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Resonantly damped oscillations of elliptically shaped stratified emerging coronal loops

The effects of both elliptical shape and stage of emergence of the coronal loop on the resonant absorption of standing kink oscillations are studied. To do so, a typical coronal loop is modeled as a zero-beta longitudinally stratified cylindrical magnetic flux tube. We developed the connection formulae for the resonant absorption of standing transversal oscillations of a coronal loop with an elliptical shape, at various stages of its emergence. Using the connection formulae, the dispersion relation is derived and solved numerically to obtain the frequencies and damping rates of the fundamental and first-overtone kink modes. Our numerical results show that both the elliptical shape and stage of emergence of the loop alter the frequencies and damping rates of the tube as well as the ratio of frequencies of the fundamental and its first-overtone modes. However, the ratio of the oscillation frequency to the damping rate is not affected by the tube shape and stage of its emergence and also is independent of the density stratification parameter.