Alfv\'en wave propagation in the partially ionized lower solar atmosphere: a test of the single-fluid approximation

TL;DR

This study compares single-fluid MHD and multi-fluid models of Alfvén wave propagation in the lower solar atmosphere, finding that the simpler single-fluid approach is generally accurate with minor discrepancies.

Contribution

It provides a validation of the single-fluid approximation for Alfvén waves in the chromosphere by comparing it with a more detailed multi-fluid model.

Findings

Single-fluid and multi-fluid models produce nearly identical results for wave energy flux and transmission.

The single-fluid model slightly overestimates energy flux reaching the corona by about 5%.

The single-fluid model underestimates plasma heating rate near 500 km altitude by a factor of two.

Abstract

Alfv\'en waves are widely believed to play an important role in the transport of energy from the solar photosphere to the corona through the partially ionized chromosphere. In previous work, the properties of torsional Alfv\'en waves were theoretically studied using a multi-fluid model. Here, we compare those multi-fluid results with those obtained using the single-fluid magnetohydrodynamic approximation, as a way to assess the performance of the latter in the context of Alfv\'enic waves in the lower solar atmosphere. We consider a broadband photospheric driver that excites torsional Alfv\'en waves with frequencies ranging from 0.1 mHz to 300 mHz. These waves propagate upwards to the corona along a magnetic flux tube expanding with height. For both models, we compare the energy flux, chromospheric reflection, transmission and absorption coefficients, and the associated heating rates. In general, the results are almost identical in the two models, with the exception of two minor differences: (1) the net energy flux reaching the corona is approximately 5% larger in the single-fluid model, mainly owing to the higher reflectivity found in the multi-fluid model for wave frequencies exceeding 10 mHz; and (2) in a narrow region around 500 km above the photosphere, the single-fluid model underestimates the plasma heating rate due to ion-neutral damping by about a factor of two compared with the multi-fluid model. Both discrepancies arise from the approximate treatment of the ion-neutral drift in the single-fluid model and are expected to have a very limited impact on practical applications.