Horizontally and vertically polarized kink oscillations in curved solar coronal loops^⋆

¹ Centre for mathematical Plasma-Astrophysics (CmPA), Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
e-mail: mingzhe.guo@kuleuven.be
² Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, Institute of Space Sciences, Shandong University, Weihai 264209, PR China

Received: 15 March 2024
Accepted: 7 April 2024

Abstract

Aims. Kink oscillations are frequently observed in coronal loops. This work aims to numerically clarify the influence of the loop curvature on horizontally and vertically polarized kink oscillations.

Methods. Working within the framework of ideal magnetohydrodynamics (MHD), we conduct three-dimensional (3D) simulations of axial fundamental kink oscillations in curved density-enhanced loops embedded in a potential magnetic field. Both horizontal and vertical polarizations are examined, and their oscillation frequencies are compared with Wentzel-Kramers-Brillouin (WKB) expectations. We discriminate between two different density specifications. In the first (dubbed “uniform density”), the density is axially uniform and varies continuously in the transverse direction toward a uniform ambient corona. Some further stratification is implemented in the second specification (dubbed “stratified”), allowing us to address the effect of evanescent barriers.

Results. Examining the oscillating profiles of the initially perturbed uniform-density loops, we found that the frequencies for both polarizations deviate from the WKB expectation by ∼10%. In the stratified loop, however, the frequency of the horizontal polarization deviates to a larger extent (∼25%). We illustrate the lateral leakage of kink modes through wave tunneling in 3D simulations, for the first time. Despite this, in the uniform density and the stratified loops, the damping time-to-period ratios are similar and are close to the analytical predictions for straight configurations under the thin-tube-thin-boundary (TTTB) assumption.

Conclusions. The WKB expectation for straight configurations can reasonably describe the eigenfrequency of kink oscillations only in loops without an asymmetrical cross-loop density profile perpendicular to the oscillating direction. Lateral leakage via wave tunneling is found to be less efficient than resonant absorption, meaning that the latter remains a robust damping mechanism for kink motions even when loop curvature is included.