migration in 3D.

Planet-induced weak vertical fields can trigger turbulence via magnetorotational instability.

Abstract

We study the effects of a large-scale, ordered magnetic field in protoplanetary disks on Type I planet migration using a combination of numerical simulations in 2D and 3D and a linear perturbation analysis. Steady-state models of such disks require the inclusion of magnetic diffusivity. To make progress using ideal MHD, we focus on simplified field configurations, involving purely vertical ($B_z$) and azimuthal ($B_\varphi$) field components and a combination of the two. For each of the models we calculate the locations of the relevant resonances and of the turning points, which delineate the propagation regions of the MHD waves that transport angular momentum from the planet to the disk. We use both numerical and semianalytic methods to evaluate the cumulative back torque acting on the planet, and explore the effect of spatial gradients in the disk's physical variables on the results. We conclude that, under realistic (3D) circumstances, a large-scale magnetic field can slow down the inward migration that characterizes the underlying unmagnetized disk --- by up to a factor of $\sim 2$ when the magnetic pressure approaches the thermal pressure --- but it cannot reverse it. A previous inference that a pure-$B_\phi$ field whose amplitude decreases fast enough with radius leads to outward migration applies only in 2D. In fact, we find that, in 3D, a pure-$B_\phi$ disk undergoes a rapid transition to turbulence on account of a magnetorotational instability that is triggered by the planet-induced appearance of a weak $B_z$ component.