Selective spatial damping of propagating kink waves due to resonant absorption

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 lowfrequency 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.

Resonant Alfvén waves in partially ionized plasmas of the solar atmosphere

“…This is the same conservation law as that in ideal and dissipative MHD (e.g., Sakurai et al 1991;Goossens et al 1995;Tirry & Goossens 1996). The Lagrangian displacement perpendicular to the magnetic field lines, ξ i⊥ = ξ iϕ B z − ξ iz B ϕ /B, is related to C A as …”

“…Functions F (τ) and G(τ) play here the role of the universal functions found in a number of previous investigations of resonant waves in both stationary and non-stationary states and for different dissipative processes (see, e.g., Mok & Einaudi 1985;Goossens et al 1995;Ruderman et al 1995;Tirry & Goossens 1996;Erdélyi et al 1995;Wright & Allan 1996;Ruderman & Wright 1999;Vanlommel et al 2002). A comprehensive review on the importance and properties of the universal F (τ) and G(τ) functions can be found in Goossens et al (2011).…”

“…(50) and (51)) are exactly the same for both propagating and standing modes. We refer the reader to, e.g., Tirry & Goossens (1996) and Vanlommel et al (2002) for details about the derivation of the jump conditions for standing quasi-modes.…”

“…In such cases, the multifluid description is a more suitable approach (see, e.g., Zaqarashvili et al 2011a,b). For resonant waves, perturbations develop very small length scales in the vicinity of the resonance position (see, e.g., Tirry & Goossens 1996;Ruderman & Wright 1999;Vasquez 2005;Terradas et al 2006), where multifluid effects may play a relevant role.…”

Statistical seismology of transverse waves in the solar corona

“…We interpret the spatial damping as attenuation due to resonant absorption Terradas et al 2010). As in the previous section, we want to perform seismology on the CoMP data in a statistical sense by fitting the data using statistical distributions for the loop cross-sectional equilibrium parameters, i.e.…”