Forbidden (magnetic-dipole) coronal emission lines are among the very few diagnostics capable of measuring magnetic fields in the Sun's million-degree corona. Dima & Schad (2020) generalized Plowman's dual-line 'single-point inversion' to arbitrary combinations of forbidden lines, showed that line pairs in which both transitions have F=0F=0 (equal upper- and lower-level Landé g-factors, or J=1→0J=1\rightarrow0) carry degenerate spectropolarimetric information, proposed the Fe XIII 1074.7 nm + Si X 1430.1 nm pair as a usable alternative, and identified the outstanding requirements for turning the technique into an operational coronal vector-magnetometry capability. Substantial progress exists: Judge, Casini & Paraschiv (2021) showed the F=0F=0 degeneracy is avoidable by solving for the scattering geometry, implemented in the CLEDB database inversion (Paraschiv & Judge 2022, Paraschiv 2026); Schiffmann et al. (2021) computed intermediate-coupling Landé g-factors (~1% departures from LS coupling); DKIST/Cryo-NIRSP delivered the first infrared coronal spectra including Si X 1430 nm and the first Zeeman-effect maps of the line-of-sight coronal field at 1074 nm. The open core remains precise and nonempty: no laboratory determination of the infrared Landé g-factors; no validated account of when the single-point approximation holds along realistic optically thin lines of sight; no demonstrated reduction of the discrete ambiguities to a unique field solution on real observations; and no demonstrated full-vector multi-line inversion of real coronal data.

Background

The solar corona is the Sun's outer atmosphere, heated to millions of degrees and permeated by magnetic fields that govern coronal heating, the solar wind, and eruptive space-weather events. Because the corona is too hot and tenuous for the absorption-line Zeeman diagnostics used on the photosphere, the primary magnetic diagnostics are 'forbidden' emission lines — weak magnetic-dipole (M1) transitions between fine-structure levels of the ground term of highly ionized atoms, observed off-limb with coronagraphs (telescopes that occult the solar disk). The brightest such lines include Fe XIII 1074.7 nm and 1079.8 nm (iron twelve times ionized), Fe XIV 530.3 nm, Si X 1430.1 nm, and Si IX 3934 nm. Their polarization encodes the magnetic field: in Stokes I,Q,U,VI,Q,U,V spectropolarimetry (intensity and the linearly and circularly polarized components), the linear polarization arises from 'atomic alignment' — anisotropic pumping of the ion's magnetic sublevels by photospheric radiation, operating in the saturated Hanle regime, where the polarization direction is set by the field orientation through the Van Vleck effect (a 90° flip of the polarization position angle when the field crosses ~54.7° to the radiation direction); circular polarization arises from the Zeeman effect and measures the line-of-sight field component. The Landé g-factor of each level sets the Zeeman splitting and, through the difference of upper- and lower-level g-factors, a coefficient FF that governs how strongly a line constrains the field: lines with F=0F=0 (equal upper/lower g-factors, or J=1→0J=1\rightarrow0 transitions) carry degenerate information. In pure LS coupling (orbit- and spin-angular momenta separately coupled) the g-factors follow a simple formula, but real coronal ions can depart from it through intermediate coupling, at the percent level. Plowman (2014) introduced a 'single-point inversion': assuming the polarized emission along a given line of sight is dominated by plasma at a single point, the full vector magnetic field can be analytically inverted from the Stokes vectors of two forbidden lines, such as the classic Fe XIII 1074.7/1079.8 nm pair. Dima & Schad (2020, ApJ 889, 109) generalized this formalism and showed, using the Casini & Judge (1999) polarized-emission coefficients (correcting an algebraic error in its Eq. 38b), that line combinations in which every transition has F=0F=0 cannot be inverted this way — which includes the Fe XIII pair under LS coupling. Because the Fe XIII ground-term level spacings violate Landé's interval rule, they argued the LS values are themselves uncertain, and proposed the Fe XIII 1074.7 nm + Si X 1430.1 nm combination, whose F≠0F\neq0 breaks the degeneracy. Their noise analysis (for a coronal-loop model) found that fields of order 10 G10\,\mathrm{G} inclined within ~35° of the line of sight could be recovered at photon-noise levels of ~10−410^{-4} of line intensity, reachable with the 4-m Daniel K. Inouye Solar Telescope (DKIST) and its Cryo-NIRSP cryogenic near-infrared spectropolarimeter. The inversion generally returns up to four discrete solutions (the classical Van Vleck and 180° ambiguities extended to all inverted parameters), reducible with auxiliary constraints such as density, temperature, projected emission height, or stereoscopy. The paper closed by identifying what is still missing before the technique can deliver real coronal vector magnetometry — the open problems addressed here. For context, these needs sit inside a decades-long community effort (CoMP routine linear-polarization observations, tomographic and seismology-based field estimates, forward modeling with codes such as FORWARD/P-CORONA/pyCELP) for which routine coronal vector magnetometry remains an unmet capability.

Problem Statement

Establish multi-line spectropolarimetry of forbidden (magnetic-dipole) coronal emission lines as a validated, operational method for measuring the coronal vector magnetic field, completing the program whose foundations Dima & Schad (2020) laid. Specifically, the open problem comprises the following linked open needs: (1) Atomic data — determine the Landé g-factors of the infrared and near-infrared coronal M1 transitions (notably the Fe XIII 1074.7/1079.8 nm levels, Si X 1430.1 nm, and other candidate M1 lines such as Mg VIII 3028.5 nm) via laboratory measurement (e.g., electron-beam ion trap Zeeman spectroscopy extending Bekker et al. 2018 to the infrared) or an independent determination validated to the accuracy this requires (accurate enough to fix the F=0F=0 versus F≠0F\neq0 classification and to keep the resulting inversion bias within the observational uncertainty), as necessary to ensure the accuracy of coronal magnetic field measurements and to enable unbiased inversions, given that percent-level departures of the g-factors from their LS-coupling values propagate into the F=0F=0 versus F≠0F\neq0 degeneracy classification and into inversion bias; (2) Line-of-sight validation — quantify when the single-point approximation holds for optically thin lines of sight, and develop tested methods for isolating or subtracting foreground/background polarized emission; the source suggests that synthesizing polarized emission through high-resolution MHD simulations of the active corona and then testing methods may be helpful toward this end; (3) Degeneracy resolution — provide operational strategies that reduce the discrete inversion ambiguities (up to four solutions; at minimum the residual two-fold ambiguity) to a unique field estimate in real observations, using auxiliary constraints such as electron density, temperature, projected emission height, or stereoscopy, the source noting that the ambiguity may be resolved by imposing physical limits on any of the solution parameters; and (4) Demonstration — apply the resulting multi-line (two or more forbidden lines) inversion to real coronal observations and validate the recovered vector fields against independent constraints; the source notes that Bayesian/MCMC formulations with plasma-diagnostic priors could also be applied to any line pair in which at least one line has F≠0F\neq0. These four needs are the linked sub-problems of this one program: each is independently attackable, a rigorous resolution of any one of them is a valid, self-contained advance, and the objective above is fully met only when all four are addressed.

References

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