Kink Oscillations in Solar Coronal Loops with Elliptical Cross-Sections. I. the linear regime

TL;DR

This study investigates linear kink oscillations in solar coronal loops with elliptical cross-sections, revealing how polarization, density contrast, and cross-sectional shape influence oscillation periods and damping, with implications for coronal seismology.

Contribution

It provides the first detailed analysis of kink oscillations in elliptical cross-section loops, highlighting polarization effects and damping behaviors, extending previous circular cross-section models.

Findings

Oscillation periods vary with elliptical axis ratio and polarization.

Damping times differ between modes and depend on transverse profile.

Resonant absorption and phase-mixing are robust in elliptical loops.

Abstract

The cross sections of solar coronal loops are suggested to be rarely circular. We examine linear kink oscillations in straight, density-enhanced, magnetic cylinders with elliptical cross-sections by solving the three-dimensional magnetohydrodynamic equations from an initial-value-problem perspective. Motivated by relevant eigen-mode analyses, we distinguish between two independent polarizations, one along the major axis (the M-modes) and the other along the minor one (the m-modes). We find that, as happens for coronal loops with circular cross-sections, the apparent damping of the transverse displacement of the loop axis is accompanied by the accumulation of transverse Alfv\'enic motions and the consequent development of small-scales therein, suggesting the robustness of the concepts of resonant absorption and phase-mixing. In addition, two stages can in general be told apart in the temporal evolution of the loop displacement; a Gaussian time dependence precedes an exponential one. For the two examined density ratios between loops and their surroundings, the periods of the M-modes (m-modes) tend to increase (decrease) with the major-to-minor-half-axis ratio, and the damping times in the exponential stage for the M-modes tend to exceed their m-mode counterparts. This is true for the two transverse profiles we examine. However, the relative magnitudes of the damping times in the exponential stage for different polarizations depend on the specification of the transverse profile and/or the density contrast. The applications of our numerical findings are discussed in the context of coronal seismology.