Damping of coronal loop oscillations: resonant absorption at work

Motivated by recent 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 beta plasma. An initially perturbed tube may vibrate in its kink mode of oscillation with the frequency w(k) 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 azimuthal oscillations within the inhomogeneous layer. We determine explicitly the decay decrement gamma for a coronal flux tube whose plasma density varies in a thin layer of thickness l << a on the tube boundary. We apply our results to the observations, suggesting that loop oscillations decay principally because of inhomogeneities in the loop. It follows from our theory that only those loops with density inhomogeneities on a small scale (confined to within a thin layer of order agamma/w(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 a scale comparable with the tube radius a, do not exhibit pronounced oscillations.