# Torsional oscillations of longitudinally inhomogeneous coronal loops

## TL;DR

This paper investigates how inhomogeneous mass density in solar coronal loops affects torsional Alfven oscillation frequencies and wave profiles, providing analytical and numerical insights crucial for coronal seismology.

## Contribution

It derives and verifies dispersion relations for torsional oscillations in inhomogeneous loops, highlighting frequency reductions due to density variations.

## Key findings

- Inhomogeneity reduces torsional wave frequencies.
- Numerical solutions confirm analytical dispersion relations.
- Results aid in interpreting spectral line width oscillations.

## Abstract

We explore the effect of an inhomogeneous mass density field on frequencies and wave profiles of torsional Alfven oscillations in solar coronal loops. Dispersion relations for torsional oscillations are derived analytically in limits of weak and strong inhomogeneities. These analytical results are verified by numerical solutions, which are valid for a wide range of inhomogeneity strength. It is shown that the inhomogeneous mass density field leads to the reduction of a wave frequency of torsional oscillations, in comparison to that of estimated from mass density at the loop apex. This frequency reduction results from the decrease of an average Alfven speed as far as the inhomogeneous loop is denser at its footpoints. The derived dispersion relations and wave profiles are important for potential observations of torsional oscillations which result in periodic variations of spectral line widths. Torsional oscillations offer an additional powerful tool for a development of coronal seismology.