A local model of warped magnetised accretion discs

Abstract

We derive expressions for the local ideal magnetohydrodynamic (MHD) equations for a warped astrophysical disc using a warped shearing box formalism. A perturbation expansion of these equations to first order in the warping amplitude leads to a linear theory for the internal local structure of magnetised warped discs in the absence of MRI turbulence. In the special case of an external magnetic field oriented normal to the disc surface these equations are solved semi-analytically via a spectral method. The relatively rapid warp propagation of low-viscosity Keplerian hydrodynamic warped discs is diminished by the presence of a magnetic field. The magnetic tension adds a stiffness to the epicyclic oscillations, detuning the natural frequency from the orbital frequency and thereby removing the resonant forcing of epicyclic modes characteristic of hydrodynamic warped discs. In contrast to a single hydrodynamic resonance we find a series of Alfvénic-epicyclic modes which may be resonantly forced by the warped geometry at critical values of the orbital shear rate $q$ and magnetic field strength. At these critical points large internal torques are generated and anomalously rapid warp propagation occurs. As our treatment omits MRI turbulence, these results are of greatest applicability to strongly magnetised discs.

15 pages, 9 figures, 1 table, MNRAS accepted

References in corpus (4)

• Global General Relativistic MHD Simulation of a Tilted Black-Hole Accretion Disk
• No Evidence for Bardeen-Petterson Alignment in GRMHD Simulations and Semi-Analytic Models of Moderately Thin, Prograde, Tilted Accretion Disks
• The dependence of protostar formation on the geometry and strength of the initial magnetic field
• Shearing box simulations of accretion disk winds

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• Linear bending wave propagation in laminar and turbulent discs
• The Interplay of Parametric and Magnetorotational Instabilities in Oscillatory Shear Flows
• Magnetorotational Instability in Diamagnetic, Misaligned Protostellar Discs
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