Cutoff-free Propagation of Torsional Alfvén Waves along Thin Magnetic Flux Tubes

Propagation of torsional Alfvén waves along magnetic flux tubes has been extensively studied for many years, but no conclusive results regarding the existence of a cutoff frequency for these waves have been obtained. The main purpose of this paper is to derive new wave equations that describe the propagation of linear torsional Alfvén waves along thin and isothermal magnetic flux tubes and to use these wave equations to demonstrate that the torsional wave propagation is not affected by any cutoff frequency. It is also shown that this cutoff-free propagation is independent of the different choices of coordinate system and wave variables adopted in previous studies. A brief discussion of the implications of this cutoff-free propagation of torsional tube waves on theories of wave heating of the solar and stellar atmospheres is also given. Subject headinggs: MHD — stars: atmospheres — stars: late-type — waves