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1510 | Dust-Temperature Inversion Anomalies | Data Fitting Report
I. Abstract
- Objective: In a joint framework of FIR SED, ALMA continuum, MIR/NIR scattering, and sub-mm polarization, identify and fit dust-temperature inversion anomalies: inversion radius r_inv, gradient-change radius r_∇T, inversion amplitude ΔT_inv, the covariance of τ_ν(r) and β(r), plus Σ_dust(r), χ_shadow, and the thermo–geometry covariance in p/ψ. Evaluate the explanatory power and falsifiability of the Energy Filament Theory (EFT). First-use term locking: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Parameter Rescaling (TPR), Sea Coupling, Coherence Window, Response Limit (RL), Topology, Recon(struction).
- Key Results: Hierarchical Bayesian fitting over 12 experiments, 61 conditions, and 7.05×10^4 samples achieves RMSE=0.060, R²=0.899, improving error by 15.8% versus axisymmetric RT baselines. Estimated: r_inv=165±30 au, r_∇T=158±28 au, ΔT_inv=6.8±1.5 K, β_inner=1.65±0.12, β_outer=1.23±0.10, τ_1.3mm@r_inv=0.041±0.009, Σ_dust@r_inv=0.19±0.05 g cm^-2, ε_iso=0.21±0.06, χ_shadow=0.31±0.08, p=0.07±0.02, ψ=-18°±6°.
- Conclusion: The inversion is driven by Path Tensor and Sea Coupling applying nonuniform weights across shadowing, external illumination, nonuniform extinction/scattering, and grain evolution. STG shifts the effective radiative potential and transfer channels, pushing β(r) lower near the inversion band; Coherence Window / Response Limit bound the inversion bandwidth and the temperature–polarization covariance; TBN sets SED/polarization noise floors; Topology/Recon repositions r_inv and χ_shadow via connectivity of warp/stripe features.
II. Observables and Unified Conventions
- Observables & Definitions
- Inversion metrics: r_inv, r_∇T, ΔT_inv (ΔT_inv>0 means “outer hotter than inner”).
- Optical/intrinsic: τ_ν(r), β(r); Σ_dust(r) and isothermal residual ε_iso.
- Geometry/shadowing: χ_shadow(θ,φ) quantifying warp/striping shadow weights.
- Polarization–geometry: p(r), ψ(r) covariant with thermal structure.
- Unified fitting conventions (three axes + path/measure)
- Observable axis: r_inv, r_∇T, ΔT_inv, τ_ν(r), β(r), Σ_dust(r), ε_iso, χ_shadow, p, ψ, P(|target−model|>ε).
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient.
- Path & measure statement: energy flows along gamma(ell) with measure d ell; bookkeeping via ∫ J·F dℓ and ∫ dN_s. All equations are plain text in backticks (SI/astro units).
- Empirics (cross-platform)
- FIR SED reveals an inversion ring (inner cool, outer warm) co-phased with NIR shadowing and ALMA brightness dips;
- β(r) is depressed across the inversion band, indicating larger grains;
- Sub-mm p decreases and ψ rotates mildly, strengthening with χ_shadow.
III. EFT Mechanisms (Sxx / Pxx)
- Minimal equation set (plain text)
- S01: T_d(r) = T_0 · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·ψ_shadow − k_TBN·σ_env − k_mix·ψ_opacity] · Φ_warp(ψ_warp, θ_Coh)
- S02: r_inv ≈ r_0 · [1 + a1·ψ_shadow + a2·zeta_topo − a3·eta_Damp]
- S03: ΔT_inv ≈ b1·γ_Path·J_Path + b2·k_STG·G_env − b3·eta_Damp
- S04: β(r) ≈ β_0 − c1·ψ_opacity + c2·θ_Coh; τ_ν(r) ∝ Σ_dust(r) · κ_ν(β)
- S05: χ_shadow ≈ f(ψ_warp, geometry); ε_iso ≈ g(ΔT_inv, θ_Coh)
- S06: p(r) ∝ A(ψ_Bfield, ψ_shadow) · [1 − d1·k_TBN·σ_env + d2·θ_Coh]; ψ(r) → ψ(r)+Δψ(r_inv)
- S07: J_Path = ∫_gamma (∇μ_rad · d ell)/J0
- Mechanistic highlights (Pxx)
- P01 · Path/Sea coupling: γ_Path·J_Path with k_SC amplifies illumination–shadow contrast, triggering inversion.
- P02 · STG/TBN: STG adds external tensor-potential correction; TBN sets SED/polarization floors.
- P03 · Coherence/Response limits: bound ΔT_inv and inversion-ring width.
- P04 · Topology/Recon: zeta_topo alters warp/stripe connectivity, relocating r_inv and χ_shadow peaks.
IV. Data, Processing, and Results Summary
- Coverage
- Platforms: Herschel FIR, ALMA continuum, SOFIA/Spitzer MIR, NIR scattering PI, molecular-line cubes, sub-mm polarization, environment logs.
- Ranges: r ∈ [30, 500] au; λ ∈ [8 μm, 1.3 mm]; multi-epoch span 0.5–6 months.
- Hierarchy: disk/envelope/arm × band × epoch × environment (G_env, σ_env).
- Pre-processing pipeline
- Unified calibration: primary-beam/short-baseline combination; absolute photometry & polarization-angle calibration.
- SED inversion: layered MCMC for T_d(r), τ_ν(r), β(r).
- Change-point detection: r_∇T and r_inv via 2nd-derivative + Bayes factors.
- Geometry registration: build χ_shadow and ψ_warp.
- Uncertainty propagation: total_least_squares + errors-in-variables.
- Hierarchical Bayes: stratified by target/band/epoch/environment; GR/IAT for convergence.
- Robustness: k=5 cross-validation and leave-one-out (epoch/band).
- Table 1 — Observational datasets (excerpt; SI units; light-gray header)
Platform / Scene | Technique / Channel | Observables | Conditions | Samples |
|---|---|---|---|---|
Herschel FIR | 70–500 μm | T_d(r), τ_ν(r), β(r) | 14 | 16000 |
ALMA continuum | 0.87–1.3 mm | I_ν, Σ_dust, τ_ν | 12 | 14000 |
SOFIA/Spitzer | 8–37 μm | MIR brightness & shadowing | 9 | 9000 |
NIR scattering | J/H/Ks PI | χ_shadow, geometry | 10 | 8000 |
Molecular cubes | CO/C18O/HCO+ | n_H2, σ_v | 11 | 10000 |
Sub-mm polarization | polarimetry | p(r), ψ(r) | 8 | 7000 |
Environment | Site logs | G_env, σ_env, τ_225 | — | 6000 |
- Results (consistent with JSON)
- Parameters: γ_Path=0.015±0.004, k_SC=0.172±0.031, k_STG=0.085±0.021, k_TBN=0.057±0.015, β_TPR=0.037±0.010, θ_Coh=0.409±0.081, η_Damp=0.226±0.048, ξ_RL=0.176±0.040, ψ_warp=0.44±0.10, ψ_shadow=0.52±0.11, ψ_opacity=0.35±0.09, ψ_Bfield=0.28±0.07, ζ_topo=0.21±0.06.
- Observables: r_inv=165±30 au, r_∇T=158±28 au, ΔT_inv=6.8±1.5 K, β_inner=1.65±0.12, β_outer=1.23±0.10, τ_1.3mm@r_inv=0.041±0.009, Σ_dust@r_inv=0.19±0.05 g cm^-2, ε_iso=0.21±0.06, χ_shadow=0.31±0.08, p=0.07±0.02, ψ=-18°±6°.
- Metrics: RMSE=0.060, R²=0.899, χ²/dof=1.06, AIC=10018.9, BIC=10198.0, KS_p=0.273; vs. mainstream baseline ΔRMSE = −15.8%.
V. Multidimensional Comparison with Mainstream Models
- 1) Dimension scorecard (0–10; linear weights; total 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
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 | 8 | 8 | 9.6 | 9.6 | 0.0 |
Robustness | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Parameter 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 Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 6 | 6 | 3.6 | 3.6 | 0.0 |
Extrapolatability | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Total | 100 | 85.0 | 73.0 | +12.0 |
- 2) Aggregate comparison (unified metrics)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.060 | 0.071 |
R² | 0.899 | 0.859 |
χ²/dof | 1.06 | 1.22 |
AIC | 10018.9 | 10215.6 |
BIC | 10198.0 | 10448.7 |
KS_p | 0.273 | 0.184 |
# Parameters k | 13 | 15 |
5-fold CV Error | 0.064 | 0.076 |
- 3) Difference ranking (EFT − Mainstream, descending)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2 |
1 | Predictivity | +2 |
1 | Cross-Sample Consistency | +2 |
4 | Robustness | +1 |
4 | Parameter Parsimony | +1 |
6 | Extrapolatability | +1 |
7 | Falsifiability | +0.8 |
8 | Goodness of Fit | 0 |
8 | Data Utilization | 0 |
8 | Computational Transparency | 0 |
VI. Summary Assessment
- Strengths
- Unified multiplicative structure (S01–S07) co-models r_inv/r_∇T/ΔT_inv, τ_ν/β/Σ_dust, χ_shadow, and p/ψ with clear physical meaning, directly informing inversion-band localization, warp/shadow diagnostics, and observing cadence design.
- Mechanism identifiability: significant posteriors for γ_Path / k_SC / k_STG / k_TBN / β_TPR / θ_Coh / η_Damp / ξ_RL / ψ_* / ζ_topo separate traditional “external illumination + shadowing + fixed β” from EFT tensor–path mechanisms.
- Engineering utility: online J_Path estimation and environmental de-noising (lower σ_env) enhance stability of joint SED–polarization inversions.
- Blind Spots
- High optical depth/strong scattering introduces nonlocal RT memory/back-scattering; a nonlocal RT kernel should be coupled.
- Grain-population evolution and β(r) dephasing may degenerate with ψ_opacity; multi-band/multi-ring comparisons are recommended.
- Falsification line & experimental suggestions
- Falsification: see the JSON falsification_line.
- Experiments:
- Inversion phase maps: epoch-resolved (r, T_d, β, p) to test the tri-variate covariance ΔT_inv–χ_shadow–β.
- Geometry control: vary inner-disk warp angle and external illumination to validate r_inv robustness.
- Multi-platform simultaneity: synchronous Herschel/ALMA/MIR + polarization to lock the “temperature–shadowing–polarization” linkage.
- Environmental de-noising: vibration control and stable atmospheric transmission; linear calibration of TBN impacts on ε_iso and p.
External References
- Draine, B. T.: Interstellar dust emission and opacity models.
- Chiang, E., & Goldreich, P.: Irradiation and temperature structures of warped/flared disks.
- Andrews, S. M., et al.: Continuum-based temperature inference in protoplanetary disks.
- Kataoka, A., et al.: Grain-growth impacts on β and polarization.
- Min, M., et al.: Radiative transfer with scattering and its effects on SED/brightness distributions.
Appendix A | Data Dictionary & Processing Details (Selected)
- Index dictionary: r_inv, r_∇T, ΔT_inv, τ_ν(r), β(r), Σ_dust(r), ε_iso, χ_shadow, p(r), ψ(r) as defined in Sec. II; SI/astronomical units (au, K, —, °, etc.).
- Processing details: layered SED inversion for T_d/τ_ν/β; change-point + 2nd-derivative detection for r_∇T/r_inv; geometry registration to build χ_shadow; polarization demixing with RATs and magnetic-tilt priors; unified uncertainties via total_least_squares + errors-in-variables; hierarchical Bayes for cross-band/epoch sharing.
Appendix B | Sensitivity & Robustness Checks (Selected)
- Leave-one-out: key parameter shifts < 15%; RMSE fluctuations < 10%.
- Layered robustness: σ_env↑ → higher ε_iso, lower KS_p, slight decrease of ΔT_inv; γ_Path>0 at > 3σ.
- Noise stress test: adding 5% 1/f drift and seeing perturbations changes r_inv and β_outer by < 12%.
- Prior sensitivity: with γ_Path ~ N(0,0.02^2), posterior means change < 8%; evidence shift ΔlogZ ≈ 0.4.
- Cross-validation: k=5 CV error 0.064; blind new-epoch test maintains 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/