Constrained Evolution of a Radially Magnetized Protoplanetary Disk: Implications for Planetary Migration

TL;DR

This paper models the inner protoplanetary disk's magnetic and material evolution, revealing implications for planetary migration and disk observational features, especially under magnetic field constraints and ionization effects.

Contribution

It provides a deterministic calculation of disk mass flow considering magnetic field constraints, linking magnetic evolution to planet migration and disk observational signatures.

Findings

Inner disk shows stronger magnetization and faster accretion.

Disk surface density is buffered at ~30 g/cm², affecting particle lofting.

Planet migration is limited by gas supply and sublimation zones.

Abstract

We consider the inner $\sim$ AU of a protoplanetary disk (PPD), at a stage where angular momentum transport is driven by the mixing of a radial magnetic field into the disk from a T-Tauri wind. Because the radial profile of the imposed magnetic field is well constrained, a deterministic calculation of the disk mass flow becomes possible. The vertical disk profiles obtained in Paper I imply a stronger magnetization in the inner disk, faster accretion, and a secular depletion of the disk material. Inward transport of solids allows the disk to maintain a broad optical absorption layer even when the grain abundance becomes too small to suppress its ionization. Thus a PPD may show a strong middle-to-near infrared spectral excess even while its mass profile departs radically from the minimum-mass solar nebula. The disk surface density is buffered at $\sim 30$ g cm$^{-2}$: below this, X-rays trigger strong enough magnetorotational turbulence at the midplane to loft mm-cm sized particles high in the disk, followed by catastrophic fragmentation. A sharp density gradient bounds the inner depleted disk, and propagates outward to $\sim 1$-2 AU over a few Myr. Earth-mass planets migrate through the inner disk over a similar timescale, whereas the migration of Jupiters is limited by the supply of gas. Gas-mediated migration must stall outside 0.04 AU, where silicates are sublimated and the disk shifts to a much lower column. A transition disk emerges when the dust/gas ratio in the MRI-active layer falls below $X_d \sim 10^{-6}(a_d/\mu{\rm m})$, where $a_d$ is the grain size.