Diagnostic Disagreement as an Information-Projection Divergence: An Information-Theoretic Reading of the Quiet-Sun Temperature Ratio
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2026
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| _version_ | 1866917437492953088 |
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| author | Edmonds, V. |
| author_facet | Edmonds, V. |
| contents | The quiet-Sun coronal electron-temperature ratio $R \equiv T_\mathrm{EUV}/T_B \approx 2.4$, stable across an eight-year solar cycle, is read here as a measurement of relative entropy between two diagnostic projections of the coronal electron distribution onto the one-parameter Maxwellian family. The EUV ionization temperature is a moment-matching projection against a Bethe-type ionization kernel; the radio brightness temperature is the Rayleigh-Jeans source function of thermal bremsstrahlung. For a kappa distribution in the mean-energy convention, Fleishman & Kuznetsov (2014) give the radio-side projection in closed form as $T_B = T_\mathrm{core}$; the EUV side returns $T_\mathrm{eff}$ up to a shape-dependent correction within the Dud\'ık et al. (2014) intensity-ratio envelope. At $κ= 2.5$ the Kullback-Leibler divergences between the true distribution and its two Maxwellian projections evaluate to $0.32$ and $1.20$ nats, and their difference satisfies $ΔD_\mathrm{KL} = (3/2)[R_0 - \ln R_0 - 1] = (3/2) d_\mathrm{IS}(T_\mathrm{eff}, T_\mathrm{core})$, where $R_0 \equiv κ/(κ- 3/2)$ is the ideal closed-form ratio and $d_\mathrm{IS}$ is the Itakura-Saito distance. The identity is offered as an analytical reference for observational systems in which two diagnostics project different moments of a common non-equilibrium distribution; the eight-year stability of $R$ expresses a stability of that projection structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23752 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diagnostic Disagreement as an Information-Projection Divergence: An Information-Theoretic Reading of the Quiet-Sun Temperature Ratio Edmonds, V. Solar and Stellar Astrophysics Statistical Mechanics Data Analysis, Statistics and Probability Plasma Physics The quiet-Sun coronal electron-temperature ratio $R \equiv T_\mathrm{EUV}/T_B \approx 2.4$, stable across an eight-year solar cycle, is read here as a measurement of relative entropy between two diagnostic projections of the coronal electron distribution onto the one-parameter Maxwellian family. The EUV ionization temperature is a moment-matching projection against a Bethe-type ionization kernel; the radio brightness temperature is the Rayleigh-Jeans source function of thermal bremsstrahlung. For a kappa distribution in the mean-energy convention, Fleishman & Kuznetsov (2014) give the radio-side projection in closed form as $T_B = T_\mathrm{core}$; the EUV side returns $T_\mathrm{eff}$ up to a shape-dependent correction within the Dud\'ık et al. (2014) intensity-ratio envelope. At $κ= 2.5$ the Kullback-Leibler divergences between the true distribution and its two Maxwellian projections evaluate to $0.32$ and $1.20$ nats, and their difference satisfies $ΔD_\mathrm{KL} = (3/2)[R_0 - \ln R_0 - 1] = (3/2) d_\mathrm{IS}(T_\mathrm{eff}, T_\mathrm{core})$, where $R_0 \equiv κ/(κ- 3/2)$ is the ideal closed-form ratio and $d_\mathrm{IS}$ is the Itakura-Saito distance. The identity is offered as an analytical reference for observational systems in which two diagnostics project different moments of a common non-equilibrium distribution; the eight-year stability of $R$ expresses a stability of that projection structure. |
| title | Diagnostic Disagreement as an Information-Projection Divergence: An Information-Theoretic Reading of the Quiet-Sun Temperature Ratio |
| topic | Solar and Stellar Astrophysics Statistical Mechanics Data Analysis, Statistics and Probability Plasma Physics |
| url | https://arxiv.org/abs/2604.23752 |