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The diagnostic temperature discrepancy as evidence for non-Maxwellian coronal electrons

Victor Edmonds

Abstract

Two independent electron temperature diagnostics applied to the quiet solar corona yield systematically different results. Radio brightness temperatures from the Nancay Radioheliograph indicate T_e ~ 0.6 MK, while hydrostatic scale-height modeling of the same plasma requires T_e ~ 1.5 MK (Mercier & Chambe 2015). Both diagnostics probe electrons; they disagree by a factor of R = 2.4 +/- 0.3. This discrepancy persists across an eight-year dataset spanning solar minimum and is consistent with LOFAR observations at lower frequencies (Vocks et al. 2018). We consider the propagation alternative (turbulent scattering of radio emission), which operates in the correct direction to suppress the apparent brightness temperature, but the ratio R is invariant over the solar cycle despite expected variations in turbulence levels. We propose that the residual, cycle-invariant discrepancy reflects non-Maxwellian electron velocity distributions. Radio bremsstrahlung samples the distribution core, while ionization rates and scale heights are dominated by the suprathermal tail. For kappa distributions, the predicted ratio is kappa/(kappa - 3/2); the observed R = 2.4 implies kappa ~ 2-3. This is consistent with spectroscopic measurements in active regions but in tension with perturbative theoretical predictions of kappa ~ 10-25. We make falsifiable predictions: Active Region cores should show a collapsed ratio (R <= 1.5) as collisionality restores thermal equilibrium. Applying fluid transport equations (Spitzer-Harm conductivity) to plasmas with kappa ~ 2-3 is physically invalid, but we do not compute the resulting heat flux, which remains an open problem.

The diagnostic temperature discrepancy as evidence for non-Maxwellian coronal electrons

Abstract

Two independent electron temperature diagnostics applied to the quiet solar corona yield systematically different results. Radio brightness temperatures from the Nancay Radioheliograph indicate T_e ~ 0.6 MK, while hydrostatic scale-height modeling of the same plasma requires T_e ~ 1.5 MK (Mercier & Chambe 2015). Both diagnostics probe electrons; they disagree by a factor of R = 2.4 +/- 0.3. This discrepancy persists across an eight-year dataset spanning solar minimum and is consistent with LOFAR observations at lower frequencies (Vocks et al. 2018). We consider the propagation alternative (turbulent scattering of radio emission), which operates in the correct direction to suppress the apparent brightness temperature, but the ratio R is invariant over the solar cycle despite expected variations in turbulence levels. We propose that the residual, cycle-invariant discrepancy reflects non-Maxwellian electron velocity distributions. Radio bremsstrahlung samples the distribution core, while ionization rates and scale heights are dominated by the suprathermal tail. For kappa distributions, the predicted ratio is kappa/(kappa - 3/2); the observed R = 2.4 implies kappa ~ 2-3. This is consistent with spectroscopic measurements in active regions but in tension with perturbative theoretical predictions of kappa ~ 10-25. We make falsifiable predictions: Active Region cores should show a collapsed ratio (R <= 1.5) as collisionality restores thermal equilibrium. Applying fluid transport equations (Spitzer-Harm conductivity) to plasmas with kappa ~ 2-3 is physically invalid, but we do not compute the resulting heat flux, which remains an open problem.
Paper Structure (30 sections, 7 equations, 1 figure, 2 tables)

This paper contains 30 sections, 7 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Scope
  3. Plan of the paper
  4. The observation
  5. What Mercier & Chambe measured
  6. The spectral evidence
  7. Independent confirmation
  8. Alternative explanations
  9. Turbulent scattering
  10. Ion-electron temperature separation
  11. Kappa distributions and temperature amplification
  12. The kappa distribution
  13. How different diagnostics weight the distribution
  14. Optical depth self-consistency
  15. Inferring kappa from the observed ratio
  16. ...and 15 more sections

Figures (1)

  • Figure 1: (a) Normalized velocity distributions for a Maxwellian (blue) and a kappa distribution with $\kappa = 2$ (red), both at the same core temperature $T_{\rm core}$. The enhanced suprathermal tail (shaded) inflates the effective temperature $T_{\rm eff}$ measured by ionization and scale-height diagnostics, while radio bremsstrahlung samples the thermal core. (b) Temperature amplification factor $T_{\rm eff}/T_{\rm core} = \kappa/(\kappa - 3/2)$ as a function of $\kappa$. The grey band marks the observed coronal range $\kappa \approx 2$--3 inferred from the Mercier & Chambe (2015) diagnostic ratio $R = 2.4$.