Effect of transitional layer on frequency of kink oscillations

In this article we study the effect of a transitional layer in a magnetic tube on the real part of the frequencies of kink oscillations. In our analysis, we use the model of a straight magnetic tube with the density and cross-section radius varying along the loop, and the thin-tube thin-boundary (TTTB) approximation. First, we calculate the correction to the fundamental frequency and show that it is positive and of the order of the ratio of the transitional layer thickness to the loop radius ℓ. The increase in the fundamental frequency results in the decrease in the estimate of the magnetic-field magnitude. Then we study the effect of the transitional layer on the ratio between the fundamental frequency and the first overtone frequency that is used for estimating the atmospheric scale height. We show that the correction to the frequency ratio is of the order of ℓ2, and thus it can be neglected for moderate values of ℓ.