Physical origin of the linear-polarization depression in solar-flare plasma sheets: quantitative forward modeling of reconnection-driven depolarization and its forbidden-line diagnostics

CoMP spectropolarimetry of the 2017 September 10 X8.2 limb flare revealed a deep, spatially broad depression of linear polarization in the Fe XIII 1074.7/1079.8 nm forbidden lines aligned with the hot plasma sheet above the flare loops, together with near-tangential polarization azimuths beneath the sheet and a striking asymmetry: the sheet is clearly traced by fractional polarization $P$ but is essentially invisible in Fe XIII intensity. Simple 2D forward models reproduce the observed minimum polarization levels but not the broad, gradual spatial width of the depression. The open problem is to give a quantitative, observationally validated physical account of these signatures: whether 3D time-dependent models of plasmoid-mediated reconnection with a turbulent cascade reproduce the observed polarization structure (depth, width, and temporal evolution, including the sheet's persistence in $P$ for roughly a day after onset), what the near-tangential azimuths and the polarization-without-intensity signature diagnose about the sheet's temperature, density, and sub-resolution magnetic structure, and how the signatures evolve from flare onset. The required synthesis and observations are not yet available, while the enabling atomic models and synthesis codes now exist.

Background

In the standard eruptive-flare picture (the Carmichael–Sturrock–Hirayama–Kopp–Pneuman, or CSHKP, model), an erupting magnetic flux rope leaves behind a vertical current sheet above the post-flare loop arcade, and reconnection in this sheet feeds hot plasma into the supra-arcade region. The 2017 September 10 X8.2-class limb flare produced one of the best-observed examples of such a 'plasma sheet': spectroscopic measurements established sheet temperatures of 15–20 MK, supra-arcade downflows, and non-thermal line broadening attributed to turbulent, plasmoid-mediated reconnection (Warren et al. 2018). A plasmoid is a magnetic island or flux rope formed when a long, thin current sheet becomes unstable to the tearing-mode (plasmoid) instability, which fragments it into a hierarchy of ever-smaller islands.

The coronal magnetic field itself is difficult to measure. One of the few accessible diagnostics is spectropolarimetry of forbidden coronal emission lines, such as Fe XIII at 1074.7 and 1079.8 nm (formation temperature about 1.5 MK). These optically thin lines are excited both by anisotropic resonant scattering of photospheric radiation and by electron collisions; the scattering geometry imprints linear polarization described by the Stokes parameters $Q$ and $U$. In the corona these lines sit in the saturated Hanle regime, in which the polarization direction encodes the plane-of-sky field direction while the degree of polarization follows the factor $3\cos^2\theta_B-1$ (Casini & Judge 1999), where $\theta_B$ is the angle between the magnetic field and the incident radiation. The polarization vanishes at the Van Vleck angle $\theta_B\approx54.74^\circ$, and the polarization azimuth flips by 90° across such a Van Vleck null. The observable is the fractional polarization $P=\sqrt{Q^2+U^2}/I$. Because the corona is optically thin, $P$ is a line-of-sight (LOS) integral, so unresolved magnetic structure or particular LOS symmetries can cancel the polarization signal ('depolarization').

The Coronal Multi-channel Polarimeter (CoMP) at the Mauna Loa Solar Observatory measured $I$, $Q$, and $U$ in the two Fe XIII lines from 1.03 to 1.5 solar radii, with a spatial resolution of about 6 Mm and a 30 s cadence. During the 2017 September 10 flare, CoMP observed from 17:07:50 UT, roughly one hour after the 16:06 UT flare peak, so the onset and early impulsive phase were not captured. French et al. (2019) found that the fractional polarization is strongly depressed in a band coincident with the hot plasma sheet, with minimum $P$ far below what any laminar current-sheet geometry allows, and unusual near-tangential polarization azimuths beneath the sheet, roughly aligned with dark 'V-shaped' structures. By elimination — after testing a laminar Sweet–Parker-type sheet, potential-field models built from infinite LOS line currents ('plasmoid' models), and random-field realizations — they concluded that magnetic structure on scales below the instrument resolution, plausibly produced by plasmoid formation during reconnection, must be depolarizing the line. Those simple 2D models reproduced the observed minimum $P$ values but not the broad, gradual spatial width of the depression, which is significantly wider than the EUV plasma sheet. The authors invoked the 3D kinetic simulations of Stanier et al. (2019), in which plasmoid cascades diffuse away from the sheet much faster than the plasma itself, as a candidate mechanism, and identified as open questions the onset-phase evolution of the polarization, the physical origin of the tangential azimuths, the reason the sheet appears in $P$ but not in Fe XIII intensity, and the need for higher-fidelity observations. The 4-m Daniel K. Inouye Solar Telescope (DKIST), whose cryogenic near-infrared spectropolarimeter Cryo-NIRSP performs coronal forbidden-line spectropolarimetry with a true spectrograph rather than CoMP's filtergraph, is the intended facility for such measurements (Rast et al. 2021).

Problem Statement

Central question: Can the observed spectropolarimetric structure of solar-flare plasma sheets be quantitatively explained by reconnection-driven fragmentation and turbulence, and what does that structure diagnose about the magnetic field on scales below the instrument resolution? A complete answer must establish the following jointly linked results in service of this single objective:

1. Forward-model reproduction. Construct 3D, time-dependent models of plasmoid-mediated reconnection (plasmoid cascades and turbulent magnetic fields) in a flare plasma-sheet geometry, synthesize the CoMP-observable Stokes $I$, $Q$, $U$ of the Fe XIII 1074.7 and 1079.8 nm lines including line-of-sight integration, and determine whether they reproduce the observed signatures of the 2017 September 10 event, reporting the extent of agreement and where the models fall short: the minimum fractional polarization $P$ aligned with the sheet, the broad and gradual spatial width of the polarization depression (significantly wider than the EUV plasma-sheet), and the temporal behavior — including the sheet's persistence in $P$ for roughly 27 hours after onset (French et al. 2020). The evolution from flare onset (initially narrow, matching the intensity profile, then broadening as fragmentation develops) enters as a model prediction rather than a match to recorded data, since it is currently unobserved and can only be tested when a comparable event occurs.

2. Interpretation of the anomalous signatures. Give a physical account of (a) the near-tangential polarization azimuths beneath the plasma sheet — unusual, since coronal azimuths are predominantly radial — for example as a line-of-sight integration effect, and of what they imply about the large-scale field structure beneath the sheet; and (b) why the sheet is clearly present in $P$ but essentially absent in Fe XIII intensity, quantifying the respective roles of temperature (sheet at 10–20 MK, with the hottest plasma at 15–20 MK, versus Fe XIII formation near 1.5 MK), density, and emission-measure distribution.

3. Observational confrontation where feasible. Test the model predictions against the recorded CoMP Stokes $I$, $Q$, $U$ structure and its stated uncertainties for the source event as reported by French et al. (2019, 2020) — this confrontation with the published CoMP measurements is the mandatory minimum — and, as a forward-looking extension, against any subsequent spectrally resolved polarimetry (DKIST Cryo-NIRSP class) of flare plasma sheets, including whether higher spatial resolution, spectrographic sampling of the Stokes parameters, and better signal-to-noise resolve the scale of the magnetic substructure and distinguish competing models of reconnection-driven fragmentation and turbulence.

The completion boundary is a validated quantitative account: an expert can judge completion by whether the synthesized observables match the recorded CoMP polarization structure of the source event within stated uncertainties — or, where they do not, by whether a quantitatively documented shortfall, benchmarked against that recorded structure and carrying a stated uncertainty budget, is reported — and whether the interpretive claims about the tangential azimuths and the polarization-without-intensity signature follow from the model physics. The components are not separable papers bolted together: the same model that must reproduce the depression's depth is the one whose cascade physics is claimed to explain its width, its day-long persistence, and its absence from the intensity channel.

References

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