Kink Waves in Non-isothermal Stratified Solar Waveguides: Effect of the External Magnetic Field

We study the effect of an external magnetic field on the properties of kink waves, propagating along a thin non-isothermal stratified and diverging magnetic flux tube. A wave equation, governing the propagation of kink waves under the adopted model is derived. It is shown that the vertical gradient of temperature introduces a spatially local cut-off frequency omega(c). The vertical distribution of the cut-off frequency is calculated for the reference VAL-C model of the solar atmosphere and for different values of a ratio of external to internal magnetic fields. The results show that the cut-off frequency is negative below the temperature minimum due to the negative temperature gradient. In the chromosphere the cut-off frequency at a given height is smaller for a stronger external magnetic field. For the appropriate range of a ratio B-e/B-i approximate to 0-0.8, the cutoff lies in the range omega(c) approximate to 0.003-0.010 s(-1) (periods 600 < P-c < 2000 s). The estimate of the cut-off frequency in the transition region is provided as well. In the propagating wave regime, the effective wave energy flux in the non-isothermal diverging flux tubes is the same as in the straight and homogeneous cylindrical waveguides. The obtained wave equation in the limit beta = 0 is used to study the kink oscillations of non-isothermal coronal loops. It is found that the gradient of temperature along the coronal loops reduces the frequency ratio of the first overtone to the fundamental mode, i.e., omega(2)/omega(1) < 2. This reduction grows for a larger ratio of temperature at the loop top to the temperature at the footpoints. Moreover, the effect of reduction is most pronounced for the steeper temperature profiles.