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Damped Coronal Loop Oscillations: Time-dependent Results

The excitation and damping of transverse coronal loop oscillations is studied using a one-dimensional model of a line-tied cylindrical loop. By solving the time-dependent magnetohydrodynamic (MHD) equations, we show how an initial disturbance produced in the solar corona induces kink-mode oscillations. We analyze the effect of the disturbance on a loop with a nonuniform boundary layer and investigate the damping of such a disturbance due to resonant absorption. We find that the period and attenuation time of the time-dependent results agree with the calculations of the corresponding quasi-mode (i.e., the kink mode resonantly coupled to Alfvén modes) and that the resonant absorption mechanism is capable of damping the oscillations almost immediately after the excitation. We study in detail the behavior of solutions in the inhomogeneous layer and show how the energy of the global oscillation is converted into torsional oscillations in the inhomogeneous layer. In addition, we estimate that the amplitude of the torsional oscillations is, for large magnetic Reynolds numbers and for thick layers, between 4 and 6 times the amplitude of the initial transverse motions. The implications of these results and their relationship with the observations are discussed.