Contribution of phase-mixing of Alfven waves to coronal heating in multi-harmonic loop oscillations

Context. Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through magnetohydrodynamics (MHD) seismology and a potential test of coronal heating through the phase mixing of Alfven waves. In particular, recent observations show that standing oscillations of loops often involve higher harmonics in addition to the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfven waves. Aims. We investigate the consequences for wave-based coronal heating of higher harmonics and which coronal heating observational signatures we may use to infer the presence of higher harmonic kink oscillations. Methods. We performed a set of non-ideal MHD simulations in which we modelled the damping of the kink oscillation of a flux tube via mode coupling. We based our MHD simulation parameters on the seismological inversion of an observation for which the first three harmonics are detected. We studied the phase mixing of Alfven waves, which leads to the deposition of heat in the system, and we applied seismological inversion techniques to the MHD simulation output. Results. We find that the heating due to phase mixing of Alfven waves triggered by the damping of kink oscillation is relatively small. We can however illustrate how the heating location drifts from subsequent damping of lower order harmonics. We also address the role of higher order harmonics and the width of the boundary shell in the energy deposition. Conclusions. We conclude that the coronal heating due to phase mixing does not seem to provide enough energy to maintain the thermal structure of the solar corona even when multi-harmonic oscillations are included; these oscillations play an inhibiting role in the development of smaller scale structures.