Hall-effect Controlled Gas Dynamics in Protoplanetary Disks: I. Wind Solutions at the Inner Disk

Abstract

The gas dynamics of protoplanetary disks (PPDs) is largely controlled by non-ideal magnetohydrodynamic (MHD) effects including Ohmic resistivity, the Hall effect and ambipolar diffusion. Among these the role of the Hall effect is the least explored and most poorly understood. We have included all three non-ideal MHD effects in a self-consistent manner to investigate the role of the Hall effect on PPD gas dynamics using local shearing-box simulations. In this first paper, we focus on the inner region of PPDs, where previous studies excluding the Hall effect have revealed that the inner disk up to ~10 AU is largely laminar, with accretion driven by a magnetocentrifugal wind. We confirm this basic picture and show that the Hall effect introduces modest modifications to the wind solutions, depending on the polarity of the large-scale poloidal magnetic field B_0 threading the disk. When B_0.Omega>0, the horizontal magnetic field is strongly amplified toward the disk interior, leading to a stronger disk wind (by ~50% or less in terms of the wind-driven accretion rate). The enhanced horizontal field also leads to much stronger large-scale Maxwell stress (magnetic braking) that contributes to a considerable fraction of the wind-driven accretion rate. When B_0.Omega<0, the horizontal magnetic field is reduced, leading to a weaker disk wind (by ~20%) and negligible magnetic braking. Moreover, we find that when B_0.Omega>0, the laminar region extends farther to ~15 AU before the magneto-rotational instability sets in, while for B_0.Omega<0, the laminar region extends only to ~3-5 AU for a typical PPD accretion rates. Scaling relations for the wind properties, especially the wind-driven accretion rate, are provided for aligned and anti-aligned field geometries. Issues with the symmetry of the wind solutions and grain abundance are also discussed.