Resonantly damped oscillations of elliptically shaped stratified emerging coronal loops

TL;DR

This study investigates how the elliptical shape and emergence stage of coronal loops influence the resonant absorption and damping of kink oscillations, providing new connection formulae and numerical analysis.

Contribution

It introduces novel connection formulae for elliptical coronal loops and analyzes how shape and emergence stage affect oscillation frequencies and damping rates.

Findings

Elliptical shape and emergence stage modify frequencies and damping rates.

The frequency-to-damping ratio remains unaffected by shape and emergence stage.

The ratio of fundamental to first-overtone frequencies is altered by loop shape and emergence.

Abstract

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.