Journal Article

Spectral and algebraic instabilities in thin Keplerian discs under poloidal and toroidal magnetic fields

Yuri M. Shtemler, Michael Mond and Edward Liverts

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 413, issue 4, pages 2957-2977
Published in print June 2011 | ISSN: 0035-8711
Published online May 2011 | e-ISSN: 1365-2966 | DOI:
Spectral and algebraic instabilities in thin Keplerian discs under poloidal and toroidal magnetic fields

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The linear instability of two equilibrium configurations with either poloidal (I) or toroidal (II) dominant magnetic field components are studied in thin vertically isothermal Keplerian discs. Solutions of the stability problem are found explicitly by asymptotic expansions in the small aspect ratio of the disc. In both the equilibrium configurations the perturbations are decoupled into in-plane and vertical modes. For equilibria of type I those two modes are the Alfvén–Coriolis and sound waves, while for equilibria of type II they are the inertia–Coriolis and magnetosonic waves. Exact expressions for the growth rates as well as the number of unstable modes for type I equilibria are derived. Those are the discrete counterpart of the continuous infinite homogeneous cylinder magnetorotational (MRI) spectrum. It is further shown that the axisymmetric MRI is completely suppressed by dominant toroidal magnetic fields (i.e. equilibria of type II). This renders the system prone to either non-axisymmetric MRI or non-modal algebraic growth mechanisms. The algebraic growth mechanism investigated in the present study occurs exclusively due to the rotation shear, generates the inertia–Coriolis driven magnetosonic modes due to non-resonant or resonant coupling that induces, respectively, linear or quadratic temporal growth of the perturbations.

Keywords: accretion, accretion discs; instabilities; MHD

Journal Article.  10311 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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