Magnetohydrodynamic Wave Modes of Solar Magnetic Flux Tubes with an Elliptical Cross Section

Abstract

The purpose of this paper is to study the behavior of magnetohydrodynamic (MHD) wave modes that propagate incompressible magnetic flux tubes with an elliptical cross section embedded in a magnetic environment. Thedispersion relation that describes the behavior of MHD wave modes permitted in an elliptical magnetic flux tube issolved numerically. Distortion of the spatial structure of the purely real eigenmodes from the well-known circularflux tube model has been considered. It has been studied under both photospheric and coronal conditions. It hasbeen shown that (i) solutions in the form of even Mathieu functions are more sensitive to the value of eccentricitythan solutions with the form of odd Mathieu functions; (ii) if the ellipticity of the cross section of the magnetic fluxtube increases, a sausage mode (m = 0) cannot be easily identified; (iii) even solutions that correspond to the flutingmode (m = 3) can be misinterpreted as a kink mode (m = 1) due to their similarities. In contrast to the flutingmodes that are polarized along the major axis and strongly depend on the ellipticity of the magnetic flux tube, thekink and sausage surface modes are practically unaffected by ellipticity. Several examples of the spatial structure ofthe eigenmodes permitted in the pores and sunspots have been visualized. The solutions obtained in theapproximation of cylindrical symmetry are in agreement with previous studies