Hall Effect–Mediated Magnetic Flux Transport in Protoplanetary Disks

Abstract

The global evolution of protoplanetary disks (PPDs) has recently been shown to be largely controlled by the amount of poloidal magnetic flux threading the disk. The amount of magnetic flux must also coevolve with the disk, as a result of magnetic flux transport, a process that is poorly understood. In weakly ionized gas as in PPDs, magnetic flux is largely frozen in the electron fluid, except when resistivity is large. When the disk is largely laminar, we show that the relative drift between the electrons and ions (the Hall drift), and the ions and neutral fluids (ambipolar drift) can play a dominant role on the transport of magnetic flux. Using two-dimensional simulations that incorporate the Hall effect and ambipolar diffusion (AD) with prescribed diffusivities, we show that when large-scale poloidal field is aligned with disk rotation, the Hall effect rapidly drags magnetic flux inward at the midplane region, while it slowly pushes flux outward above/below the midplane. This leads to a highly radially elongated field configuration as a global manifestation of the Hall-shear instability. This field configuration further promotes rapid outward flux transport by AD at the midplane, leading to instability saturation. In quasi-steady state, magnetic flux is transported outward at approximately the same rate at all heights, and the rate is comparable to the Hall-free case. For anti-aligned field polarity, the Hall effect consistently transports magnetic flux outward, leading to a largely vertical field configuration in the midplane region. The field lines in the upper layer first bend radially inward and then outward to launch a disk wind. Overall, the net rate of outward flux transport is about twice as fast as that of the aligned case. In addition, the rate of flux transport increases with increasing disk magnetization. The absolute rate of transport is sensitive to disk microphysics, which remains to be explored in future studies.

Global Simulations of the Vertical Shear Instability with Nonideal Magnetohydrodynamic Effects

“…The poloidal magnetic fields are initialized by specifying an azimuthal vector potential (Zanni et al 2007;Bai & Stone 2017),…”

“…The terminology utilized for thermodynamics throughout this paper is i) locally isothermal, which for ∆t τ the disk temperature is kept to its equilibrium value at each position; ii) thermal relaxation, for which disk temperature is recovered to its equilibrium value on some timescale determined by τ . Following Bai (2017) and Bai & Stone (2017), the wind zone is set to be locally isothermal for all runs with a smooth transition from disk zone. 2…”

“…As the first numerical simulations on the interplay between the VSI and the non-ideal MHD, we aim to make the problem as clean as possible. Therefore, we do not employ sophisticated implementations of realistic disk physics as in Bai (2017), but rather conduct numerical experiments similar to those in Bai & Stone (2017) with prescribed AD coefficients to mimic outer PPD conditions. We anticipate our results to serve as a benchmark for future studies that incorporate more realistic thermodynamics together with non-ideal MHD physics.…”

The Role of Magnetic Fields in Protostellar Outflows and Star Formation

“…One of the intriguing aspects of the Hall effect is that the direction of transport of the magnetic flux in disks depends on the polarity of the threading poloidal field component B p with respect to the disk rotation axis. If its direction is parallel to Ω , then flux transport is inwards, and if anti-aligned, outwards [Bai and Stone, 2017]. Since the flux distribution affects the strength of the wind torques, these Hall effects could be significant for the physics of Type I migration (migration of low mass bodies that do not open gaps in the disk).…”

Molecular outflow launched beyond the disk edge

“…In comparison, field lines inside the Keplerian disk are much less pinched because of the rotation support and the lack of fast infall motions. Therefore, more sophisticated non-ideal magnetohydrodynamics (MHD) mechanisms are required for launching wind on the disk itself, which is likely to be weak and unsteady (e.g., Bai & Stone 2017;Zhu & Stone 2017).…”