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

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.

💡 Research Summary

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This paper presents a comprehensive validation of the two‑dimensional (2D) coronal seismology technique that has recently been applied to spectral‑imaging data from the Coronal Multi‑channel Polarimeter (CoMP) and its upgraded version, UCoMP. The method combines measurements of transverse wave phase speed, derived from Doppler‑velocity time series, with electron density estimates obtained from the intensity ratio of the Fe XIII 10798 Å and 10747 Å infrared lines. The wave propagation direction, inferred from the same Doppler data, is used as a proxy for the plane‑of‑sky magnetic‑field direction, while the phase speed together with the density yields the magnetic‑field strength via the kink‑wave dispersion relation.

To test the accuracy and robustness of this approach under realistic solar‑corona conditions, the authors employ forward modeling based on a state‑of‑the‑art MURaM simulation that includes the upper convection zone, photosphere, chromosphere, and lower corona. The simulation domain (≈295 × 295 × 197 Mm) contains both open flux tubes and closed loops, forming a pseudo‑streamer topology with a magnetic null point near 80 Mm height. Convective motions naturally excite transverse (kink‑like) waves throughout the volume; no artificial boundary drivers are imposed, ensuring that the wave field mimics that of the real Sun.

Synthetic observables are generated at the native simulation resolution. Line intensities for Fe XIII 10747 Å and 10798 Å are computed using CHIANTI v11 contribution functions that include collisional and height‑dependent photo‑excitation effects. Doppler velocities are obtained as emissivity‑weighted line‑of‑sight (LOS) averages, and linear polarization (Stokes Q and U) is synthesized with the Gibson forward‑modeling package to provide an independent magnetic‑azimuth measurement.

Applying the exact 2D coronal seismology pipeline used on CoMP/UCoMP data, the authors first retrieve electron densities from the synthetic line‑ratio maps, then perform a wave‑tracking algorithm on the Doppler series to extract propagation directions and phase speeds. The magnetic‑field strength is calculated from the relation (B = v_k \sqrt{\mu \langle \rho \rangle}), where (\langle \rho \rangle) is the LOS‑averaged density. The inferred magnetic‑field vectors are then compared with the LOS‑integrated “ground‑truth” fields from the simulation.

The comparison shows excellent agreement: the recovered field strength deviates by less than 5 % on average (maximum ≈ 9 %) and the inferred azimuth differs by only 6–7° on average (worst‑case ≈ 12°). These errors are significantly smaller than those reported in earlier validation studies that used highly idealized flux‑tube models. Importantly, the method remains accurate even in regions where the Alfvén speed changes rapidly (near the null point) and where field lines are strongly curved, demonstrating its applicability to a wide range of coronal environments.

A systematic parameter‑space study explores the sensitivity of the results to three key choices: (1) the temporal window length used in the wave‑tracking cross‑correlation, (2) the high‑frequency cutoff applied to the Doppler time series, and (3) the signal‑to‑noise ratio (SNR) required for reliable line‑ratio density diagnostics. Short windows (< 3 min) lead to unstable phase‑speed estimates and increase magnetic‑field errors to ≈ 15 %; optimal windows of 5–7 min provide stable results. A high‑frequency cutoff around 0.5 mHz efficiently suppresses noise without erasing genuine wave power. Finally, an SNR of at least 20 in the Fe XIII intensity ratio is necessary to keep density‑related errors below 5 %; lower SNR values cause density over‑ or under‑estimation, propagating into magnetic‑field errors of 20 % or more.

The authors discuss limitations. In LOSs that contain multiple temperature components or several overlapping flux tubes, the linear‑polarization azimuth can differ from the wave‑propagation direction by up to 10–20°, reflecting the averaging inherent in the measurement. At very high altitudes (> 150 Mm) where the Alfvén speed gradient is steep, the phase‑speed extraction becomes less reliable, suggesting that complementary diagnostics (e.g., additional spectral lines such as Fe XIV) could improve robustness. Moreover, the simulation’s spatial resolution (384 km) exceeds that of current CoMP/UCoMP observations, implying that small‑scale structures will be further averaged in real data; however, the validation confirms that the technique still yields the correct LOS‑weighted magnetic field.

In conclusion, the study provides the first rigorous, forward‑modeling validation of 2D coronal seismology under realistic, mixed open‑closed magnetic configurations with naturally excited waves. It demonstrates that the method can reliably retrieve LOS‑emissivity‑weighted magnetic‑field strength and direction, quantifies the optimal parameter regime for its application, and outlines the remaining challenges. These results give strong confidence that routine, global coronal magnetic‑field maps derived from CoMP/UCoMP observations are physically meaningful, opening new avenues for data‑driven coronal modeling, space‑weather forecasting, and the interpretation of forthcoming high‑resolution DKIST coronal polarimetry.