MHD Wave Modes in Solar Magnetic Flux Tubes with Various Cross-Sectional Shapes

Abstract

Here we present three different models that can be tested against observed sunspot oscillations: (i) A magnetic flux tube of circular cross-sectional shape with the axis parallel to the observer’s line of sight; (ii) a magnetic flux tube of elliptical cross-sectional shape with the axis parallel to the observer’s line of sight; (iii) a magnetic flux tube of actual cross-sectional shape with the axis parallel to the observer’s line of sight. The theory of MHD wave modes in cylindrical magnetic waveguides is well developed. In this work we will solve the dispersion relation in cylindrical magnetic waveguides using a new numerical algorithm for solving transcendental equations. Next, we will present a model that predicts the MHD wave modes of compressible magnetic flux tubes with an elliptical cross-section. Therefore, the developed numerical algorithm is also implemented to solve the dispersion relation for elliptical magnetic waveguides. From a practical point of view the information from the resultant dispersion diagrams does not actually show what these MHD modes will actually look like in observational data. Therefore, we will illustrate the spatial structure of the eigenfunctions of these MHD wave modes to explain how the eccentricity affects different wave modes when the flux tube axis is parallel to the observers line of sight. Finally, we present a model that predicts the MHD wave modes of compressible magnetic flux tubes using the actual observed cross-sectional shape. We will illustrate the spatial structure of the eigenfunctions of these MHD wave modes and compare them with other models, i.e cylindrical and elliptical.