Measuring the Coronal Magnetic Field with 2D Coronal Seismology: A Forward-Modeling Validation

TL;DR

The study validates 2D coronal seismology as a robust method for routine measurements of the coronal magnetic field by forward-modeling with a realistic MURaM simulation. It shows that combining wave-tracking-derived phase speed with Fe XIII line ratio–based densities and polarization-derived azimuth yields a LOS emissivity-weighted magnetic-field direction and magnitude that closely match the ground truth. A parameter-space analysis identifies an optimal regime characterized by a dimensionless quantity $\alpha$ around 0.5, guiding practical choices for wave-path length and filtering frequency in CoMP/UCoMP-like observations. The findings support the method's practical use for mapping the global coronal magnetic field and provide guidance on handling uncertainties and observational conditions in real data.

Abstract

In recent years, a two-dimensional (2D) coronal seismology technique applied to spectral-imaging data from the Coronal Multi-channel Polarimeter (CoMP) and UCoMP has enabled routine measurement of the global coronal magnetic field. The technique combines coronal transverse wave phase speed from Doppler measurements with electron densities from the Fe \sc{xiii}\rm{} 10798/10747 Å intensity ratio to infer the magnetic field strength, while the wave propagation directions from Doppler measurements trace the magnetic field direction. To validate the accuracy and robustness of this method, we use forward modeling of a MURaM simulation that produces open and closed magnetic structures with excited waves. From the synthetic Doppler velocity, Fe \sc{xiii}\rm{} infrared line intensities, and linear polarization signals, we apply the 2D coronal seismology technique to estimate the magnetic field strength and direction. A comparison with the simulation ground truth shows close agreement, indicating that the technique can recover the line-of-sight emissivity-weighted magnetic field direction and strength with high accuracy. We also perform a parameter-space analysis to quantify sensitivities of the method to parameter choice. These findings provide practical guidance for CoMP/UCoMP-like analysis and demonstrate that 2D coronal seismology can deliver reliable, LOS emissivity-weighted measurements of the coronal magnetic field from coronal wave observations.

Figures (10)

• Figure 1: Three-dimensional visualization of the simulated coronal emissivity of Fe xiii from the MURaM simulation. The three orthogonal planes show emissivity cross sections at the selected slices, revealing the structures of the 3D data cube. The X, Y and Z axes correspond to the horizontal and vertical directions in the simulation domain.
• Figure 2: Diagnostics of electron density from synthetic Fe xiii line intensities. (A-B) Synthetic Fe xiii 10747 Å and 10798 Å intensities, respectively. Both collisional excitation and height-dependent photo-excitation are included in the synthesis. (C) Diagnosed electron density from the intensity ratio of the synthetic lines. (D) The LOS emissivity-weighted electron density from the MURaM simulation, representing the ground truth. (E) A 2D histogram showing the strong agreement between the diagnosed result and the ground truth. (F) Examples of the ratio-density curves with photo-excitation at the heights of 1.05 solar radii (blue solid curves) and 1.30 solar radii (red solid curves), respectively, and the curve without photo-excitation (black dashed curve).
• Figure 3: The calculation of wave propagation angle (magnetic field direction). (A) The ground-truth of the magnetic field direction: LOS emissivity-weighted average of the POS direction of magnetic field in the simulation. The reference direction is the vertical (radial) direction. The angle between the local magnetic field direction and the reference direction is defined as negative for clockwise rotation from the reference direction, and positive otherwise. (B) Calculated wave propagation angle using the wave-tracking procedure, which traces the POS magnetic field direction. The sign convention is the same as in panel A. (C) A 2D histogram showing strong agreement between the calculated wave angle and the ground truth magnetic field direction.
• Figure 4: Comparison between the calculated wave propagation angle and magnetic azimuth. (A) Same as Fig. \ref{['fig:direction']}(B). This measurement is free of the Van Vleck ambiguity. (B) Similar to (A), but with Van Vleck ambiguity explicitly imposed to the calculated angles (angles $>54.7^{\circ}$ shifted by $-90^{\circ}$, angles $<54.7^{\circ}$ shifted by $+90^{\circ}$). (C) Magnetic azimuth derived from synthetic Stokes Q and U signals. The Van Vleck ambiguity is implicit in the azimuth. (D) A 2D histogram comparing the original wave propagation angle with the magnetic azimuth. In addition to the 1:1 ridge (blue line), two secondary ridges offset by $\pm 90^{\circ}$ arise from the Van Vleck ambiguity, which causes a $90^{\circ}$ rotation of the linear polarization when the magnetic field inclination exceeds the Van Vleck angle ($\sim 54.7^{\circ}$). (E) Similar to (D), but using the wave angle with Van Vleck ambiguity explicitly imposed. The two parameters now show close agreement.
• Figure 5: Calculation of wave phase speed. (A) One snapshot of the Fe xiii Doppler velocity image from the simulation. The blue line marks a representative long wave path. (B) Unfiltered Doppler velocity time-distance diagram derived along the wave path in panel A, showing signatures of counter-propagating waves components. (C) Doppler velocity time-distance diagram after isolating the prograde wave component. (D) Filtered version of panel C using the selected filtering frequency. Distinct inclined Doppler velocity ridges representing the propagating waves are clearly visible.