CONSTRAINED EVOLUTION of A RADIALLY MAGNETIZED PROTOPLANETARY DISK: IMPLICATIONS for PLANETARY MIGRATION

Abstract

We consider the inner ∼1 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 constrained 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 mid- 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 ∼30 g cm-2; below this, X-rays trigger magnetorotational turbulence at the midplane strong enough to loft millimeter- to centimeter-sized particles high in the disk, followed by catastrophic fragmentation. A sharp density gradient bounds the inner depleted disk and propagates outward to ∼1-2 AU over a few megayears. 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 Xd ∼ 10-6(ad/μm), where ad is the grain size.