Linear polarization observed in chromospheric spectral lines during solar flares (Hα\alpha, Ca II K, Na D2, He I D3 and 10830 Å) has been debated for decades, with competing explanations by impact polarization from non-thermal particle beams and by resonant scattering polarization from anisotropic radiation in the inhomogeneous ribbon atmosphere. A two-dimensional schematic model showed that horizontal plasma inhomogeneities at ribbon edges can produce fractional scattering polarization of several percent, with the Hanle effect of a strong vertical field making the signal radial or tangential — but the model neglected three-dimensional geometry, ribbon asymmetries, collisional depolarization, and realistic non-thermal excitation, and left their combined influence unquantified. The open problem is to compute, by self-consistent multi-dimensional non-LTE polarized radiative transfer in realistic flare-ribbon models, the magnitude, spatial distribution, and spectral profiles of scattering polarization for the observationally relevant lines, and to determine whether it accounts quantitatively for the observational record, including recent detections of flare scattering polarization in He I D3 at the 10−310^{-3} level.

Background

Solar flares release magnetic energy in the corona, part of which is transported to the chromosphere and photosphere along magnetic loops, producing bright elongated emissions called flare ribbons. The chromospheric lines used to observe flares — Hα\alpha (hydrogen Balmer-α, 6563 Å), Ca II K (3934 Å), Na D2 (5890 Å), and the He I triplet lines D3 (5876 Å) and 10830 Å — are formed under non-LTE conditions, meaning that the atomic level populations are not determined by the local thermodynamic temperature but must be computed from the balance between radiative and collisional processes, with the radiation field itself obtained by solving the radiative transfer equation.

Polarization enters through two mechanisms. First, resonance (scattering) polarization: when the radiation field illuminating an atom is anisotropic, the excitation process produces population imbalances among the magnetic sublevels of an atomic level (atomic alignment), and the subsequent spontaneous emission is linearly polarized. The polarization state of radiation is described by the Stokes parameters II (intensity), QQ and UU (linear polarization), with the reference direction for positive QQ conventionally taken parallel to the nearest solar limb. Second, a magnetic field modifies scattering polarization through the Hanle effect, which rotates the polarization direction and reduces its degree when the field is comparable to or larger than a line-dependent critical field (for chromospheric lines, typically between milligauss and a few tens of gauss); in the saturation regime the polarization is either parallel or perpendicular to the plane containing the magnetic field and the propagation direction.

Competing with this is impact polarization: anisotropic collisions by particle beams (electrons, protons) or return currents that directly populate the atomic sublevels unevenly. Reports of linear polarization of several percent in Hα\alpha and other lines during flares — typically at ribbon edges rather than centers, oriented radially or tangentially to the limb, sometimes persisting into the gradual phase — have traditionally been interpreted as impact polarization from beams, while other careful campaigns found no Hα\alpha polarization above 0.1%. Self-consistent one-dimensional non-LTE polarized radiative transfer modeling of proton-beam excitation (Štěpán, Heinzel & Sahal-Bréchot 2007) showed that collisional depolarization keeps beam-induced Hα\alpha polarization at the level of at most a few percent, sharpening the tension with the larger reported signals.

Štěpán & Heinzel (2013) pointed out that the ribbons are a fundamentally multi-dimensional radiative transfer environment: at ribbon edges, the plane-parallel symmetry of the atmosphere is broken and the anisotropy of the radiation field — the driver of scattering polarization — is strongly enhanced. Solving the non-LTE problem self-consistently in a two-dimensional, x=0x=0-symmetric model ribbon with a generic two-level atom (resonant transition at 5000 Å, complete frequency redistribution, i.e. the assumption that emitted and absorbed photon frequencies are uncorrelated), an isothermal exponentially stratified atmosphere, an ad hoc ten-fold enhancement of collisional excitation mimicking beam energy deposition, and an imposed vertical 500 G magnetic field, they found fractional linear polarization reaching about 8% at the ribbon edges for an inclined line of sight, with the Hanle effect forcing the polarization to be radial or tangential. This single mechanism naturally explains the observed edge localization, the radial/tangential orientations, and the persistence of polarization into the gradual phase.

The authors explicitly identified what the model omitted: full three-dimensional geometry and interactions between nearby ribbons; the different physical conditions at inner ribbon edges affected by post-flare loops (the imposed symmetry about x=0x=0 being, in their words, probably the most severe approximation); collisional depolarization by thermal electrons, protons, and neutral hydrogen — important for hydrogen Balmer lines, while for lines of Na D2 and Ca II K, which are mainly depolarized by collisions with neutral hydrogen, its role is questionable because the neutral-hydrogen density actually decreases in the ribbons; non-thermal excitation rates larger and differently distributed than the conservative factor-of-ten enhancement adopted; horizontal temperature gradients, realistic magnetic-field geometries and strengths; and the use of a generic line rather than the actual observed transitions. They concluded that exploration of this multi-dimensional parameter space remains a task for future detailed investigations, and that radiative transfer in realistic multi-dimensional flare models is an essential ingredient for understanding the observed line polarization. The enabling numerical methodology now exists — three-dimensional multilevel polarized radiative transfer codes such as PORTA (Štěpán & Trujillo Bueno 2013) and 3D Stokes inversion frameworks — and has been applied extensively to quiet-Sun magnetohydrodynamic models, but not to flare ribbons; meanwhile new collisional depolarization rate calculations (Derouich & Qutub 2024) supply part of the missing atomic data.

Problem Statement

Compute, by self-consistent multi-dimensional non-LTE polarized radiative transfer in realistic models of the flaring chromosphere and flare ribbons, the scattering (resonance) polarization and Hanle-effect signatures of the chromospheric lines observed in solar flares — at minimum Hα\alpha and one of He I D3, He I 10830 Å, Ca II K, or Na D2 — and determine whether scattering polarization can account quantitatively for the observational record. The modeling must remove the approximations identified by Štěpán & Heinzel (2013): it should include (i) at least two-dimensional, and desirably three-dimensional, ribbon geometry with distinct inner and outer ribbon edges (the inner edges being influenced by post-flare loops) rather than imposed mirror symmetry, and the influence of a nearby second ribbon where relevant; (ii) realistic magnetic-field strengths and geometries, covering sub-critical, Hanle-sensitive, and saturated regimes; (iii) collisional depolarization by thermal electrons, protons, and neutral hydrogen at the level of current atomic data; and (iv) non-thermal collisional excitation rates grounded in beam-propagation theory or flare simulations rather than a fixed ad hoc enhancement, and their spatial variation across the ribbon. The required deliverable is the magnitude, spatial distribution across and along the ribbon, and spectral profiles of the emergent fractional linear polarization (Q/IQ/I, U/IU/I) for each modeled line, with an analysis of which combinations of geometry, field, and rates reproduce the observed phenomenology — polarization concentrated at ribbon edges, radial or tangential orientations, persistence into the gradual phase, amplitudes ranging from the 10−310^{-3} level detected in He I D3 (Vitali et al. 2026) to the several-percent levels reported in Hα\alpha and Ca II K — and of where impact polarization remains necessary. A complete answer establishes whether scattering polarization, alone or combined with beam-induced impact polarization, explains the measured flare polarization signals, and turns them into a quantitative diagnostic of flare energy transport.

References

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