Fast kink modes of longitudinally stratified coronal loops

¹ Institute for Advanced Studies in Basic Sciences, Gava Zang, PO Box 45195-1159, Zanjan, Iran e-mail: hsafary@isbs.ac.ir
² Department of Physics, Zanjan University, Zanjan, Iran

Received: 9 July 2006
Accepted: 17 April 2007

Abstract

Aims. We investigate the standing kink modes of a cylindrical model of coronal loops. The density is stratified along the loop axis and changes discontinuously at the surface of the cylinder. The periods and mode profiles are studies with their deviation from those of the unstratified loops. The aim is to extract information on the density scale heights prevailing in the solar corona.

Methods. The problem is reduced to solving a single second-order partial differential equation for , the longitudinal component of the Eulerian perturbations of the magnetic field. This equation, in turn, is separated into two second-order ordinary, differential equations in r and z that are, however, connected through a dispersion relation between the frequencies and the longitudinal wave numbers. In the thin tube approximation, the eigensolutions are obtained by a perturbation technique, where the perturbation parameter is the density stratification parameter. Otherwise the problem is solved numerically.

Results. 1) On functional dependencies of the dispersion relation the radial wave number is independent of the longitudinal stratification. 2) We verify the earlier computational finding that the first overtone frequencies increase with increasing stratification and the observational finding (from analysis of TRACE data) that the ratio of the first to the fundamental overtone frequency decreases with increasing stratification. The method we use to arrive at these conclusions, however, is more analytical than computational, and yet our numerical results agree with the earlier results. 3) The mode profiles depart from the sinusoidal mode profiles of the unstratified loops. This departure and its dependence on the scale height is obtained, and might serve to determine scale heights once high resolution data become available.