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

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. In this series, we have included, for the first time, 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 (Bai & Stone 2013; Bai 2013) 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 modifies the wind solutions depending on the polarity of the large-scale poloidal magnetic field {{\boldsymbol B}}_0 threading the disk. When {{\boldsymbol B}}_0\cdot {{\boldsymbol Ω }}\gt0, 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 {{\boldsymbol B}}_0\cdot {{\boldsymbol Ω }}<0, the horizontal magnetic field is reduced, leading to a weaker disk wind (by <~ 20%) and negligible magnetic braking. Under fiducial parameters, we find that when {{\boldsymbol B}}_0\cdot {{\boldsymbol Ω }}\gt0, the laminar region extends farther to ~10-15 AU before the magnetorotational instability sets in, while for {{\boldsymbol B}}_0\cdot {{\boldsymbol Ω }}<0, the laminar region extends only to ~3-5 AU for a typical accretion rate of ~10^-8 to10^-7 M _⊙ yr^-1. Scaling relations for the wind properties, especially the wind-driven accretion rate, are provided for aligned and anti-aligned field geometries.