Spectrograms of high spatial resolution taken every 15s reveal rapid variations of the continuum intensity and line width. Variations of the latter seem to be related to Doppler velocity gradients.

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 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 different choices of the coordinate systems and wave variables adopted in the previous studies. A brief discussion of implications of this cutofffree propagation of torsional tube waves on theories of wave heating of the solar and stellar atmospheres is also given.

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Fundamental modes supported by a thin magnetic flux tube embedded in the solar atmosphere are typically classified as longitudinal, transverse, and torsional waves. If the tube is isothermal, then the propagation of longitudinal and transverse tube waves is restricted to frequencies that are higher than the corresponding global cutoff frequency for each wave. However, no such global cutoff frequency exists for torsional tube waves, which means that a thin and isothermal flux tube supports torsional tube waves of any frequency. In this paper, we consider a thin and non-isothermal magnetic flux tube and demonstrate that temperature gradients inside this tube are responsible for the origin of a cutoff frequency for torsional tube waves. The cutoff frequency is used to determine conditions for the wave propagation in the solar atmosphere, and the obtained results are compared to the recent observational data that support the existence of torsional tube waves in the Sun.

Propagation of torsional waves along isothermal and initially-untwisted magneticflux tubes embedded in the solar atmosphere is studied analytically. Conditions for wave propagation along thin and wide magnetic-flux tubes are determined, and it is shown that the propagation along thin tubes is cutoff free; however, for wide tubes the propagation is affected by a cutoff frequency. A method to determine the cutoff frequency is presented and applied to a specific model of solar magnetic flux tubes. An interesting result is that the cutoff frequency is a local quantity in the model and that its value at a given height determines the frequency that torsional tube waves must have to propagate at this height.