The Diagnostic Temperature Discrepancy as Evidence for Non-Maxwellian Coronal Electrons

Two independent electron temperature diagnostics applied to the quiet solar corona yield systematically different results. Radio brightness temperatures from the Nançay Radioheliograph indicate Tₑ ≈ 0.6 MK, while hydrostatic scale-height modeling of the same plasma requires Tₑ ≈ 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. Comparison with the FORWARD/PSIMAS Maxwellian model (Sharma & Oberoi 2020) shows that the standard thermal structure predicts ~1.6 MK; scattering accounts for the modest reduction toward observed MWA values but not the gap to 620 kK. The ratio R is also invariant over the solar cycle despite measured variations in turbulence levels (Gautam et al. 2024). We propose that the residual discrepancy reflects non-Maxwellian electron velocity distributions. Radio bremsstrahlung samples the distribution core (Chiuderi & Chiuderi Drago 2004; Fleishman & Kuznetsov 2014), while ionization rates and scale heights are dominated by the suprathermal tail (Owocki & Scudder 1983). For kappa distributions, the predicted ratio is κ/(κ − 3/2); the observed R = 2.4 implies κ ≈ 2–3. This is consistent with spectroscopic measurements in active regions (Dudík et al. 2015) but in tension with perturbative theoretical predictions of κ ≈ 10–25 (Cranmer 2014). 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-Härm conductivity) to plasmas with κ ≈ 2–3 is physically invalid, but we do not compute the resulting heat flux, which remains an open problem.