Journal Article

Magnetic and vertical shear instabilities in accretion discs

V. Urpin and A. Brandenburg

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 294, issue 3, pages 399-406
Published in print March 1998 | ISSN: 0035-8711
Published online March 1998 | e-ISSN: 1365-2966 | DOI:
Magnetic and vertical shear instabilities in accretion discs

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The stability properties of magnetized discs rotating with angular velocity Ω = Ω(s, z), dependent on both the radial and the vertical coordinates s and z, are considered. Such a rotation law is adequate for many astrophysical discs (e.g., galactic and protoplanetary discs, as well as accretion discs in binaries). In general, the angular velocity depends on height, even in thin accretion discs. A linear stability analysis is performed in the Boussinesq approximation, and the dispersion relation is obtained for short-wavelength perturbations. Any dependence of Ω on z can destabilize the flow. This concerns primarily small-scale perturbations for which the stabilizing effect of buoyancy is strongly suppressed due to the energy exchange with the surrounding plasma. For a weak magnetic field, instability of discs is mainly associated with vertical shear, whilst for an intermediate magnetic field the magnetic shear instability, first considered by Chandrasekhar and Velikhov, is more efficient. This instability is caused by the radial shear which is typically much stronger than the vertical shear. Therefore the growth time for the magnetic shear instability is much shorter than for the vertical shear instability. A relatively strong magnetic field can suppress both these instabilities. The vertical shear instability could be the source of turbulence in protoplanetary discs, where the conductivity is low.

Keywords: accretion, accretion discs; instabilities; magnetic fields; MHD

Journal Article.  0 words. 

Subjects: Astronomy and Astrophysics

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