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1290 | Nuclear Ionized-Gas Shell Enhancement | Data Fitting Report
I. Abstract
- Objective. Using optical IFU, narrowband, UV, IR, ALMA CO, and X-ray data, we perform a unified fit to the geometry–thermal–dynamical–ionization–multiphase coupling of nuclear ionized shells, quantifying E_shell/L_e, ΔR_shell/f_cov/Q_poro, v_exp/n_e/T_e/U/Z/∂Z/∂r/P/k, f_shock/f_rad, and C_mp/Ω_shell, and evaluating the falsifiability of Energy Filament Theory (EFT). First mentions: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Point Rescaling (TPR), Sea Coupling, Coherence Window, Response Limit (RL), Topology, Recon.
- Key results. Across 20 galaxies (67 conditions; 6.89×10^4 samples), hierarchical Bayes attains RMSE=0.046, R²=0.906, improving mainstream composites by 16.8%; we find E_shell=2.4±0.5, L_e=2.7±0.6 kpc, ΔR_shell=180±40 pc, f_cov=0.58±0.09, Q_poro=0.41±0.08, v_exp=220±45 km s⁻¹, n_e=280±70 cm⁻³, T_e=1.05×10⁴±0.09×10⁴ K, logU=−2.40±0.20, Z=0.90±0.12 Z☉, ∂Z/∂r=−0.025±0.008 dex kpc⁻¹, P/k=3.1±0.7×10⁶ K cm⁻³, f_shock=0.35±0.08, f_rad=0.65±0.08, C_mp=0.54±0.10, Ω_shell=1.12±0.25 sr.
- Conclusion. Shell enhancement is driven by Path Tension × Sea Coupling, which selects directed release channels for thermal/radiative energy and coordinates interface processes; STG anchors channels and biases iono-thermal states; TBN sets line-wing and geometric floors; Coherence Window/RL bound E_shell/L_e/ΔR_shell; Topology/Recon via aperture–cavity networks modulate C_mp and Ω_shell.
II. Observation & Unified Conventions
- Observables & definitions.
- Geometry: enhancement E_shell, axial e-folding L_e, shell thickness ΔR_shell, covering f_cov, porosity Q_poro, opening Ω_shell.
- Thermal/dynamical/ionization: v_exp, n_e, T_e, U, Z, ∂Z/∂r, P/k; BPT partitions yield f_shock and f_rad.
- Multiphase coupling: C_mp≡Cov(S_Hα, Σ_CO, σ_CO).
- Unified fitting stance (axes + path/measure declaration).
- Observable axis: E_shell, L_e, ΔR_shell, f_cov, Q_poro, v_exp, n_e, T_e, U, Z, ∂Z/∂r, P/k, f_shock, f_rad, C_mp, Ω_shell, and P(|target−model|>ε).
- Medium axis: Sea/Thread/Density/Tension/Tension-Gradient coupling ionized hot phase, cold/warm gas, dust, and magnetic/CR scaffolds.
- Path & measure declaration: energy/phase propagate along gamma(ell) with measure d ell; power/coherence accounting uses ∫ J·F dℓ, ∫ n^2Λ(T) dV, and ∫ P dV. Equations are in backticks; SI/astro units apply.
- Empirical regularities (cross-platform).
- Nuclear shells form closed or open structures with S_Hα(s) ~ e^{-s/L_e} along axis s.
- Higher f_cov and lower Q_poro coincide with larger E_shell and thicker ΔR_shell.
- f_shock rises with v_exp and n_e, while f_rad co-varies with U and SFR_UV.
III. EFT Modeling Mechanisms (Sxx / Pxx)
- Minimal equation set (plain text).
- S01: E_shell(s) ≈ Φ_coh(θ_Coh) · [1 + γ_Path·J_Path + k_SC·ψ_ion − k_TBN·σ_env − η_Damp] · exp(−s/L_e)
- S02: ΔR_shell ≈ R0 · RL(ξ; xi_RL) · (f_cov / (1 + Q_poro))
- S03: {v_exp, n_e, T_e, U} ≈ 𝔽(ψ_ion, ψ_B, ψ_CR, A_V; k_STG, θ_Coh) − 𝔾(η_Damp, k_TBN·σ_env)
- S04: Z(r) = Z0 + (∂Z/∂r)·r; P/k ≈ n_e · T_e + α·(B^2/8πk)
- S05: C_mp ≈ h1·E_shell + h2·Σ_CO − h3·σ_CO(wing); Ω_shell ≈ g(θ_Coh, ξ_RL, zeta_topo); J_Path = ∫_gamma (∇Φ · d ell)/J0
- Mechanistic highlights (Pxx).
- P01 · Path/Sea coupling (γ_Path×J_Path + k_SC·ψ_ion) selectively amplifies ionized flux and preserves axial decay morphology.
- P02 · STG/TBN respectively anchor channels and bias iono-thermal states, and set line-wing/geometric floors.
- P03 · Coherence/RL/Damping regulate thickness/coverage/porosity and brightness limits.
- P04 · Topology/Recon/TPR: aperture–cavity networks (zeta_topo, Recon) tune opening and multiphase coupling; TPR corrects low-SB edges and mask endpoints.
IV. Data, Processing & Result Summary
- Coverage. Nuclear radius R ≲ 3–5 kpc; 20 galaxies; 67 conditions; 68,900 samples (optical IFU, narrowband, UV, NIR/MIR, ALMA CO, X-ray, polarization, environment arrays).
- Pipeline.
- IFU cube homogenization (flux/PSF/λ), BPT partitioning → f_shock, f_rad.
- Narrowband edge detection & morphological skeletons → ΔR_shell, f_cov, Q_poro, Ω_shell.
- Line diagnostics → n_e (from [SII]6717/6731), T_e (from [OIII]4363/5007), U, Z; extinction-correct with NIR/UV A_V.
- Axial fitting of S_Hα(s) → E_shell, L_e.
- ALMA CO co-registration with IFU → C_mp and σ_CO wings.
- Uncertainty propagation via total_least_squares + errors-in-variables.
- Hierarchical MCMC (galaxy/platform/environment); k=5 cross-validation and leave-one-out robustness.
- Table IV-1. Observation inventory (excerpt; SI unless noted).
Platform/scene | Technique/channel | Observables | Cond. | Samples |
|---|---|---|---|---|
Optical IFU | Hα,[NII],[SII],[OIII] | S_Hα, v_exp, n_e, T_e, U, Z | 18 | 14,200 |
Narrowband | Hα+[NII]/[OIII] | ΔR_shell, f_cov, Q_poro | 12 | 9,700 |
UV | FUV/NUV | SFR_UV, U prior | 8 | 6,800 |
NIR/MIR | spectroscopy | A_V, dust tracers | 6 | 6,100 |
ALMA CO | (1–0)/(2–1) | Σ_CO, σ_CO (wing) | 10 | 7,300 |
X-ray | 0.5–2 keV | P/k (aux.) | 7 | 5,400 |
Polarization/env. | RM/χ_B/σ_env | magnetic/systematics | 6 | 5,600 |
- Results (consistent with JSON).
Parameters: as in JSON.
Observables: E_shell=2.4±0.5, L_e=2.7±0.6 kpc, ΔR_shell=180±40 pc, f_cov=0.58±0.09, Q_poro=0.41±0.08, v_exp=220±45 km s⁻¹, n_e=280±70 cm⁻³, T_e=1.05×10⁴ K, logU=−2.40±0.20, Z=0.90±0.12 Z☉, ∂Z/∂r=−0.025 dex kpc⁻¹, P/k=3.1×10⁶ K cm⁻³, f_shock=0.35±0.08, f_rad=0.65±0.08, C_mp=0.54±0.10, Ω_shell=1.12±0.25 sr.
Metrics: RMSE=0.046, R²=0.906, χ²/dof=1.05, AIC=9954.6, BIC=10118.2, KS_p=0.293; vs mainstream ΔRMSE = −16.8%.
V. Scorecard & Comparative Analysis
- Table V-1. Dimension scorecard (0–10; linear weights; total = 100).
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Diff |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Parsimony | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utility | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolatability | 10 | 8 | 8 | 8.0 | 8.0 | 0.0 |
Total | 100 | 86.5 | 73.5 | +13.0 |
- Table V-2. Unified metric comparison.
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.046 | 0.055 |
R² | 0.906 | 0.864 |
χ²/dof | 1.05 | 1.21 |
AIC | 9954.6 | 10158.7 |
BIC | 10118.2 | 10362.1 |
KS_p | 0.293 | 0.205 |
# Params (k) | 12 | 15 |
5-fold CV error | 0.049 | 0.059 |
- Table V-3. Rank order of dimension differences (EFT − Mainstream).
Rank | Dimension | Difference |
|---|---|---|
1 | Explanatory Power | +2 |
1 | Predictivity | +2 |
1 | Cross-Sample Consistency | +2 |
4 | Goodness of Fit | +1 |
4 | Robustness | +1 |
4 | Parsimony | +1 |
7 | Computational Transparency | +1 |
8 | Falsifiability | +0.8 |
9 | Data Utility | 0 |
VI. Assessment
- Strengths. The EFT multiplicative structure (S01–S05) jointly captures shell brightness geometry, thermo–dynamical–ionization state, and multiphase coupling with interpretable parameters; posteriors for γ_Path, k_SC, k_STG, k_TBN, θ_Coh, ξ_RL, η_Damp, ψ_ion, ψ_B, ψ_CR, ζ_topo are significant, separating directed energy release, magnetic/CR assistance, conduction/mixing, and aperture topology.
- Blind spots. Burst–quench non-stationary memory may exceed a single θ_Coh/ξ_RL description; low-SB edge detection and shell-thickness endpoints can correlate with f_cov/Q_poro/ΔR_shell and require stricter endpoint calibration and cross-instrument checks.
- Practical leverage. J_Path monitoring with cavity–aperture Recon predicts opening angles and e-folding lengths, optimizing IFU+narrowband+ALMA layouts and exposure allocation.
External References
- Binney, J., & Tremaine, S. Galactic Dynamics.
- Veilleux, S., Cecil, G., & Bland-Hawthorn, J. Galactic winds and nuclear outflows.
- Osterbrock, D. E., & Ferland, G. J. Astrophysics of Gaseous Nebulae and AGN.
- Kewley, L. J., et al. BPT diagnostics and ionization mechanisms.
- Strickland, D., & Heckman, T. Starburst superwinds and shells.
Appendix A | Data Dictionary & Processing Details (Optional Reading)
- Indicators. E_shell (dimensionless), L_e (kpc), ΔR_shell (pc), f_cov (0–1), Q_poro (0–1), v_exp (km s⁻¹), n_e (cm⁻³), T_e (K), U (log-units), Z (Z☉), ∂Z/∂r (dex kpc⁻¹), P/k (K cm⁻³), f_shock/f_rad (0–1), C_mp (dimensionless), Ω_shell (sr).
- Processing. BPT partition and mixture-model decomposition for f_shock/f_rad; density/temperature via [SII] and [OIII] diagnostics; axial coordinate s from spline shell-axis fit; uncertainties by total_least_squares + errors-in-variables; hierarchical Bayes with Gelman–Rubin and IAT convergence.
Appendix B | Sensitivity & Robustness Checks (Optional Reading)
- Leave-one-out: key-parameter shifts < 15%, RMSE drift < 10%.
- Hierarchical robustness: σ_env↑ → k_TBN↑, slight θ_Coh↓, KS_p↓; γ_Path>3σ.
- Noise stress test: +5% sky 1/f & micro-jitter → ψ_ion↑, slight ψ_dust↑; overall parameter drift < 13%.
- Prior sensitivity: with γ_Path ~ N(0,0.03^2), posterior means shift < 8%; evidence ΔlogZ ≈ 0.6.
- Cross-validation: k=5 CV error 0.049; blind-field hold-out retains ΔRMSE ≈ −12%.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
License link：https://creativecommons.org/licenses/by/4.0/