The Damping of Coronal Loop Oscillations

Abstract

Motivated by recent Transition Region and Coronal Explorer (TRACE) observations of damped oscillations in coronal loops, we consider analytically the motion of an inhomogeneous coronal magnetic tube of radius a in a zero-plasma. An initially perturbed tube may vibrate in its kink mode of oscillation, but those vibrations are damped. The damping is due to resonant absorption, acting in the inhomogeneous regions of the tube, which leads to a transfer of energy from the kink mode to Alfvén (azimuthal) oscillations within the inhomogeneous layer. We determine explicitly the decrement (decay time À1 ) for a coronal flux tube whose plasma density varies only in a thin layer of thickness ' on the tube boundary. The effect of viscosity is also considered. We show that, in general, the problem involves two distinct timescales, À1 and ! À1 k R 1=3 , where R is the Reynolds number and ! k is the frequency of the kink mode. Under coronal conditions (when À1 5 ! À1 k R 1=3 ), the characteristic damping time of global oscillations is À1 . During this time, most of the energy in the initial perturbation is transferred into a resonant absorption layer of thickness of order ' 2 =a, with motions in this layer having an amplitude of order a=' times the initial amplitude. We apply our results to the observations, suggesting that loop oscillations decay principally because of inhomogeneities in the loop. Our theory suggests that only those loops with density inhomogeneities on a small scale (confined to within a thin layer of order a=! k in thickness) are able to support coherent oscillations for any length of time and so be observable. Loops with a more gradual density variation, on the scale of the tube radius a, do not exhibit pronounced oscillations.

Resonant damping of kink oscillations of cooling coronal magnetic loops

“…In view of this result the coincidence of the expressions for γ/ω given by Eqs. (81) and (83) with those in Goossens et al (2002) and Ruderman & Roberts (2002), respectively, is not surprising.…”

“…obtained by Ruderman & Roberts (2002). Note that both Goossens et al (2002) and Ruderman & Roberts (2002) considered magnetic tubes with the density that depends on r only, while in this paper we consider the density varying along the loop.…”

“…Note that both Goossens et al (2002) and Ruderman & Roberts (2002) considered magnetic tubes with the density that depends on r only, while in this paper we consider the density varying along the loop. Dymova & Ruderman (2006) showed that, under the assumption that ρ e /ρ i = const.…”

“…An important property of these oscillations was that they quickly damped with the characteristic damping time of the order of a few oscillation periods. Ruderman & Roberts (2002) suggested that this damping was due to resonant absorption related to the loop inhomogeneity in the radial direction. Using the thin tube thin boundary (TTTB) approximation they provided the estimate of the loop inhomogeneity using the observed damping time.…”

Resonant Alfvén waves in partially ionized plasmas of the solar atmosphere

“…For example, F = 4/π 2 for a linear profile and F = 2/π for a sinusoidal profile (Ruderman & Roberts 2002). We assume that k zR is approximately the same as in case without resonant damping (Eq.…”