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

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 ($B_{\phi }$) 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-$B_{\varphi }$ 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-$B_{\varphi }$ 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.

22 pages, 15 figures, ancillary material in the form of both a Mathematica notebook and a PDF document. Accepted for publication in The Astrophysical Journal

References in corpus (10)

• PLUTO: a Numerical Code for Computational Astrophysics
• Toward a Deterministic Model of Planetary Formation V. Accumulation Near the Ice Line
• On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration
• Properties of gravitoturbulent accretion disks
• Massive planet migration: Theoretical predictions and comparison with observations
• Diffusive Migration of Low-Mass Proto-planets in Turbulent Disks
• 3D MHD Simulations of Planet Migration in Turbulent Stratified Disks
• On the width and shape of the corotation region for low-mass planets
• Corotational Instability, Magnetic Resonances and Global Inertial-Acoustic Oscillations in Magnetized Black-Hole Accretion Discs
• The Effect of Poloidal Magnetic Field on Type I Planetary Migration: Significance of Magnetic Resonance

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• Effects of global gas flows on type I migration
• Turbulence destroys thermal lobes around Mars-sized planetary embryos