Alfvén wave propagation from the photosphere to the corona: Temporal evolution against stationary results

Recent observations have confirmed that a significant fraction of the coronal Alfvénic 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 Alfvén waves under the assumption of stationary propagation. Here, we relax that assumption and investigate the time-dependent propagation of Alfvén waves driven at the photosphere. Using an idealized chromospheric background model, we compared the coefficients obtained from time-dependent simulations with those derived under the stationary approximation. Additionally, we examined 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 Alfvén crossing times, and the reflectivity convergences well for frequencies below 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 increases 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.