Selective spatial damping of propagating kink waves due to resonant absorption

¹ Departament de Física, Universitat de les Illes Balears, Spain
e-mail: jaume.terradas@uib.es
² Centre Plasma Astrophysics and Leuven Mathematical Modeling and Computational Science Centre, Katholieke Universiteit Leuven, Leuven, 3001, Belgium
e-mail: Marcel.Goossens@wis.kuleuven.be; Gary.Verth@wis.kuleuven.be

Received: 22 April 2010
Accepted: 11 August 2010

Abstract

Context. There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona.

Aims. We show that resonant absorption provides a simple explanation to the spatial damping of these waves.

Methods. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes, which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated in the thin tube (TT) approximation, valid for coronal waves. This assumption is relaxed in the case of chromospheric tube waves and filament thread waves.

Results. The damping length of propagating kink waves due to resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies, the damping length is exactly inversely proportional to frequency, and we denote this as the TGV relation. When moving to high frequencies, the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours low-frequency waves and can efficiently remove high-frequency waves from a broad band spectrum of kink waves. The efficiency of the damping due to resonant absorption depends on the properties of the equilibrium model, in particular on the width of the non-uniform layer and the steepness of the variation in the local Alfvén speed.

Conclusions. Resonant absorption is an effective mechanism for the spatial damping of propagating kink waves. It is selective because the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Kink wave trains travelling along, e.g., coronal loops, will therefore have a greater proportion of the high-frequency components dissipated lower down in the atmosphere. This could have important consequences for the spatial distribution of wave heating in the solar atmosphere.