# A local model of warped magnetised accretion discs

## TL;DR

This paper develops a local ideal MHD model for warped magnetised accretion discs, revealing how magnetic fields influence warp propagation and introduce resonant Alfvénic-epicyclic modes, especially in strongly magnetised discs.

## Contribution

It derives a linear local theory for warped magnetised discs and analyzes the impact of magnetic tension on warp dynamics, including the discovery of resonant Alfvénic-epicyclic modes.

## Key findings

- Magnetic tension reduces warp propagation speed.
- Presence of resonant Alfvénic-epicyclic modes at critical parameters.
- Large internal torques occur at resonance points.

## 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 Alfv\'{e}nic-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.