Investigating “Dark” Energy in the Solar Corona Using Forward Modeling of MHD Waves

Abstract

It is now well established that the Alfvénic waves are ubiquitous in the solar corona. However, the Alfvénic 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 Alfvénic 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 Alfvénic 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.

Oscillation and Evolution of Coronal Loops in a Dynamical Solar Corona

“…Previous studies have demonstrated that the damping of kink oscillations by resonant absorption is also not sensitive to loops being multi-stranded (Terradas et al, 2008b;Pascoe et al, 2011). However, the presence of such structuring is of interest since it can lead to a significant underestimation of the wave energy estimated using Doppler measurements (De Moortel and Pascoe, 2012;Pant et al, 2019) or an overestimation of the broadness of DEM spectra (Van Doorsselaere et al, 2018). Due to LOS integration of optically thin EUV emission it is difficult to interpret fine structure in transverse intensity profiles, particularly when using a single channel as may be the case for coronal loops which are often identifiable only in the 171 Å channel of SDO/AIA.…”

“…A transfer of wave energy from collective kink motions to localized azimuthal perturbations (m = 1 Alfvén waves) will appear as a damping of the periodic loop displacement. The azimuthal motions will typically appear as unresolved Doppler velocity perturbations due to line-of-sight (LOS) integration of multiple waves and structures (e.g., De Moortel and Pascoe, 2012;Pant et al, 2019). Although this transfer is a linear and ideal process, subsequent phase-mixing of the Alfvén waves in the inhomogeneous layer can generate small spatial scales which enhance dissipative processes such as viscosity and resistivity (e.g., Pagano and De Moortel, 2017;Pagano et al, 2018).…”

Forward modelling of MHD waves in braided magnetic fields

“…In practice, estimates of the total kinetic energy are likely to be between these two cases and could underestimate the true kinetic energy by an order of magnitude, where some of this energy will be represented by enhanced non-thermal line widths (e.g. McIntosh & De Pontieu 2012;Pant et al 2019). Of course, additional uncertainties in the density profile and the LOS integration length may further increase the uncertainty in the energy measurements.…”

“…McIntosh & De Pontieu 2012). Similarly, Pant et al (2019) investigate the discrepancy between the observed wave energy, calculated from the Doppler velocities, and the true wave energy and find that the additional energy is present in the non-thermal line widths. Figure 22 shows the evolution of the average line width, calculated using the full-width-half-maximum (FWHM) of the Fig.…”

Non-thermal line broadening due to braiding-induced turbulence in solar coronal loops

“…More quantitative predictions of the line profiles have recently been developed based on waves injected into the loophowever, they fail to simultaneously reproduce both observed temperatures and non-thermal broadening. On the one hand, 3D MHD models that excite transverse MHD waves through velocity drivers with prescribed amplitudes find that the line-ofsight superposition of large-amplitude Alfvénic waves in the coronal loops could result in a large non-thermal broadening of the spectral lines (Pant et al 2019). However, those models do not simultaneously heat the plasma with those waves to the required temperatures.…”