# Energy transport and heating by torsional Alfv\'en waves propagating from the photosphere to the corona in the quiet Sun

## TL;DR

This study uses numerical simulations to analyze how torsional Alfvén waves propagate and dissipate energy in the quiet Sun's magnetic flux tubes, contributing to chromospheric heating and coronal energy balance.

## Contribution

It provides new insights into the frequency-dependent transmission and dissipation of torsional Alfvén waves in the quiet Sun, including empirical fits for use in coronal modeling.

## Key findings

- Only a small fraction (~10%) of wave energy reaches the corona.
- Maximum energy transmission occurs around 5 mHz for a 1 kG magnetic field.
- Different dissipation mechanisms dominate in various chromospheric layers.

## Abstract

In the solar atmosphere, Alfv\'en waves are believed to play an important role in the transfer of energy from the photosphere to the corona and solar wind, and in the heating of the chromosphere. We perform numerical computations to investigate energy transport and dissipation associated with torsional Alfv\'en waves propagating in magnetic flux tubes that expand from the photosphere to the corona in quiet-Sun conditions. We place a broadband driver at the photosphere that injects a wave energy flux of $10^7$ erg cm$^{-2}$ s$^{-1}$ and consider Ohm's magnetic diffusion and ion-neutral collisions as dissipation mechanisms. We find that only a small fraction of the driven flux, $\sim 10^5$ erg cm$^{-2}$ s$^{-1}$, is able to reach coronal heights, but it may be sufficient to partly compensate the total coronal energy loss. The frequency of maximal transmittance is $\sim 5$ mHz for a photospheric field strength of 1 kG and is shifted to smaller/larger frequencies for weaker/stronger fields. Lower frequencies are reflected at the transition region, while higher frequencies are dissipated producing enough heat to balance chromospheric radiative losses. Heating in the low and middle chromosphere is due to Ohmic dissipation, while ion-neutral friction dominates in the high chromosphere. Ohmic diffusion is enhanced by phase mixing because of the expansion of the magnetic field. This effect has the important consequence of increasing the chromospheric dissipation and, therefore, reducing the energy flux that reaches the corona. We provide empirical fits of the transmission coefficient that could be used as input for coronal models.