Longitudinal oscillations in density stratified and expanding solar waveguides

TL;DR

This paper analytically and numerically investigates how density and magnetic stratification affect longitudinal MHD waves in expanding solar waveguides, providing insights for solar magneto-seismology.

Contribution

It offers new analytical solutions and numerical analysis of longitudinal MHD waves in non-uniform, expanding flux tubes with density stratification, enhancing understanding of solar waveguide oscillations.

Findings

Frequency ratio depends linearly on expansion factor for small expansions.

Numerical results agree with analytical solutions across different density profiles.

Results have implications for solar magneto-seismology diagnostics.

Abstract

Waves and oscillations can provide vital information about the internal structure of waveguides they propagate in. Here, we analytically investigate the effects of density and magnetic stratification on linear longitudinal magnetohydrodynamic (MHD) waves. The focus of this paper is to study the eigenmodes of these oscillations. It is our specific aim is to understand what happens to these MHD waves generated in flux tubes with non-constant (e.g., expanding or magnetic bottle) cross-sectional area and density variations. The governing equation of the longitudinal mode is derived and solved analytically and numerically. In particular, the limit of the thin flux tube approximation is examined. The general solution describing the slow longitudinal MHD waves in an expanding magnetic flux tube with constant density is found. Longitudinal MHD waves in density stratified loops with constant magnetic field are also analyzed. From analytical solutions, the frequency ratio of the first overtone and fundamental mode is investigated in stratified waveguides. For small expansion, a linear dependence between the frequency ratio and the expansion factor is found. From numerical calculations it was found that the frequency ratio strongly depends on the density profile chosen and, in general, the numerical results are in agreement with the analytical results. The relevance of these results for solar magneto-seismology is discussed.