Investigating coronal wave energy estimates using synthetic non-thermal line widths

TL;DR

This study investigates the relationship between non-thermal line widths and wave amplitudes in the solar corona using 3D MHD simulations, revealing that the ratio varies significantly and challenges previous assumptions for estimating wave energy.

Contribution

The paper demonstrates that the ratio between non-thermal line widths and wave amplitudes is highly variable, questioning the robustness of previous methods for coronal wave energy estimation.

Findings

The ratio depends on line-of-sight angles, velocity, interference, and exposure time.

Different models yield varying ratios, some matching previous claims, others deviating.

A single ratio value cannot reliably estimate wave energy across different conditions.

Abstract

Aims. Estimates of coronal wave energy remain uncertain as a large fraction of the energy is likely hidden in the non-thermal line widths of emission lines. In order to estimate these wave energies, many previous studies have considered the root mean squared wave amplitudes to be a factor of $\sqrt{2}$ greater than the non-thermal line widths. However, other studies have used different factors. To investigate this problem, we consider the relation between wave amplitudes and the non-thermal line widths within a variety of 3D magnetohydrodynamic (MHD) simulations. Methods. We consider the following 3D numerical models: Alfv\'en waves in a uniform magnetic field, transverse waves in a complex braided magnetic field, and two simulations of coronal heating in an arcade. We applied the forward modelling code FoMo to generate the synthetic emission data required to analyse the non-thermal line widths. Results. Determining a single value for the ratio between the non-thermal line widths and the root mean squared wave amplitudes is not possible across multiple simulations. It was found to depend on a variety of factors, including line-of-sight angles, velocity magnitudes, wave interference, and exposure time. Indeed, some of our models achieved the values claimed in recent articles while other more complex models deviated from these ratios. Conclusions. To estimate wave energies, an appropriate relation between the non-thermal line widths and root mean squared wave amplitudes is required. However, evaluating this ratio to be a singular value, or even providing a lower or upper bound on it, is not realistically possible given its sensitivity to various MHD models and factors. As the ratio between wave amplitudes and non-thermal line widths is not constant across our models, we suggest that this widely used method for estimating wave energy is not robust.