Flow instabilities of magnetic flux tubes

II. Longitudinal flow

Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany e-mail: [holzwarth;schmitt;schuessler]@mps.mpg.de

Received: 9 February 2007
Accepted: 4 April 2007

Abstract

Context.Flow-induced instabilities are relevant for the storage and dynamics of magnetic fields in stellar convection zones and possibly also in other astrophysical contexts.

Aims.We continue the study started in the first paper of this series by considering the stability properties of longitudinal flows along magnetic flux tubes.

Methods.A linear stability analysis was carried out to determine criteria for the onset of instability in the framework of the approximation of thin magnetic flux tubes.

Results.In the non-dissipative case, we find Kelvin-Helmholtz instability for flow velocities exceeding a critical speed that depends on the Alfvén speed and on the ratio of the internal and external densities. Inclusion of a friction term proportional to the relative transverse velocity leads to a friction-driven instability connected with backward (or negative energy) waves. We discuss the physical nature of this instability. In the case of a stratified external medium, the Kelvin-Helmholtz instability and the friction-driven instability can set in for flow speeds significantly lower than the Alfvén speed.

Conclusions.Dissipative effects can excite flow-driven instability below the thresholds for the Kelvin-Helmholtz and the undulatory (Parker-type) instabilities. This may be important for magnetic flux storage in stellar convection zones and for the stability of astrophysical jets.