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.
The P1/P2 period ratio of transversal loop oscillations is currently used forthe diagnostics of longitudinal structuring of coronal loops as its deviationfrom 2 is intrinsically connected to the density scale-height along coronalloops and/or the sub-resolution structure of the magnetic field. The sametechnique can be applied not only to coronal structures, but also to otheroscillating magnetic structures. The oscillations in magnetic structures aredescribed by differential equations whose coefficients depend on thelongitudinal structure of the plasma. Using a variational principle written forthe transversal component of the velocity vector, developed earlier by McEwanet al. (2008), we investigate how the different temperature of the environmentcompared to the temperature of the magnetic structure will influence the P1/P2ratio for typical coronal and prominence conditions. The possible changes aretranslated into quantities that are used in the process of remote plasmadiagnostics in the solar atmosphere.
Authors: B. Orza, I. Ballai, R. Jain and K. Murawski
Publication Status: Accepted
Last Modified: 2011-11-23 13:24