Transverse kink oscillations of expanding coronal loops

Solar Physics and Space Plasma Research Centre (SP 2RC), Department of Applied MathematicsThe University of Sheffield, Sheffield S3 7RH, UK
e-mail: i.ballai@sheffield.ac.uk; b.orzai@sheffield.ac.uk

Received: 22 May 2012
Accepted: 24 July 2012

Abstract

Aims. We investigate the nature of transverse kink oscillations of loops expanding through the solar corona and examine how can oscillations be used to diagnose 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.

Methods. 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 evolves into an elliptical-shape loop from a semi-circular shape. The equations that describe the oscillations in an 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.

Results. 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 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 when the loop is expanding but not after it has reached its final stage.

Conclusions. The present study improves our understanding of the complexity of dynamical processes in the solar corona, in particular the changes of periods of kink oscillations due to temporal changes in the characteristics of the coronal loop. Our results clearly show that the problem of expansion of coronal loops can introduce significant changes in the period of oscillations, with consequences on the seismological diagnostics of the plasma and magnetic field.