[Paper Review] Investigating `dark' energy in the solar corona using forward modeling of MHD waves

Vaibhav Pant, Norbert Magyar+2 more|arXiv (Cornell University)|Jun 26, 2019

Solar and Space Plasma DynamicsPhysics and Astronomy67 references46 citations

TL;DR

This study uses 3D magnetohydrodynamic (MHD) simulations to demonstrate that the apparent discrepancy between low Doppler velocity amplitudes and high non-thermal line widths in the solar corona—previously attributed to 'dark' energy—arises from line-of-sight (LOS) superposition of unresolved transverse MHD waves. The simulations show that only 0.2–1% of true wave energy is captured in Doppler velocities, with the remainder hidden in non-thermal line widths, thus ruling out the need for an additional unknown energy source.

ABSTRACT

It is now well established that the Alfv\'enic waves are ubiquitous in the solar corona. However, the Alfv\'enic wave energy estimated from the Doppler velocity measurements in the corona was found to be four orders of magnitude less than that estimated from non-thermal line widths. McIntosh & De Pontieu (2012) suggested that this discrepancy in energy might be due to the line-of-sight (LOS) superposition of the several oscillating structures, which can lead to an underestimation of the Alfv\'enic wave amplitudes and energies. McIntosh & De Pontieu (2012) termed this coronal `dark' or `hidden' energy. However, their simulations required the use of an additional, unknown source of Alfv\'enic wave energy to provide agreement with measurements of the coronal non-thermal line widths. In this study, we investigate the requirement of this unknown source of additional `dark' energy in the solar corona using gravitationally stratified 3D magnetohydrodynamic (MHD) simulations of propagating waves. We excite the transverse MHD waves and generate synthetic observations for the Fe XIII emission line. We establish that the LOS superposition greatly reduces the Doppler velocity amplitudes and increases the non-thermal line widths. Importantly, our model generates the observed wedge-shaped correlation between Doppler velocities and non-thermal line widths. We find that the observed wave energy is only 0.2-1\% of the true wave energy which explains 2-3 orders of magnitude of the energy discrepancy. We conclusively establish that the true wave energies are hidden in the non-thermal line widths. Hence, our results rule out the requirement for an additional `dark' energy in the solar corona.

Motivation & Objective

• To investigate the origin of the energy discrepancy between Doppler velocity measurements and non-thermal line widths in the solar corona.
• To test whether line-of-sight (LOS) superposition of unresolved MHD wave motions can explain the observed wedge-shaped correlation between Doppler velocities and non-thermal line widths.
• To determine whether an additional, unknown 'dark' energy source is required to explain coronal wave energy budgets, as previously suggested.
• To assess the role of gravitational stratification and wave damping in shaping observed line width profiles in synthetic CoMP-like observations.
• To establish a physical link between true wave amplitudes and non-thermal line broadening without introducing artificial energy components.

Proposed method

• Conducting gravitationally stratified 3D MHD simulations of propagating transverse Alfvénic waves in a coronal-like magnetic flux tube.
• Exciting transverse MHD waves at the base of the simulation domain (50 Mm in height) with a prescribed wave driver to mimic coronal wave excitation.
• Generating synthetic observations of the Fe XIII 10749 Å emission line using forward modeling techniques, including radiative transfer and ionization equilibrium calculations.
• Computing synthetic Doppler velocity fluctuations and non-thermal line widths along the line-of-sight (LOS) to mimic CoMP observations.
• Comparing simulated Doppler velocity amplitudes and non-thermal line widths with observed correlations, particularly the wedge-shaped pattern.
• Performing control simulations without gravitational stratification to isolate the role of density gradients and wave reflection in non-thermal broadening.

Experimental results

Research questions

• RQ1 To what extent does line-of-sight (LOS) superposition of unresolved transverse MHD wave motions explain the observed discrepancy between Doppler velocity amplitudes and non-thermal line widths in the solar corona?
• RQ2 Can the wedge-shaped correlation between Doppler velocity fluctuations and non-thermal line widths—observed in CoMP data—be reproduced using realistic 3D MHD simulations without adding an artificial energy source?
• RQ3 What fraction of the true Alfvén wave energy is actually captured in Doppler velocity measurements, and where is the remainder hidden?
• RQ4 Is wave damping via resonant absorption or numerical viscosity responsible for the observed leveling-off of non-thermal line widths with height, or is it primarily due to LOS projection effects?
• RQ5 Does photoionization significantly affect the synthetic Fe XIII line profiles in the simulation domain, particularly near 1.07 R⊙?

Key findings

• The LOS superposition of multiple oscillating coronal structures reduces Doppler velocity amplitudes by a factor of 100–500, leading to an underestimation of wave energy by 99–99.8%.
• Only 0.2–1% of the true Alfvén wave energy flux is captured in Doppler velocity fluctuations, which explains 2–3 orders of magnitude of the observed energy discrepancy.
• The wedge-shaped correlation between root mean square (rms) Doppler velocities and non-thermal line widths is successfully reproduced in the simulations without requiring an additional unknown energy source.
• Non-thermal line widths increase with height initially and then level off due to wave reflection from density gradients, not due to wave damping or energy loss mechanisms.
• The inclusion of photoionization effects in the Fe XIII line modeling does not alter the results, as collisional excitation dominates in the simulation domain (up to 1.07 R⊙).
• The study conclusively rules out the need for an additional 'dark' energy source in the solar corona, as the missing energy is fully accounted for by unresolved wave amplitudes in the LOS projection.