# Alfven wave propagation from the photosphere to the corona: temporal evolution against stationary results

## TL;DR

This study compares time-dependent and stationary models of Alfven wave propagation from the photosphere to the corona, showing that stationary assumptions are generally valid with sufficient spatial resolution and simulation time.

## Contribution

It introduces a time-dependent simulation approach to analyze Alfven wave transmission, reflection, and absorption, validating stationary models under realistic conditions.

## Key findings

- Time-dependent transmission converges to stationary values after few crossing times.
- Reflectivity is accurately captured for frequencies below 30 mHz.
- Absorption coefficients align at high frequencies, but differ at low frequencies.

## Abstract

Recent observations have confirmed that a significant fraction of the coronal Alfvenic wave spectrum originates in the photosphere. These waves travel from the photosphere to the corona, overcoming the barriers of reflection and dissipation posed by the chromosphere. Previous studies have theoretically calculated the chromospheric reflection, transmission, and absorption coefficients for pure Alfven waves under the assumption of stationary propagation. Here, we relax that assumption and investigate the time-dependent propagation of Alfven waves driven at the photosphere. Using an idealized chromospheric background model, we compare the coefficients obtained from time-dependent simulations with those derived under the stationary approximation. Additionally, we examine the impact of the spatial resolution in the numerical simulations. Considering a spatial resolution of 250 m, we find that the time-dependent transmission coefficient converges to the stationary value across the entire frequency range after only a few chromospheric Alfven crossing times, while the reflectivity displays a good convergence for frequencies lower than 30 mHz. The absorption coefficient also converges for wave frequencies above 1 mHz, for which chromospheric dissipation is significant. In contrast, at lower frequencies, wave energy dissipation is weak and the time-dependent simulations typically overestimate the absorption. Inadequate spatial resolution artificially enhances the chromospheric reflectivity, reduces wave transmission to the corona, and poorly describes the wave energy absorption. Overall, the differences between the stationary and time-dependent approaches are only minor and gradually decrease as spatial resolution and simulation time increase, which reinforces the validity of the stationary approximation.