Hall equilibrium of thin Keplerian disks embedded in mixed poloidal and toroidal magnetic fields

Abstract

Axisymmetric steady-state weakly ionized Hall-MHD Keplerian thin disks are investigated by using asymptotic expansions in the small disk aspect ratio ε. The model incorporates the azimuthal and poloidal components of the magnetic fields in the leading order in ε. The disk structure is described by an appropriate Grad-Shafranov equation for the poloidal flux function ψthat involves two arbitrary functions of ψfor the toroidal and poloidal currents. The flux function is symmetric about the midplane and satisfies certain boundary conditions at the near-horizontal disk edges. The boundary conditions model the combined effect of the primordial as well as the dipole-like magnetic fields. An analytical solution for the Hall equilibrium is achieved by further expanding the relevant equations in an additional small parameter δthat is inversely proportional to the Hall parameter. It is thus found that the Hall equilibrium disks fall into two types: Keplerian disks with (i) small (Rd ~δ^0) and (ii) large (Rd > δ^k, k > 0) radius of the disk. The numerical examples that are presented demonstrate the richness and great variety of magnetic and density configurations that may be achieved under the Hall-MHD equilibrium.

References in corpus (3)

• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. I. The issue of convergence
• Hall magnetohydrodynamics of partially ionized plasmas
• Evolution of initially localized perturbations in stratified ionized disks

Cited by in corpus (8)

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• Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs
• The role of Hall diffusion in the magnetically threaded thin accretion discs
• Thermomagnetic instability in hot discs
• Regimes of the non-exponential temporal growth in thin Keplerian discs under toroidally-dominated magnetic fields
• The Magneto-Rotational Decay Instability in Keplerian Disks
• On dynamics of nonmagnetic accretion disks