Origin of the linear polarization of the hydrogen H$\alpha$ line in solar flares: can energetic-proton beams (or any particle-beam mechanism) reproduce the observed several-percent polarization under self-consistent NLTE polarized radiative transfer?

Solar flares occasionally show linear polarization of the hydrogen H$\alpha$ line (656.3 nm) at the several-percent level, radially or tangentially oriented and concentrated near flare kernels and ribbon edges. A self-consistent non-local thermodynamic equilibrium (NLTE) polarized radiative-transfer study by Štěpán, Heinzel and Sahal-Bréchot (2007) found that impact polarization by proton beams with standard power-law energy distributions is suppressed below 0.1% by collisional depolarization and the strong flare radiation field, and concluded that, in the models studied, proton beams are unlikely to be a satisfying explanation of the observed polarization — while leaving open, in its conclusions, whether initial proton distributions with a very narrow band of energies (which preferentially excite hydrogen at low energies in the H$\alpha$-forming layers) are physically possible and can lead to measurable impact polarization, and whether the return-current effect invoked for the Xu et al. (2005) observations is responsible. The open problem is to determine the physical origin of flare H$\alpha$ linear polarization: either to exhibit a physically realizable energetic-particle distribution that reproduces the observed polarization degree, orientation and spatial localization in such a self-consistent treatment, or to establish that the beam candidates the source leaves open cannot do so and that an alternative mechanism (multi-dimensional resonance scattering, return-current excitation, or CME-related processes) is responsible.

Background

The H$\alpha$ line (the $n=3\to 2$ Balmer-$\alpha$ transition of neutral hydrogen at 656.3 nm) forms in the solar chromosphere and is a principal diagnostic of solar flares. Beyond its intensity, the linear polarization of H$\alpha$ carries information about the geometry and energy content of the particles that deposit flare energy in the chromosphere. Two physical mechanisms can polarize a spectral line: (i) resonance (scattering) polarization — anisotropic irradiation of the line-forming region produces population imbalances and quantum coherences between magnetic sublevels (atomic alignment, described formally by the multipole components of the atomic density matrix), so that scattered photons are linearly polarized, with the Hanle effect modifying this polarization in weak magnetic fields; and (ii) impact polarization — collisional excitation of hydrogen by a directed beam of energetic particles populates the upper level with a preferential magnetic-sublevel distribution, again producing aligned atoms and linearly polarized emitted radiation. Because impact polarization depends directly on the beam's directionality and energy content, it has long been proposed as a diagnostic of accelerated particle beams in flares. A return current is the neutralizing electron current that flows to compensate the charge displacement of an injected particle beam propagating through the stratified flare atmosphere; its drifting electrons can themselves excite atoms anisotropically. NLTE radiative transfer means solving for the atomic level populations and the radiation field jointly, since the chromosphere departs strongly from local thermodynamic equilibrium; a polarized treatment extends this to the Stokes parameters — $I$ (total intensity) and $Q$, $U$ (the two independent components of linear polarization) — and to the multipolar components of the atomic density matrix. Observations of flare H$\alpha$ linear polarization have been persistently conflicting: impact-polarization detections at the 4–8% (radial) and up to 25% (tangential) level in the 2002 July 23 X4.8 flare by the Irkutsk group (Firstova et al.), detections above 5% near the limb reported by Emslie et al. (2000) and Hanaoka (2003), and the multiwavelength analysis of the 2001 June 15 flare by Xu et al. (2005) — against Bianda et al. (2005), who found no significant H$\alpha$ polarization in 30 flares, and Kawate and Hanaoka (2019), who found significant polarization in only 1 of 71 flares (1.16%), at a minor kernel uncorrelated with hard X-rays. Štěpán, Heinzel and Sahal-Bréchot (2007) performed the first self-consistent NLTE polarized radiative-transfer computation of proton-beam impact polarization of H$\alpha$, using a unidirectional, non-deflecting vertical beam with a power-law energy spectrum injected at the top of static one-dimensional semiempirical chromosphere models (F1 and VAL F — standard static one-dimensional atmosphere models constructed by fitting observed spectra), a hydrogen atom with three principal levels, complete redistribution (CRD — the assumption that scattered photons completely lose the frequency correlation of the absorbed radiation, i.e. no partial-redistribution effects), and approximate proton–hydrogen collision cross-sections. Their result: the impact-polarization contribution is below 0.1% — depolarized by collisions with background electrons and protons and by the strong radiation field — while tangential resonance-scattering polarization dominates in all models; proton beams with standard initial power-law distributions therefore cannot explain the reported several-percent polarization. Their conclusions leave open whether narrow-band, non-power-law proton energy distributions concentrated at few-keV energies (the only ones that could deliver enough low-energy protons to the H$\alpha$-forming depths) are 'physically possible' and 'can lead to measurable impact polarization', and state that investigation of the return-current process invoked for the Xu et al. (2005) observations 'remains the subject of further observational and theoretical research'; they further note that the null result of Bianda et al. (2005) does not require beam isotropization, since a sufficient number of unidirectional low-energy protons at the H$\alpha$-forming layer cannot be achieved for beams with initial power-law distributions. The simplifications the paper adopts for its own calculation — a static one-dimensional atmosphere with a unidirectional, non-deflecting vertical beam (that is, no pitch-angle scattering or isotropization, the progressive deflection of the beam particles' velocity directions relative to the magnetic field); charge exchange (the process in which a beam proton captures the electron of a background hydrogen atom, producing a fast excited neutral) treated as symmetric, with no Doppler shift and with a density matrix independent of atomic velocity; complete frequency redistribution; three principal levels of hydrogen; and semiclassical cross-sections used where adequate data are lacking (notably for the fine-structure transitions between $n=2$ and $n=3$ and above 100 keV) — mark the directions in which the treatment of any remaining candidate distribution would have to be extended, together with dedicated polarized-transfer modeling of alternative mechanisms such as return-current-driven excitation.

Problem Statement

Determine the physical origin of the linear polarization of the hydrogen H$\alpha$ line observed in solar flares at the several-percent level. The task is resolved by either of two routes, and a finding that no energetic-particle distribution reproduces the reference observations does not by itself resolve it unless the second route is also satisfied: (1) Exhibit a physically realizable energetic-particle distribution — in particular a proton beam, including the narrow-band or non-power-law few-keV distributions that Štěpán, Heinzel and Sahal-Bréchot (2007) identified as the only candidate able to deliver sufficient low-energy protons to the H$\alpha$-forming depths, and whose physical possibility and polarimetric effect their conclusions leave open, but also the electron beams and return-current electrons invoked for the Irkutsk detections and for the Xu et al. (2005) flare — that reproduces the reference H$\alpha$ polarization (degree, radial/tangential orientation, and spatial concentration at flare kernels and ribbon edges — the compact bright points and the boundaries of the elongated chromospheric brightenings that mark where flare energy is deposited) when evaluated with a self-consistent NLTE polarized radiative-transfer model of the flaring chromosphere. The reference observations that define the phenomenon to be reproduced are the several-percent detections: the 4–8% radially oriented and up to 25% tangentially oriented H$\alpha$ linear polarization measured across the ribbons of the 2002 July 23 X4.8 flare (Firstova, Polyakov & Firstova 2008, 2012), the detections above 5% near the limb (Emslie et al. 2000; Hanaoka 2003), and the multiwavelength 2001 June 15 flare measurements (Xu et al. 2005). These observations define a single phenomenon to be reproduced rather than three independent targets: a self-consistent model must reproduce the polarization degree to within a factor of two together with the radial/tangential orientation and the concentration at kernels and ribbon edges, and matching that phenomenon in a representative model of each listed kind of observation — ribbon, near-limb, and multiwavelength — suffices; an exact match to every individual measurement is not required. (2) Establish that the beam candidates the source leaves open cannot reproduce those reference observations and positively identify the mechanism that is instead responsible — resonance-scattering polarization driven by radiation anisotropy in multi-dimensional flare atmospheres, return-current-driven excitation, or processes related to coronal mass ejections (CMEs — large-scale eruptions of magnetized plasma from the solar corona) — through dedicated polarized-transfer modeling of that mechanism. A negative answer to the particle-beam question that names no responsible alternative mechanism satisfies neither route. The two routes are not disjoint with respect to the return current: because it is driven by the injected beam, a model in which return-current electron excitation reproduces the reference observations satisfies route (1) on its own, without the route-(2) impossibility result for the remaining candidates. In these gates, 'a physically realizable energetic-particle distribution' means one produced by a stated acceleration or transport mechanism acting in the flaring atmosphere and consistent with the flare's observed energetics, so that distributions that no stated mechanism produces do not qualify; and 'the beam candidates the source leaves open' means the narrow-band, non-power-law few-keV proton distributions — those confined to a few-keV energy range rather than extending as a power law, whose energy is deposited preferentially in the H$\alpha$-forming layers — so that the negative claim required by route (2) is complete once it covers that class. Whichever route is taken, the treatment must be consistent with the full observational record, including the rarity of the detections: the absence of significant H$\alpha$ polarization in 30 flares (Bianda et al. 2005) and the significant detection in only 1 of 71 flares, at 1.16% in a minor kernel uncorrelated with hard X-rays (Kawate & Hanaoka 2019), are part of the completion standard and must be accounted for. The aim is a quantitative, self-consistent treatment that satisfies route (1) or route (2) so that a diagnostic conclusion of the form 'H$\alpha$ linear polarization in flares is/is not a viable diagnostic of energetic particle beams, because mechanism X accounts for observations Y' can be drawn.

References

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