Non-axisymmetric oscillations of stratified coronal magnetic loops with elliptical cross-sections

TL;DR

This paper analyzes non-axisymmetric oscillations in stratified coronal magnetic loops with elliptical cross-sections, deriving governing equations and revealing that frequency ratios are unaffected by ellipticity, aiding coronal seismology.

Contribution

It introduces a theoretical framework for kink and fluting modes in elliptical loops, showing frequency ratios are independent of cross-sectional ellipticity.

Findings

Frequency ratio of first overtone to fundamental harmonic is constant for both kink modes.

Estimates of atmospheric scale height are unaffected by loop ellipticity.

Two distinct kink modes polarized along the ellipse axes are identified.

Abstract

We study non-axisymmetric oscillations of a straight magnetic tube with an elliptic cross-section and density varying along the tube. The governing equations for kink and fluting modes in the thin tube approximation are derived. We found that there are two kink modes, polarised along the large and small axes of the elliptic cross-section. We have shown that the ratio of frequencies of the first overtone and fundamental harmonic is the same for both kink modes and independent of the ratio of the ellipse axes. On the basis of this result we concluded that the estimates of the atmospheric scale height obtained using simultaneous observations of the fundamental harmonic and first overtone of the coronal loop kink oscillations are independent of the ellipticity of the loop cross-section.