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Astron. Astrophys. 346, 190-198 (1999)

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Waves and instabilities in a stratified isothermal atmosphere with constant Alfvén speed - revisited

B. Pintér *  1, V.M. Cade 2 and B. Roberts 3

1 Center for Plasma-Astrophysics, K.U. Leuven, Celestijnenlaan 200 B, B-3001 Heverlee, Belgium
2 Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent, Belgium
3 School of Mathematical and Computational Sciences, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland

Received 8 February 1999 / Accepted 19 March 1999


Harmonic perturbations are studied for a plane parallel model for the solar magnetic atmosphere. In the present model, the magnetic field lines are horizontal, the sound speed and the Alfvén speed are constants. It is known that in this model, analytical solutions can be obtained for linearized perturbations. The harmonic perturbations can either propagate as MHD modes modified by the action of gravity or be unstable due to magnetic buoyancy. Dispersion properties and stability limits of these waves as well as the growthrates of the instability are displayed for various combinations of parameters: directional angles [FORMULA] and [FORMULA] of wave propagation, wave number k and the plasma parameter [FORMULA].

There are three modes propagating in the considered atmosphere: the fast, the slow and the Alfvén mode, all modified by gravity. Only the modified slow MHD mode can become unstable; the modified Alfvén and fast MHD modes are always stable. In the limit of a vanishing magnetic field the modified fast mode becomes an acoustic gravity mode, the modified Alfvén mode becomes a mode oscillating with the Brunt-Väisälä frequency at large k, while the modified slow mode disappears.

Key words: instabilities – Magnetohydrodynamics (MHD) – stars: atmospheres

* On leave from Department of Astronomy, Eötvös University, Budapest, Hungary.

Send offprint requests to: B. Pintér

Correspondence to: B. Pintér

© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999