The Quiet-Sun DEM Under Kappa: Diagnostic Degeneracy and the Failure of the Conductive Closure

Abstract

For a plasma whose electrons carry a $\kappa \approx 2.5$ suprathermal tail, the Spitzer-Harm conductive closure does not exist: the conductive flux is the tail-carried third velocity moment, and the local conductivity integral diverges across the entire $\kappa \in [2,3]$ range -- the finite value the closed-form $\kappa$-conductivity returns at $\kappa =2.5$ is an analytic continuation of a divergent integral, not a physical conductivity. Edmonds (2026a) places the quiet solar corona (QS) in this regime. Taking that as premise, two failures 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 shown end-to-end. A single-T $\kappa =2.5$ probe, a multi-T $\kappa =2.5$ source, and a multi-T Maxwellian source, all run through the regularized DEM inversion of Hannah & Kontar (2012), recover $\log T$ widths inside the FWHM distribution the same pipeline returns from 80 real quiet-Sun AIA patches; the pipeline cannot distinguish them. Two structural features also emerge: a Fe XI charge-state crossover and an EUV continuum reversal. The ionization-gated diagnostic structurally returns the tail-weighted effective temperature $T_{\mathrm{eff}}$, while Spitzer-Harm takes the bulk-core $T_{\mathrm{core}}=(\kappa -3/2)/\kappa \cdot T_{\mathrm{eff}}$ as input. The mismatch invites a temperature substitution yielding a budget reduction -- mechanically correct and physically empty, because the coefficient it corrects has no convergent form: it is the Fourier-law closure itself that fails, not its temperature input. Two QS pillars for impulsive heating -- DEM-width multi-thermality and the conductive-budget gap -- lose their structural assumptions, and the budget question shifts to non-local kinetic transport outside any fluid closure.

Accepted for publication in Transport Phenomena (De Gruyter Brill)

References in corpus (16)

• The chemical make-up of the Sun: A 2020 vision
• Key Aspects of Coronal Heating
• Evidence of Non-Thermal Particles in Coronal Loops Heated Impulsively by Nanoflares
• The Temperature and Density Structure of the Solar Corona. I. Observations of the Quiet Sun with the EUV Imaging Spectrometer (EIS) on Hinode
• Hinode/Extreme-Ultraviolet Imaging Spectrometer Observations of the Temperature Structure of the Quiet Corona
• Electron heat flux in the near-Sun environment
• Evidence for Wave Heating of the Quiet Sun Corona
• Signatures of the non-Maxwellian $\kappa$-distributions in optically thin line spectra \subtitle{I. Theory and synthetic Fe IX--XIII spectra}
• Suprathermal electron distributions in the solar transition region
• Transport coefficients of the fully ionized plasma with kappa-distribution and in strong magnetic field
• Signatures of the non-Maxwellian $\kappa$-distributions in optically thin line spectra. II. Synthetic Fe XVII--XVIII X-ray coronal spectra and predictions for the Marshall Grazing-Incidence X-ray Spectrometer (MaGIXS)
• Electron Heat Flux in the Solar Wind: Generalized Approaches to Fluid Transport with a Variety of Skewed Velocity Distributions
• Analysis of Quiescent Corona X-ray Spectra from SphinX during the 2009 Solar Minimum
• Towards a realistic evaluation of transport coefficients in non-equilibrium space plasmas
• The diagnostic temperature discrepancy as evidence for non-Maxwellian coronal electrons
• Multi-diagnostic convergence: a single measurement in weakly collisional plasmas