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1604 | High-Polarization Supernova Anomaly | Data Fitting Report
I. Abstract
- Objective. Within a multi-platform framework of optical/NIR spectropolarimetry and imaging polarimetry, we jointly fit the continuum polarization P_cont, line polarization peak P_line, Stokes trajectories and Q–U loop area S_loop, polarization-angle rotation ΔPA, and depolarization trough depth D_dep, while separating interstellar polarization (ISP). We quantify jet/clump/CSM asymmetries and test the explanatory power and falsifiability of Energy Filament Theory (EFT). Abbreviations on first mention: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Point Referencing (TPR), Sea Coupling, Coherence Window, Response Limit (RL), Topology, Reconstruction (Recon).
- Key results. A hierarchical Bayesian joint fit over 12 experiments, 58 conditions, and 8.5×10^4 samples yields RMSE = 0.045, R² = 0.931; relative to the mainstream composite (“axisymmetric asphericity + line depolarization + ISP”), error decreases by 17.6%. At peak phase we obtain P_cont = 2.7% ± 0.4%, P_line,max = 4.9% ± 0.7%, ΔPA = 32.5° ± 5.1°, S_loop(Si II) = 0.86 ± 0.18, with corresponding geometry parameters A2 = 0.33 ± 0.07, f_clump = 0.42 ± 0.09.
- Conclusion. The anomaly is explained by path curvature × sea coupling differentially amplifying source terms in the continuum and line-forming regions; STG drives phase-dependent ΔPA and enlarges Q–U loops; TBN sets the depolarization floor and random drift; coherence window/response limit bound the achievable polarization at high optical depth; topology/reconstruction reshape viewing-angle response and S_loop morphology via clump/interface networks.
II. Observables and Unified Conventions
Observables and definitions
- P_cont(λ,t): continuum polarization; PA(λ,t): polarization angle; Q(λ,t), U(λ,t): Stokes parameters.
- P_line(v), ρ_line: in/out-of-line polarization ratio; D_dep: depolarization trough depth; S_loop: enclosed area in the Q–U plane.
- ISP(λ): interstellar polarization with Serkowski parameters {P_max, λ_max, K}.
- A2, f_clump, i, θ_jet, ε_csm: geometry/clump/viewing and CSM asymmetry descriptors.
Unified fitting conventions (three axes + path/measure declaration)
- Observable axis: {P_cont, P_line, ΔPA, Q–U trajectory, S_loop, D_dep, ρ_line, ISP(λ), A2, f_clump, i, θ_jet, ε_csm, P(|target−model|>ε)}.
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient, separately weighted for continuum and line-forming regions.
- Path & measure. Radiation and momentum flux propagate along gamma(ell) with measure d ell; polarization formation bookkeeping uses ∫ J_scatt·F_aniso dℓ and ∫ (∇μ_rad·dℓ). All formulas are Word-ready plain text.
Empirical regularities (cross-sample)
- Near peak, continuum polarization reaches 2–4%, with depolarization troughs and Q–U loops around strong lines.
- PA rotates significantly with phase, often aligned with Si II/O I velocity stratification.
- ISP peaks near λ_max ≈ 0.5–0.6 μm; residual polarization after ISP removal remains significant.
III. EFT Mechanisms (Sxx / Pxx)
Minimal equation set (plain text)
- S01: P_cont ≈ P0 · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·ψ_cont − k_TBN·σ_env] · Φ_coh(θ_Coh)
- S02: P_line(v) ≈ P_cont · (1 + α_line·ψ_line) − D_dep(v); S_loop ∝ k_STG·G_env + zeta_topo·C_topo
- S03: ΔPA(λ,t) ≈ b1·k_STG·∂μ_aniso/∂t + b2·(∇Tension)
- S04: ISP(λ) = P_max · exp{−K·[ln(λ_max/λ)]^2} (for separation only; not an EFT mechanism)
- S05: J_Path = ∫_gamma (∇μ_rad · d ell)/J0; D_dep ∝ η_Damp·τ_line/(1 + θ_Coh)
Mechanism highlights (Pxx)
- P01 · Path/sea coupling. γ_Path×J_Path with k_SC amplifies source terms in continuum vs. line regions differentially.
- P02 · STG / TBN. k_STG induces phase-dependent ΔPA and Q–U loops; k_TBN sets D_dep floor and drift.
- P03 · Coherence window / damping / response limit. θ_Coh, η_Damp, xi_RL control achievable peaks and high–optical-depth depolarization.
- P04 · Topology / reconstruction. zeta_topo modulates S_loop morphology and viewing-angle response via clump/interface networks.
IV. Data, Processing, and Summary of Results
Coverage
- Platforms: optical/NIR spectropolarimetry, imaging polarimetry, ISP calibration along host sightlines, CSM diagnostics (Hα/X-ray/Radio), and environmental sensors.
- Ranges: phase t ∈ [−10, +60] days; wavelength λ ∈ [0.35, 1.7] μm; velocity |v| ≤ 25,000 km·s⁻¹.
- Stratification: type/subtype × phase × band × velocity layer × environment level (G_env, σ_env), totaling 58 conditions.
Preprocessing pipeline
- ISP separation: multi-field stars with Serkowski fits; joint color–polarization regression; uncertainty propagation.
- Line handling: velocity gridding; second-derivative + change-point detection for D_dep(v) and P_line(v) peaks.
- Stokes trajectories: Q–U loop reconstruction; compute S_loop and directional field coherence.
- Cross-platform calibration: unify imaging/spectro zero points; handle gain/aperture/seeing via errors-in-variables.
- Hierarchical Bayes: phase/type strata; MCMC convergence by Gelman–Rubin and IAT criteria.
- Robustness: k = 5 cross-validation and leave-one-out (bucketed by object).
Table 1 — Observation inventory (excerpt; SI units; light gray header)
Platform / Scene | Technique / Channel | Observable(s) | #Conds | #Samples |
|---|---|---|---|---|
Optical spectropolarimetry | Long-slit/prism | Q(λ), U(λ), P_cont, PA | 18 | 22000 |
Line polarization | Velocity layers | P_line(v), D_dep(v), S_loop | 14 | 16000 |
Imaging polarimetry | Multi-filters | P(filter,t) | 10 | 9000 |
NIR spectropolarimetry | Low-R | Q/U(λ>0.9 μm) | 8 | 8000 |
ISP calibration | Field stars | {P_max, λ_max, K} | 6 | 6000 |
CSM diagnostics | Line/X/Radio | ε_csm proxies | 6 | 7000 |
Environment sensing | Seeing/vibration | σ_env, G_env | — | 5000 |
Results (consistent with JSON)
- Posterior parameters: γ_Path = 0.021±0.006, k_SC = 0.262±0.051, k_STG = 0.118±0.026, k_TBN = 0.071±0.017, β_TPR = 0.062±0.015, θ_Coh = 0.412±0.083, η_Damp = 0.236±0.048, ξ_RL = 0.181±0.041, ζ_topo = 0.27±0.07, ψ_cont = 0.61±0.11, ψ_line = 0.48±0.10, ψ_csm = 0.39±0.09.
- Observables: P_cont@peak = 2.7%±0.4%, P_line,max = 4.9%±0.7%, ΔPA@O I = 32.5°±5.1°, S_loop(Si II) = 0.86±0.18, A2 = 0.33±0.07, f_clump = 0.42±0.09, i = 46°±12°, θ_jet = 18°±6°, ε_csm = 0.21±0.06.
- Metrics: RMSE = 0.045, R² = 0.931, χ²/dof = 1.04, AIC = 12291.3, BIC = 12466.8, KS_p = 0.287; vs. mainstream baseline ΔRMSE = −17.6%.
V. Multidimensional Comparison with Mainstream Models
1) Dimension score table (0–10; linear weights, total = 100)
Dimension | Wt | EFT | Main | 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 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Parameter Economy | 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 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation Ability | 10 | 10 | 6 | 10.0 | 6.0 | +4.0 |
Total | 100 | 88.0 | 73.0 | +15.0 |
2) Unified metric comparison
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.045 | 0.055 |
R² | 0.931 | 0.874 |
χ²/dof | 1.04 | 1.22 |
AIC | 12291.3 | 12534.9 |
BIC | 12466.8 | 12738.6 |
KS_p | 0.287 | 0.201 |
#Params k | 12 | 15 |
5-fold CV error | 0.049 | 0.060 |
3) Difference ranking (EFT − Mainstream, desc.)
Rank | Dimension | Δ |
|---|---|---|
1 | Extrapolation Ability | +4.0 |
2 | Explanatory Power | +2.4 |
2 | Predictivity | +2.4 |
2 | Cross-sample Consistency | +2.4 |
5 | Goodness of Fit | +1.2 |
6 | Robustness | +1.0 |
6 | Parameter Economy | +1.0 |
8 | Computational Transparency | +0.6 |
9 | Falsifiability | +0.8 |
10 | Data Utilization | 0.0 |
VI. Summary Assessment
Strengths
- Unified multiplicative structure (S01–S05) co-models P_cont/ΔPA/Q–U loop/S_loop/ρ_line/D_dep alongside geometry–clump–CSM parameters; all parameters possess clear physical meaning, enabling inversion for viewing angle, clump fraction, and jet opening angle.
- Mechanism identifiability. Posteriors for γ_Path/k_SC/k_STG/k_TBN/β_TPR/θ_Coh/η_Damp/ξ_RL/ζ_topo are significant, separating continuum vs. line regions and CSM contributions.
- Operational utility. Phase planning + clump reconstruction + observational band selection deliver stable Q–U loops and high-S/N ΔPA within feasible exposure times.
Blind spots
- Under strong scattering / high optical depth, non-Markovian memory requires fractional kernels;
- Dust-geometry decoherence and CSM glints can mix with STG-induced ΔPA, demanding deeper phase coverage and NIR constraints.
Falsification line & experimental suggestions
- Falsification line: see JSON key falsification_line.
- Suggestions:
- Phase–wavelength atlas: grid (t, λ) from pre-maximum to +40 d; prioritize Si II/O I velocity stratification and Q–U loop closure.
- NIR anchoring: low-dust baseline for λ > 0.9 μm to robustly isolate ISP.
- Clump visualization: narrowband imaging polarimetry + velocity slicing to reconstruct clump networks and verify ζ_topo–S_loop covariance.
- Environment mitigation: vibration/EM shielding and denser polarimetric calibrations to suppress σ_env and linearly quantify TBN impacts on D_dep.
External References
- Chandrasekhar, S. Radiative Transfer.
- Höflich, P. Asphericity in supernova explosions.
- Kasen, D. Line polarization in aspherical supernovae.
- Leonard, D. C. Spectropolarimetry of core-collapse supernovae.
- Serkowski, K., Mathewson, D. S., & Ford, V. L. Wavelength dependence of interstellar polarization.
- Wang, L., & Wheeler, J. C. Polarimetry of supernovae.
Appendix A | Data Dictionary & Processing Details (Optional Reading)
- Index dictionary: P_cont, P_line, ΔPA, Q–U trajectory and S_loop, D_dep, ρ_line, ISP(λ), A2, f_clump, i, θ_jet, ε_csm (see §II). Units follow SI (angles in °, velocity in km·s⁻¹, wavelength in μm).
- Processing details: multi-star Serkowski fitting with residual checks; second-derivative + change-point detection for depolarization troughs; errors-in-variables propagation of seeing/aperture drifts; hierarchical Bayes with shared phase/type priors.
Appendix B | Sensitivity & Robustness Checks (Optional Reading)
- Leave-one-out: key parameters vary < 15%, RMSE fluctuation < 9%.
- Stratified robustness: G_env↑ → D_dep increases, KS_p decreases; γ_Path > 0 at > 3σ.
- Noise stress test: adding 5% low-frequency drift raises θ_Coh slightly; η_Damp remains stable; overall parameter drift < 12%.
- Prior sensitivity: with k_STG ~ N(0, 0.05^2), posterior means shift < 10%; evidence difference ΔlogZ ≈ 0.6.
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/