Local semi-analytic models of magnetic flux transport in protoplanetary discs

Abstract

The evolution of a large-scale poloidal magnetic field in an accretion disc is an important problem because it determines the launching of winds and the feasibility of the magnetorotational instability to generate turbulence or channel flows. Recent studies, both semi-analytical calculations and numerical simulations, have highlighted the crucial role non-ideal MHD effects (Ohmic resistivity, Hall drift and ambipolar diffusion), relevant in the protoplanetary disc context, might play in magnetic flux evolution in the disc. We investigate the flux transport in discs through the use of two one-dimensional semi-analytic models in the vertical direction, exploring regimes where different physical source terms and effects dominate. The governing equations for both models are derived by performing an asymptotic expansion in the limit of a thin disc, with the different regimes isolated through setting the relative order of the leading terms between variables. Flux transport rates and vertical structure profiles are calculated for a range of diffusivities and disc magnetisations. We found that Ohmic and ambipolar diffusivities drive radially outward flux transport with an outwardly inclined field. A wind outflow drives inward flux transport, which is significantly enhanced in the presence of Hall drift in the positive polarity case, ${\eta }_H({\mathbf{B}}_z\cdot \mathbf{\Omega })>0$, an effect which has only been briefly noted before. Coupled only with outward inclination, the Hall effect reduces the flux transport given by a background Ohmic and/or ambipolar diffusivity, but drives no flux transport when it is the only non-ideal effect present.

In press. Accepted by MNRAS

References in corpus (9)

• Magnetic fields in protoplanetary disks
• Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics
• Advection of Magnetic Fields in Accretion Disks: Not So Difficult After All
• On the Linear Stability of Weakly-Ionized, Magnetized Planar Shear Flows
• Hall-effect Mediated Magnetic Flux Transport in Protoplanetary Disks
• Advection/Diffusion of Large-Scale B-Field in Accretion Disks
• Global evolution of the magnetic field in a thin disc and its consequences for protoplanetary systems
• Rings and gaps produced by variable magnetic disk winds and avalanche accretion streams: I. Axisymmetric resistive MHD simulations
• Magnetohydrodynamics of Protostellar Disks

Cited by in corpus (10)

• A systematic description of wind-driven protoplanetary discs
• Global Hydromagnetic Simulations of Protoplanetary Disks with Stellar Irradiation and Simplified Thermochemistry
• Evolution of the Water Snow Line in Magnetically Accreting Protoplanetary Disks
• The vertical shear instability in poorly ionised, magnetized protoplanetary discs
• Electric heating and angular momentum transport in laminar models of protoplanetary disks
• Magnetohydrodynamics of protoplanetary discs
• Global magnetohydrodynamic simulations of the inner regions of protoplanetary discs. I. Zero-net flux regime
• Gravito-turbulence and dynamo in poorly ionised protostellar discs. I. Zero-net-flux case
• Protoplanetary disks around magnetized young stars with large-scale magnetic fields I: Steady-state solutions
• Global Non-ideal Magnetohydrodynamic Simulations of Protoplanetary Disks with Outer Truncation