Seismology of Curved Coronal Loops Using Multiperiodic Kink Oscillations

It was shown recently that the model of a semicircular magnetic slab with oblique wave propagation and finite plasma-\(\beta \) supports two fast surface modes, one of which produces vertical and the other horizontal kink-like motions. Their phase speeds (frequencies) depend upon the internal plasma-\(\beta \) and slab aspect ratio. Thus the theory predicts the coexistence of two kink modes with different polarizations and periods in a single oscillating loop. In the present work, we aim to perform some analytical extensions of the developed theory and propose methods for seismological estimation of internal plasma-\(\beta \) and internal Alfvén speed on the bases of multiperiodic kink oscillations of coronal loops. We show that when two fundamental modes of vertically and horizontally polarized kink oscillations with different periods are observed in a single coronal loop, this provides the seismological estimation of the internal plasma-\(\beta \) and Alfvén speed. We also show that the combined effect of a finite plasma-\(\beta \) and a slab curvature modifies the ratio of periods \(P_{1}/2P_{2}\) of the fundamental mode and first overtone of a certain kink oscillation and the internal plasma-\(\beta \) can be estimated using detected \(P_{1}/2P_{2}\). We also suggest that the strands with different temperatures that constitute the multithermal loops should oscillate with different periods and this may provide an estimate to the internal Alfvén speed in such loops. These findings are applied to a number of observations of multiperiodic coronal loop kink oscillations. Furthermore, a number of unusual observational results and the results of numerical simulations of kink oscillations in curved magnetic loops were interpreted on the bases of the developed theory.