Kink Oscillations of Expanding Coronal Loops in the Presence of Bulk Flow

Transverse coronal loop oscillations were first observed by TRACE in 1998 and reported by Aschwanden et al. (1999) and Nakariakov et al. (1999). One important property of transverse coronal loop oscillations is that they are usually strongly damped with the damping time being comparable with the oscillation period. However, sometimes this is not the case. At present, a generally accepted mechanism of this damping is resonant absorption. Observations show that very often oscillating coronal loops are in a highly dynamic state. In particular, they can cool quickly with a characteristic cooling time of the order of a few periods of kink oscillation. It was later showed theoretically that cooling causes amplification and may result in existence of oscillations for which amplitude does not vary in time. Although the coronal loop expansion is relatively small, the ratio of the loop crosssection radii at the apex and at the foot-points still can be about 1.5. These leads to particular interest the effect of expansion on kink oscillations. A coronal loop is modelled as a cylindrical magnetic flux tube. The tube consists of a core region and a thin transitional region at the tube boundary. The plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using multiscale expansions, the system of two equations describing the kink oscillations was derived. This model is studied both analytically by employing Wentzel- Kramer-Brillouin (WKB) method and numerically. We found out that the expansion of cross-section enhances the amplification of amplitude of kink oscillations and decreases the frequency of the oscillations. In addition we showed theoretically that a coronal loop cooling may lead to amplification of amplitude or non-monotonic amplitude profile even in presence of resonant damping. That result is particularly interesting from the coronal seismology point of view, since it is a good candidate for physical mechanism behind recent observation of kink oscillations of coronal loops with amplified and varying amplitudes.