Alfvén instability of steady state flux tubes

II. Upflows in stratified atmospheres

Department of Physics, IMPACSAberystwyth University, Penglais, Aberystwyth SY23 3BZ, UK
e-mail: yot@aber.ac.uk

Received: 7 July 2014
Accepted: 21 January 2015

Abstract

Context. MHD instabilities play an important role in the dynamics and energetics of the solar atmosphere.

Aims. An open vertical magnetic flux tube is permeated by an upflow in a stratified atmosphere with variable temperature. The stability of the tube is investigated with respect to small-amplitude torsional perturbations generated at the footpoint by random convective motions.

Methods. A steady state equilibrium incorporating the effects of a vertical body force, heating, and losses is derived analytically. The governing equations for torsional motions are integrated with a fourth-order Runge-Kutta method and matched with the analytical solutions in the upper regions to obtain a numerical dispersion relation. The dependence of the eigenmode frequencies on different parameters is analysed. Unstable modes are found for a range of Alfvén and flow speeds in the photosphere, as well as expansion factors of the flux tubes. Both supersonic and subsonic flows are considered.

Results. It is shown that torsional perturbations are exponentially amplified in time if a section of the tube exists where the upflowing plasma decelerates and the tube expands. The flow speeds required for the instability are sub-Alfvénic.

Conclusions. The instability may be important for understanding the abundance of Alfvén waves seen in recent observations and the associated heating in magnetic regions of the solar atmosphere.