The quiet-Sun DEM under kappa: diagnostic degeneracy and the failure of the conductive closure

Abstract

For a plasma whose electron distribution carries a κ ≈ 2.5 suprathermal tail, the Spitzer–Härm conductive closure does not exist: the conductive flux is the third velocity moment, carried by the tail, and the local conductivity integral diverges across the entire κ ∈ [2, 3] range – the finite value the closed-form κ -conductivity returns at κ = 2.5 is an analytic continuation of that divergent integral, not a physical conductivity. Edmonds (“The diagnostic temperature discrepancy as evidence for non-Maxwellian coronal electrons,” Open J. Astrophys. , vol. 9, 2026a) places the quiet solar corona (QS) in this regime. The present paper takes that as its premise and establishes the two failures that follow for any plasma in the class: the standard EUV-DEM diagnostic cannot resolve such a plasma, and the conductive term of the standard QS energy budget has no valid form. The diagnostic failure is demonstrated end-to-end. Three synthetic source families processed through the standard EUV imaging + regularized DEM inversion pipeline of Hannah & Kontar (“Differential emission measures from the regularized inversion of Hinode and SDO data,” A&A , vol. 539, 2012, Art. no. A146) – a single-T κ = 2.5 probe, a multi-T κ = 2.5 source on the Brooks et al. (“Hinode/extreme-ultraviolet imaging spectrometer observations of the temperature structure of the quiet corona,” APJ , vol. 705, 2009, Art. no. 1522) shape, and the Brooks-shape Maxwellian forward model – recover FWHMs of 0.222, 0.305, and 0.319 in log  T at χ ² /dof ≤ 1.00. The same pipeline applied to 80 real quiet-Sun AIA patches at solar minimum returns FWHM median 0.283 (range 0.230–0.401), stable across two solar-minimum dates to within 0.003 dex. All three synthetic sources sit inside or just below this distribution; the pipeline does not distinguish them. Independent of the FWHM degeneracy, two structural features emerge: an iron charge-state crossover at Fe XI ( κ /Mxw

across κ ∈ [2, 3]), and an EUV continuum reversal at AIA wavelengths – suppressed near 94 Å, enhanced at longer wavelengths – contrary to the X-ray-extrapolated expectation of uniform κ hardening. The ionization-gated diagnostic structurally returns the effective temperature T _eff , the tail-weighted moment of the distribution. The Spitzer–Härm closure governs bulk transport and takes the bulk-core temperature T _core = ( κ − 3/2)/ κ ⋅ T _eff as physical input. The mismatch invites a temperature substitution that yields a concrete fluid-budget reduction – mechanically correct and physically empty, because the coefficient it corrects has no convergent form – a worked demonstration of the trap latent in any κ -corrected fluid budget, not a corrected number: it is the Fourier-law closure itself that fails, not merely its temperature input. Two QS-specific empirical pillars for impulsive heating – DEM-width multi-thermality and the fluid-conductive-budget gap – lose their structural assumptions, and the quiet-Sun budget question shifts to the non-local kinetic transport that no fluid closure represents.