Transverse kink oscillations of expanding coronal loops

TL;DR

This paper studies how the expansion of coronal loops affects transverse kink oscillations, providing analytical and numerical insights into how these oscillations can diagnose plasma and magnetic field parameters in the solar corona.

Contribution

It introduces a detailed analysis of how loop expansion influences oscillation periods and ratios, using WKB and perturbation methods for different loop shapes and expansion stages.

Findings

Oscillation periods increase with loop expansion, especially in structured corona.

Period ratios P1/P2 are affected by the expansion, impacting coronal stratification diagnostics.

Expansion effects are significant only during the expansion process, not at the final stage.

Abstract

We investigate the nature of transverse kink oscillations of loops expanding through the solar corona and how can oscillations be used to diagnose the plasma parameters and the magnetic field. In particular, we aim to analyse how the temporal dependence of the loop length (here modelling the expansion) will affect the P1 /P2 period ratio of transverse loop oscillations. Due to the uncertainty of the loop's shape through its expansion, we discuss separately the case of the loop that maintains its initial semi-circular shape and the case of the loop that from a semi-circular shape evolve into an elliptical shape loop. The equations that describe the oscillations in expanding flux tube are complicated due to the spatial and temporal dependence of coefficients. Using the WKB approximation we find approximative values for periods and their evolution, as well as the period ratio. For small values of time (near the start of the expansion) we can employ a regular perturbation method to find approximative relations for eigenfunctions and eigenfrequencies. Using simple analytical and numerical methods we show that the period of oscillations are affected by the rising of the coronal loop. The change in the period due to the increase in the loop's length is more pronounced for those loops that expand into a more structured (or cooler corona). The deviation of periods will have significant implications in determining the degree of stratification in the solar corona. The effect of expansion on the periods of oscillations is considerable only in the process of expansion of the loop but not when it reached its final stage.