The P1/P2 period ratio for kink oscillations of an asymmetrical coronal loop

Abstract

AbstractHere we investigate the effect of asymmetry of coronal loops on the P1/P2 period ratio of kink transverse loop oscillations. The P1/P2 period ratio technique is used for the diagnostics of the longitudinal structuring of coronal loops as its deviation from the canonical value of 2 is related to the density scale‐height along coronal loops. The analysis is carried out by calculating the period of the fundamental and first overtone of magnetohydrodynamic (MHD) kink oscillations for loops with different asymmetry degrees and density stratification. Taking into account the stratification and the deviation of the loop from a semi‐circular shape, we derive the equation that describes the dynamics of transversal kink oscillations and we use a numerical method to estimate the ratio of periods of oscillations. Solving numerically the problem, we show that the P1/P2 period ratio can change under the influence of loop asymmetry, e.g. for an asymmetrical loop with the displacement parameter α = 0.6, the change can reach 5–8%, i.e. density scale‐height estimations are overestimated by this amount. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)