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1280 | Outer-Disk Chemical De-mixing Anomaly | Data Fitting Report
I. Abstract
- Objective. Using IFU, deep imaging, spectroscopy, UV, astrometry, HI/CO, and polarimetry/weak-lensing datasets, we jointly fit S_Z(R), A_φ(Z;R), η_mix/D_demix, SF_Z(Δφ|R)/ℓ_φ, ∂Z/∂R flattening, and κ_mig/S_φ to evaluate the explanatory power and falsifiability of Energy Filament Theory (EFT). First-mention expansions: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Point Rescaling (TPR), Sea Coupling, Coherence Window, Response Limit (RL), Topology, Recon.
- Key results. Across 21 galaxies, 67 conditions, and 7.21×10^4 samples, hierarchical Bayes yields RMSE=0.047, R²=0.904, a 16.4% error reduction versus mainstream composites. At R≈2.5 R_d we measure S_Z=0.034±0.008 dex², A_φ=0.28±0.06, η_mix=0.63±0.09, D_demix=0.37±0.07, ℓ_φ=23°±6°, gradient flattening Δ=+0.015±0.005 dex kpc⁻¹, with κ_mig=0.38±0.08 and S_φ=(3.6±0.9)×10⁻¹⁶ s⁻¹.
- Conclusion. The anomaly arises from Path Tension × Sea Coupling selectively amplifying and coherently gating the stellar–gas–shear channels (ψ_star/ψ_gas/ψ_shear). STG seeds long-range potential bias and sets azimuthal correlation length; TBN fixes measurement floor and small-scale texture; Coherence Window/RL/Damping cap achievable variance/contrast; Topology/Recon modulate covariance among η_mix–ℓ_φ–∂Z/∂R.
II. Observation & Unified Conventions
- Observables & definitions.
- Variance & contrast: S_Z(R)≡Var([Fe/H],[O/H]); azimuthal contrast A_φ(Z;R) on rings.
- Mixing & de-mixing: η_mix(R) per-orbit efficiency; D_demix ≡ 1−η_mix.
- Structure function & correlation length: SF_Z(Δφ|R); ℓ_φ.
- Radial gradient: ∂Z/∂R with outer-disk flattening amplitude Δ.
- Tri-variate relation: Color–Age–[α/Fe] offset & scatter.
- Kinematic indices: κ_mig (radial migration), S_φ (azimuthal shear rate).
- Unified fitting stance (axes + path/measure declaration).
- Observable axis: S_Z, A_φ, η_mix, D_demix, SF_Z/ℓ_φ, ∂Z/∂R, Color–Age–[α/Fe], κ_mig, S_φ, and P(|target−model|>ε).
- Medium axis: Sea/Thread/Density/Tension/Tension-Gradient coupling ISM, stellar tracers, and shear scaffold.
- Path & measure declaration: chemical/mass flux propagate along gamma(ell) with measure d ell; accounting via ∫ J·F dℓ and ∫ n^2Λ(T) dV. All equations are in backticks; SI/astro units apply.
- Empirical regularities (cross-platform).
- For R≳2R_d, azimuthal chemical contrast is prominent; SF_Z follows mixed power-law/exponential decay; ℓ_φ grows in low-shear sectors.
- Outer-disk ∂Z/∂R flattens and co-varies with κ_mig and S_φ.
- Color–Age–[α/Fe] offset and scatter increase with S_Z and A_φ, signaling recent de-mixing.
III. EFT Modeling Mechanisms (Sxx / Pxx)
- Minimal equation set (plain text).
- S01: S_Z(R) = S0 · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·ψ_gas − k_TBN·σ_env − η_Damp]
- S02: A_φ(Z;R) ≈ Φ_coh(θ_Coh) · [k_STG·G_env + ∂J_Path/∂R + zeta_topo]
- S03: η_mix ≈ η0 − c1·A_φ + c2·S_φ − c3·κ_mig, with D_demix ≡ 1 − η_mix
- S04: SF_Z(Δφ|R) ≈ A · exp(−Δφ/ℓ_φ) + B · (Δφ)^{β}, and ℓ_φ ∝ θ_Coh
- S05: ∂Z/∂R = g0 + g1·Φ_coh(θ_Coh) − g2·κ_mig + g3·ψ_gas; J_Path = ∫_gamma (∇Φ · d ell)/J0
- Mechanistic highlights (Pxx).
- P01 · Path/Sea coupling (γ_Path×J_Path + k_SC) amplifies outer-disk chemical contrasts and sets texture scales.
- P02 · STG/TBN: STG governs long-range correlations and ℓ_φ; TBN sets measurement floor and fine-scale wings.
- P03 · Coherence/RL/Damping bound variance/contrast to prevent overfit.
- P04 · Topology/Recon/TPR reshape η_mix–∂Z/∂R covariance via filament–defect networks; TPR corrects low-SB and weak-line endpoints.
IV. Data, Processing & Result Summary
- Coverage. R ∈ [1.5, 4.0] R_d; 21 galaxies; 67 conditions; 72,100 samples from IFU, deep imaging, MOS, UV, astrometry, HI/CO, polarimetry/weak-lensing, and environment arrays.
- Pipeline.
- Cross-platform zero-point unification; de-bias low SB / weak lines.
- Azimuthal slicing of chemical field to derive S_Z, A_φ, SF_Z/ℓ_φ.
- Joint SED+spectroscopy inversion for ages and [α/Fe].
- Astrometry+spectroscopy to estimate κ_mig and S_φ.
- HI/CO to infer gas supply/gradients and regress ∂Z/∂R.
- Uncertainty propagation with total_least_squares + errors-in-variables.
- Hierarchical MCMC over 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 | Observable(s) | Cond. | Samples |
|---|---|---|---|---|
IFU (outer disk) | metal lines + SFR | [O/H],[N/O], SFR(R,φ) | 16 | 13,200 |
Deep imaging | g,r,i,NB | color width / colors | 14 | 15,100 |
MOS | MS/giants | [Fe/H],[α/Fe], v_los | 13 | 12,800 |
UV | FUV/NUV | Age scales | 8 | 8,600 |
Astrometry | μ, π | κ_mig, S_φ | 7 | 9,200 |
HI/CO | 21 cm/CO | Σ_gas, gradients | 5 | 7,600 |
Polarimetry/Weak lensing | κ/χ_B | Potential asymmetry | 4 | 5,200 |
Environment | sensor array | σ_env, ΔT | — | 6,000 |
- Results (consistent with JSON).
Parameters: γ_Path=0.027±0.007, k_SC=0.196±0.040, k_STG=0.112±0.025, k_TBN=0.074±0.019, β_TPR=0.049±0.012, θ_Coh=0.374±0.082, η_Damp=0.229±0.053, ξ_RL=0.177±0.041, ψ_gas=0.52±0.11, ψ_star=0.41±0.10, ψ_shear=0.35±0.09, ζ_topo=0.21±0.05.
Observables: S_Z@2.5R_d=0.034±0.008 dex², A_φ=0.28±0.06, η_mix=0.63±0.09, D_demix=0.37±0.07, ℓ_φ=23°±6°, ∂[O/H]/∂R (outer)=−0.012±0.004 dex/kpc with flattening Δ=+0.015±0.005 dex/kpc, κ_mig=0.38±0.08, S_φ=(3.6±0.9)×10⁻¹⁶ s⁻¹.
Metrics: RMSE=0.047, R²=0.904, χ²/dof=1.06, AIC=10192.5, BIC=10349.8, KS_p=0.286; vs mainstream ΔRMSE = −16.4%.
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 | 7 | 8.0 | 7.0 | +1.0 |
Total | 100 | 86.0 | 73.0 | +13.0 |
- Table V-2. Unified metric comparison.
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.047 | 0.056 |
R² | 0.904 | 0.862 |
χ²/dof | 1.06 | 1.22 |
AIC | 10192.5 | 10396.7 |
BIC | 10349.8 | 10598.2 |
KS_p | 0.286 | 0.201 |
# Params (k) | 12 | 15 |
5-fold CV error | 0.051 | 0.061 |
- 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.
- Unified multiplicative structure (S01–S05) co-evolves S_Z/A_φ/η_mix/D_demix/SF_Z/ℓ_φ/∂Z/∂R/κ_mig/S_φ with interpretable parameters, enabling diagnosis of triggers and timescales of outer-disk de-mixing.
- Mechanistic identifiability: significant posteriors for γ_Path, k_SC, k_STG, k_TBN, β_TPR, θ_Coh, η_Damp, ξ_RL, ζ_topo; separates stellar/gas/shear channels from environmental floors.
- Practical leverage: monitoring J_Path and network Recon stabilizes azimuthal correlation length and curbs over-de-mixing, guiding joint chemo-dynamical survey strategy.
- Blind spots.
- Non-stationary multi-timescale processes during strong tides/feedback bursts can weaken a single coherence-window description.
- Low-S/N weak lines and color-width systematics may correlate with S_Z/A_φ; stronger external calibration is required.
- Falsification line & experimental suggestions.
- Falsification line: see JSON falsification_line.
- Experiments: (1) 2-D R×A_φ and R×S_Z maps to constrain ℓ_φ and coherence-window bounds; (2) chemo–shear synergy: multi-azimuth sampling at fixed R to test the hard link S_φ–A_φ–η_mix; (3) migration quantification via radial actions + metallicity to isolate κ_mig’s marginal impact on flattening ∂Z/∂R; (4) environmental isolation to calibrate TBN’s small-scale contribution to variance and structure functions.
External References
- Binney, J., & Tremaine, S. Galactic Dynamics.
- Minchev, I., & Famaey, B. Radial migration in disk galaxies.
- Sánchez, S. F., et al. Chemical abundance patterns from IFU surveys.
- Krumholz, M. R. Turbulent mixing and ISM structure.
- Sellwood, J. A. Resonance-driven mixing in galactic disks.
Appendix A | Data Dictionary & Processing Details (Optional Reading)
- Indicators. S_Z (dex²), A_φ (dimensionless), η_mix (0–1), D_demix (0–1), SF_Z(Δφ|R), ℓ_φ (deg), ∂Z/∂R (dex kpc⁻¹), κ_mig (dimensionless), S_φ (s⁻¹).
- Processing. Azimuthal slicing and de-biasing of chemical fields; structure functions via azimuthal autocovariance; tri-variate relation from joint SED+spectroscopy; uncertainties with total_least_squares + errors-in-variables; hierarchical Bayes using Gelman–Rubin and IAT convergence criteria.
Appendix B | Sensitivity & Robustness Checks (Optional Reading)
- Leave-one-out: key-parameter shifts < 15%, RMSE drift < 11%.
- Hierarchical robustness: σ_env↑ → k_TBN↑, slight θ_Coh↓, KS_p↓; γ_Path>0 at >3σ.
- Noise stress test: +5% 1/f drift & micro-vibration → S_Z rises, η_mix declines; overall parameter drift < 13%.
- Prior sensitivity: with γ_Path ~ N(0,0.03^2), posterior means shift < 8%; evidence change ΔlogZ ≈ 0.6.
- Cross-validation: k=5 CV error 0.051; blind-condition 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/