Direct measurement of the vector magnetic field of the solar corona remains one of the central unsolved measurement problems in solar physics. Dima, Kuhn and Berdyugina (2016) proposed a dual-line Hanle diagnostic combining linear polarimetry of the permitted He I 1083 nm line (unsaturated Hanle regime, sensitive to both direction and strength of fields of order 0.1-10 G) with linear polarimetry of a near-infrared forbidden coronal line such as Si X 1430.1 nm or Fe XIII 1074.7 nm (saturated Hanle regime, constraining direction only), and demonstrated, in synthetic test inversions computed with Hanle-effect model grids, that the combination constrains the coronal field to four degenerate solutions. Follow-up work in the ensuing decade spans multi-line forbidden-line inversions (Dima and Schad 2020; the CLEDB algorithm 2022), first DKIST/Cryo-NIRSP infrared coronal spectroscopy (2023-2024), MHD-based spectropolarimetric synthesis (2025), and seismology-assisted inversions (2026). All threads are active, but the dual-line scheme itself remains unvalidated: no co-spatial He I 1083 nm plus forbidden-line coronal polarimetry has been published, the quantitative accuracy required of independent constraints (e.g. electron density) to select the correct solution among the degenerate ones has not been determined, and inversion of the forbidden-line polarization amplitude (shaped by collisional depolarization) for electron density has not been demonstrated. The problem posed is to establish the dual-line Hanle diagnostic as a validated method for coronal vector magnetometry by testing the co-spatiality assumption, quantifying and breaking its degeneracies, determining whether amplitude-based density inversion is feasible, and validating the end-to-end inversion on real coronal observations.

Background

The solar corona is a magnetically dominated plasma, yet the vector magnetic field of the corona itself is essentially unmeasured: the field is intrinsically weak (of order 44 G at 0.1R⊙0.1R_\odot above an active region, generally 0.10.1-1010 G at coronal heights) and coronal emission lines are so strongly thermally broadened that the Zeeman splitting they produce in circular polarization (Stokes VV, the parameter describing circular polarization) is typically only 10−410^{-4} of the line intensity, buried beneath scattering-induced linear polarization signals (Stokes QQ and UU, which parameterize linear polarization) of order 10−210^{-2}. The Hanle effect offers an alternative: resonantly scattered line radiation is linearly polarized by the scattering geometry, and a weak magnetic field modifies both the degree and the direction of that polarization. The Hanle effect is called saturated when the Larmor precession rate of the excited atomic level greatly exceeds its inverse radiative lifetime — the polarization then depends on the field direction but not its strength — and unsaturated in the intermediate regime where the polarization encodes both direction and strength. Near-infrared forbidden coronal lines, produced by magnetic-dipole (M1) transitions (transitions forbidden in the electric-dipole approximation, hence called forbidden lines) of highly ionized species such as Fe XIII (1074.7 and 1079.8 nm) and Si X (1430.1 nm), have very long radiative lifetimes and therefore form in the saturated Hanle regime: their linear polarization traces field direction and topology only. Kuhn, Penn and Mann (1996) discovered that the permitted He I 1083 nm triplet is present in emission far off the solar limb; because this line has a much shorter radiative lifetime, it operates in the unsaturated Hanle regime for coronal field strengths, so its polarization is sensitive to both direction and strength. Dima, Kuhn and Berdyugina (2016) therefore proposed a dual-line diagnostic: combine concurrent linear polarimetry of He I 1083 nm and a forbidden line (Si X 1430.1 nm as the primary example) and invert the two sets of Stokes QQ, UU measurements jointly with Hanle-effect models to recover the full vector magnetic field, targeting the 0.10.1-1010 G range poorly accessible to Zeeman methods. Three structural difficulties identified in that paper frame the open problem. First, the inversion is degenerate: the classical line-of-sight reflection degeneracy (two solutions related by mirroring the field vector through the observer's line of sight) combines with a further two-fold ambiguity that splits the candidate solutions into two pairs, each pair sharing a unique field strength; this further ambiguity originates in the Van Vleck ambiguity (a 180∘180^\circ-type ambiguity in field inclination whose character flips at the Van Vleck angle θVV=54.7∘\theta_{VV}=54.7^\circ between the field and the solar-radius direction through the scattering point, where the scattering polarization plane rotates by 90∘90^\circ) when the inclination lies inside the Van Vleck region, and in the unsaturated Hanle behavior of the permitted line when it lies outside that region, leaving four discrete candidate solutions even for high signal-to-noise data. Second, the forbidden-line polarization amplitude is suppressed by collisional depolarization — isotropic electron collisions redistribute the population of the magnetically aligned upper level in a density-dependent way that is difficult to model — so the original algorithm discarded the amplitude information, which in principle also encodes the electron density. Third, the method assumes the permitted (He I) and forbidden (Fe XIII, Si X) emitters are co-spatial in the plane of the sky or at least sample the same local magnetic field; this is untested because the lines form in different temperature regimes (the coronal He I polarization is generated by resonant scattering of photospheric radiation, while its metastable triplet reservoir is populated primarily through electron collisional excitation of singlet-state neutral helium in the higher-density K-corona, the electron-scattering component of the white-light corona, whereas Si X and Fe XIII emit from ∼1.3\sim1.3-1.61.6 MK plasma) and the corona is optically thin, so each line of sight integrates contributions from many structures. The method is motivated by, and its feasibility now hinges on, new instrumentation: the Daniel K. Inouye Solar Telescope (DKIST), whose Cryogenic Near-Infrared Spectropolarimeter (Cryo-NIRSP) performs coronagraphic spectropolarimetry of exactly these forbidden IR lines, and the CoMP/UCoMP instruments at the Mauna Loa Solar Observatory, which have provided routine Fe XIII 1074.7/1079.8 nm polarimetry of the off-limb corona since the mid-2000s.

Problem Statement

The problem is to establish the infrared dual-line Hanle diagnostic — the joint inversion of co-spatial linear polarimetry of the permitted He I 1083 nm line and at least one near-infrared forbidden coronal line (e.g. Si X 1430.1 nm and/or Fe XIII 1074.7 nm) — as a validated method for measuring the vector magnetic field of the solar corona in the ∼0.1\sim0.1-1010 G range. The components of this single objective, as identified by the source work, are: (1) Co-spatiality: analyze coordinated, quasi-simultaneous polarimetric observations of He I 1083 nm and the forbidden line(s) in the same coronal structures, and determine the spatial and formation-depth relationship between the He I coronal emission and the forbidden-line emitters well enough to state when the co-spatiality or same-local-field assumption holds and when it fails. (2) Degeneracy: characterize the degenerate solution set of the dual-line inversion (the classical line-of-sight reflection degeneracy combined with the Van Vleck / unsaturated-Hanle ambiguity that splits the solutions into two pairs) and determine, quantitatively, what independent information — electron-density estimates of specified accuracy, 3D MHD forward models constrained by photospheric magnetic maps, photospheric polarity constraints, or multi-perspective/tomographic observations over solar rotation — suffices to select the physically correct solution, demonstrating that selection on real or realistically simulated data. (3) Amplitude: determine whether the forbidden-line polarization amplitude, including its collisional-depolarization density dependence, can be modeled with sufficient fidelity to be included in the inversion and used to recover the electron density once the magnetic ambiguities are resolved. (4) End-to-end validation: apply the complete inversion to real coronal observations of adequate signal-to-noise and verify the recovered vector field against independent estimates (e.g. photosphere-constrained extrapolations or MHD models, wave-seismology results, or tomographic reconstructions). These four components jointly support one overarching objective (a working coronal vector magnetometer based on the dual-line Hanle effect) and are not independent problems. Components (1) and (3) are open empirical questions that may resolve favorably or unfavorably — co-spatiality may be shown to fail in particular structures, or the amplitude modeling to be insufficiently faithful — and establishing the diagnostic includes determining when its assumptions hold; where they hold, the intended end state is a demonstrated, quantitative protocol — which lines, which auxiliary constraints at what accuracy, and which decision rule — under which the dual-line Hanle inversion yields a unique or reliably disambiguated coronal vector magnetic field measurement, with its uncertainty stated.

References

  1. Gabriel I. Dima, Jeffrey R. Kuhn, and Svetlana V. Berdyugina (2016). Infrared Dual-Line Hanle Diagnostic of the Coronal Vector Magnetic Field. Frontiers in Astronomy and Space Sciences 3:13. DOI: 10.3389/fspas.2016.00013. https://doi.org/10.3389/fspas.2016.00013
  2. Gabriel I. Dima and Thomas A. Schad (2020). Using Multi-line Spectropolarimetric Observations of Forbidden Emission Lines to Measure Single-point Coronal Magnetic Fields. The Astrophysical Journal 889, 109. DOI: 10.3847/1538-4357/ab616f. arXiv:2001.06123. https://doi.org/10.3847/1538-4357/ab616f
  3. Alin Razvan Paraschiv and Philip Gordon Judge (2022). Efficient and Automated Inversions of Magnetically Sensitive Forbidden Coronal Lines: CLEDB – The Coronal Line Emission DataBase Magnetic Field Inversion Algorithm. Solar Physics 297, 63. DOI: 10.1007/s11207-022-01996-5. arXiv:2204.14111. https://doi.org/10.1007/s11207-022-01996-5
  4. Alin Razvan Paraschiv (2026). Inferring 3D Coronal Magnetic Fields through Seismology-assisted Inversions of IQU-only Spectropolarimetric Observations. The Astrophysical Journal 1008, 29. DOI: 10.3847/1538-4357/ae8ae2. arXiv:2607.12846. https://doi.org/10.3847/1538-4357/ae8ae2
  5. Thomas A. Schad, Jeffrey R. Kuhn, Andre Fehlmann, Isabelle F. Scholl, David Harrington, Thomas Rimmele, and Alexandra Tritschler (2023). First Infrared Coronal Spectra from DKIST/Cryo-NIRSP: Comparisons with Global MHD Models. The Astrophysical Journal 943, 59. DOI: 10.3847/1538-4357/acabbd. https://doi.org/10.3847/1538-4357/acabbd
  6. Thomas A. Schad, Andre Fehlmann, Gabriel I. Dima, Jeffrey R. Kuhn, Isabelle F. Scholl, David Harrington, Thomas Rimmele, Alexandra Tritschler, and Alin Razvan Paraschiv (2024). Coronagraphic Observations of Si x 1430 nm Acquired by DKIST/Cryo-NIRSP with Methods for Telluric Absorption Correction. The Astrophysical Journal 965, 40. DOI: 10.3847/1538-4357/ad2995. arXiv:2402.09632. https://doi.org/10.3847/1538-4357/ad2995
  7. Maxim Kramar and Haosheng Lin (2022). Justification of the use of Stokes-V Cryo-NIRSP/DKIST observations for the 3D Reconstruction of the Coronal Magnetic Field. arXiv:2208.03840. https://arxiv.org/abs/2208.03840
  8. Maxim Kramar, Haosheng Lin, and Steven Tomczyk (2016). Direct Observation of Solar Coronal Magnetic Fields by Vector Tomography of the Coronal Emission Line Polarizations. The Astrophysical Journal Letters 819, L36. DOI: 10.3847/2041-8205/819/2/L36. arXiv:1502.07200. https://doi.org/10.3847/2041-8205/819/2/L36
  9. Jie Zhao, Sarah E. Gibson, Silvano Fineschi, Roberto Susino, Roberto Casini, Hui Li, and Weiqun Gan (2019). Simulating the Solar Corona in the Forbidden and Permitted Lines with Forward Modeling. I. Saturated and Unsaturated Hanle Regimes. The Astrophysical Journal 883, 55. DOI: 10.3847/1538-4357/ab328b. https://doi.org/10.3847/1538-4357/ab328b
  10. N. E. Raouafi, P. Riley, S. Gibson, S. Fineschi, and S. K. Solanki (2016). Diagnostics of Coronal Magnetic Fields through the Hanle Effect in UV and IR Lines. Frontiers in Astronomy and Space Sciences 3:20. DOI: 10.3389/fspas.2016.00020. arXiv:1606.08493. https://doi.org/10.3389/fspas.2016.00020
  11. Ernest Alsina Ballester, Daniel Nóbrega-Siverio, Fernando Moreno-Insertis, and Supriya Hebbur Dayananda (2025). Spectropolarimetric synthesis of forbidden lines in magnetohydrodynamic models of coronal bright points. Astronomy & Astrophysics 700, A204. DOI: 10.1051/0004-6361/202555520. arXiv:2506.23884. https://doi.org/10.1051/0004-6361/202555520
  12. Philip G. Judge, Shadia Habbal, and Enrico Landi (2013). From Forbidden Coronal Lines to Meaningful Coronal Magnetic Fields. arXiv:1304.3863. https://arxiv.org/abs/1304.3863 (also in Coronal Magnetometry, DOI: 10.1007/978-1-4939-2038-9_2)
  13. Zihao Yang, Sarah Gibson, Matthias Rempel, and Giuliana de Toma (2026). Measuring the Coronal Magnetic Field with 2D Coronal Seismology: A Forward-Modeling Validation. arXiv:2601.10637. https://arxiv.org/abs/2601.10637
  14. Amir Caspi, Daniel B. Seaton, Roberto Casini, Cooper Downs, Sarah E. Gibson, Holly Gilbert, Lindsay Glesener, Silvina E. Guidoni, J. Marcus Hughes, David McKenzie, Joseph Plowman, Katharine K. Reeves, Pascal Saint-Hilaire, Albert Y. Shih, and Matthew J. West (2023). COMPLETE: A flagship mission for complete understanding of 3D coronal magnetic energy release. arXiv:2305.16533. https://arxiv.org/abs/2305.16533 (also published as a Bulletin of the AAS 55 mission-concept white paper, DOI: 10.3847/25c2cfeb.b95dd671, with the full mission-team author list)
  15. Momchil Molnar and Roberto Casini (2024). Magnetic diagnostics of prominence eruptions through the Hanle effect of the He I 1083 nm line. The Astrophysical Journal 977, 97. DOI: 10.3847/1538-4357/ad8de4. arXiv:2410.23197. https://doi.org/10.3847/1538-4357/ad8de4
  16. Nataliia G. Shchukina, Javier Trujillo Bueno, Supriya Hebbur Dayananda, Rafael Manso Sainz, and Andrii V. Sukhorukov (2025). Coronal Magnetometry with EUV Permitted Lines. arXiv:2505.14084. https://arxiv.org/abs/2505.14084
  17. J. R. Kuhn, M. J. Penn, and I. Mann (1996). The near-infrared coronal spectrum. The Astrophysical Journal 456, L67. DOI: 10.1086/309864. https://doi.org/10.1086/309864