# Contribution of observed multi frequency spectrum of Alfv\'en waves to coronal heating

## TL;DR

This study investigates whether phase-mixing of observed Alfvén wave spectra can heat the solar corona, concluding it is unlikely to be the primary heating mechanism but may influence small-scale structures.

## Contribution

The paper provides the first detailed 3D MHD simulation using observed wave spectra to assess coronal heating via phase-mixing, highlighting its insufficiency for maintaining coronal temperatures.

## Key findings

- Observed wave spectrum does not supply enough energy for coronal heating.
- Kelvin-Helmholtz instabilities are likely in coronal loops, affecting their lifetime.
- Phase-mixing alone is insufficient to heat the active region corona.

## Abstract

Whilst there are observational indications that transverse MHD waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfv\'en waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum for transverse oscillations in the corona. We aim to investigate the heating generated by phase-mixing of transverse oscillations triggered by buffeting of a coronal loop that follows from the observed coronal power spectrum as well as the impact of these persistent oscillations on the structure of coronal loops. We consider a 3D MHD model of an active region coronal loop and we perturb its footpoints with a 2D horizontal driver that represents a random buffeting motion of the loop footpoints. Our driver is composed of 1000 pulses superimposed to generate the observed power spectrum. We find that the heating supply from the observed power spectrum in the solar corona through phase mixing is not sufficient to maintain the million degree active region solar corona. We also find that the development of Kelvin-Helmholtz instabilities could be a common phenomenon in coronal loops that could affect their apparent life time. This study concludes that is unlikely that phase-mixing of Alfv\'en waves resulting from an observed power spectrum of transverse coronal loop oscillations can heat the active region solar corona. However, transverse waves could play an important role in the development of small scale structures.