The Diagnostic Temperature Discrepancy as a Kinetic Measurement: Shape, Transport, and Termination of the Suprathermal Electron Tail

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Original abstract

Two standard thermometers applied to the same quiet-Sun corona disagree by a stable factor: radio brightness reads about 0.6 MK while ionization- and scale-height-based diagnostics read about 1.5 MK, a ratio of 2.4 +/- 0.3 over eight years. We argue this discrepancy is not an anomaly awaiting reconciliation but a kinetic measurement, and we read it three times: for the shape of the electron distribution, for its origin, and for the energy where it must end. First, a temperature diagnostic is a projection onto the Maxwellian family; the quiet-Sun distribution carries a power-law tail of index kappa ~ 2.5, so different projections return different temperatures, and their disagreement decomposes exactly into a temperature gap fixed by the measured ratio alone and a residue no scalar temperature can carry: a fifth of the electron thermal energy, stored in shape, whose presence means no local conductive closure exists for this plasma. Second, reading one model atmosphere two independent ways returns kappa = 2.52 from its temperature-density structure at the height where the diagnostics read 2.57, while the local electric field on the same column is 39-56 times too weak to seed the tail in place: the tail was transported, not made there. Third, a transported tail terminates at the energy whose collisional stopping column equals the column traversed; the tabulated column puts that termination at 1.8-3.5 keV, overlapping the 1.7-3 keV bracket independently required by the diagnostic ratio and the hard X-ray limits, with no tuned parameters, and the computed termination reproduces the measured ratio: the spectrum's edge is a pressure gauge on the tail's loading layer. The premise is audited, a deciding within-ion test on archived spectra is specified, and nine falsification conditions are stated. The discrepancy, read kinetically, returns more than either thermometer was built to measure.

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• Official / arXiv page
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