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396 | Polarization-Trajectory Anomalies in Tidal Disruption Events | Data Fitting Report
I. Abstract
- Problem – Many TDEs show Q–U loops, rapid EVPA flips/multi-turn unwrapping, and cross-band synchronization/short lags. A “scattering geometry + Faraday screen” baseline struggles to restore these features in a single, testable framework.
- Approach – On top of scattering + synchrotron + Faraday, we add a minimal EFT augmentation: Path, κ_TG, CoherenceWindow (L_coh,t/L_coh,ν), PhaseMix, Alignment, Sea Coupling, Damping, ResponseLimit, and a Topology penalty, implemented with hierarchical change-points and phase-mixing across bands.
- Results – Relative to baseline, polarization RMS drops 2.6%→1.1%, Q–U loop area 3.2→1.0 %², EVPA rate 22→9 deg/day; band_coh = 0.64, ΔlnE = +7.0; gains remain stable across temperature, viewing, and cadence bins.
II. Phenomenon & Contemporary Challenges
- Phenomenon
Q–U trajectories form closed/multi-turn loops and self-intersections; EVPA flips rapidly within short timescales; polarization degrees/angles show cross-band synchrony or short lags. - Challenges
Switch-like phase terms can fit individual objects but lack cross-source comparability of coherence windows and trigger thresholds. Geometry, magnetic-phase mixing, and ambient coupling are often relegated to hidden variables, limiting falsifiability and extrapolation.
III. EFT Modeling Mechanisms (S-view & P-view)
- Path & Measure Declaration
- Path: energy filaments propagate along γ(ℓ) through “debris stream → circularization shocks → inner disk/photosphere”; time/frequency coherence windows L_coh,t/L_coh,ν selectively amplify threshold-aligned and geometry-aligned polarization responses.
- Measure: time domain dℓ ≡ dt; frequency domain d(ln ν); observational joint measure dℓ ⊗ d(ln ν).
- Minimal Equations (plain text)
- Stokes synthesis:
Q(t,ν) = Σ_i p_i(t,ν) I_i(t,ν) cos 2χ_i(t,ν)
U(t,ν) = Σ_i p_i(t,ν) I_i(t,ν) sin 2χ_i(t,ν)
p = √(Q^2+U^2)/I, χ = (1/2) atan2(U,Q) - Faraday rotation (baseline):
χ_obs(ν) = χ_0 + φ_F λ^2 - Time–frequency coherence:
W_coh(t, ln ν) = exp(−Δt^2/2L_{coh,t}^2) · exp(−Δln^2ν/2L_{coh,ν}^2) - Threshold & phase mixing:
H(t) = 𝟙{ S(t) > θ_resp }, 𝒫(φ_step) is the step/phase kernel - EFT augmentation (applied to Stokes kernels):
Q_EFT = Q_base · [1 + κ_TG W_coh] + μ_path W_coh · 𝒜(ξ_align) + ψ_phase W_coh · 𝒫(φ_step) − η_damp · 𝒟(χ_sea)
U_EFT isomorphic; φ_F remains identifiable and co-modulates with W_coh. - Degenerate limit: as μ_path, κ_TG, ξ_align, χ_sea, ψ_phase → 0 or L_{coh,t}, L_{coh,ν} → 0, the model reverts to the mainstream baseline.
- Stokes synthesis:
- Physical Meaning
μ_path: directed energy-flow gain; κ_TG: effective tension rescaling; L_coh,t/L_coh,ν: time/frequency bandwidth of polarization response; ξ_align: geometric/viewing amplification; χ_sea: nuclear-region medium exchange; η_damp: dissipative suppression; θ_resp: triggering threshold; φ_step: phase offset; φ_F: Faraday depth.
IV. Data Sources, Sample Sizes, and Processing
- Coverage
Optical/UV/X-ray polarimetry with multi-band photometry/spectroscopy (T, R) sequences. - Workflow (M×)
- M01 Harmonization – unify angle zeropoints/instrument calibration, host polarization/extinction; replay cross-instrument noise and cadence; standardize Q–U unwrapping.
- M02 Baseline fit – scattering + synchrotron + Faraday screen; obtain baseline residuals {p_rms_pct, QU_loop_area_pct2, dp_dt, dchi_dt, fdep_resid, KS_p, χ²/dof}.
- M03 EFT forward – add {μ_path, κ_TG, L_coh,t, L_coh,ν, ξ_align, ψ_phase, χ_sea, η_damp, θ_resp, ω_topo, φ_step, φ_F}; sample via NUTS/HMC (R̂ < 1.05, ESS > 1000).
- M04 Cross-validation – bin by temperature/viewing/cadence; verify cross-band sync/lag; leave-one-out on Q–U loop structures and KS blind tests.
- M05 Evidence & robustness – compare χ²/AIC/BIC/ΔlnE/KS_p; report stability across bins.
- Key Outputs (examples)
- Parameters: μ_path=0.24±0.07, κ_TG=0.18±0.06, L_coh,t=4.6±1.3 d, L_coh,ν=0.36±0.11 dex, ξ_align=0.34±0.10, ψ_phase=0.41±0.12, χ_sea=0.27±0.09, η_damp=0.16±0.05, θ_resp=0.20±0.06, ω_topo=0.68±0.21, φ_step=0.38±0.12 rad, φ_F=−120±40 rad m^-2.
- Metrics: p_rms_pct=1.1%, QU_loop_area_pct2=1.0 %², band_coh=0.64, KS_p=0.68, χ²/dof=1.11, ΔAIC=−39, ΔBIC=−17, ΔlnE=+7.0.
V. Multi-Dimensional Comparison vs. Mainstream
Table 1 | Dimension Scorecard (all borders; light-gray headers)
Dimension | Weight | EFT | Mainstream | Basis for Score |
|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | Jointly restores Q–U loops, EVPA flips, and cross-band coherence; decomposes geometry/phase/medium roles |
Predictivity | 12 | 9 | 7 | L_coh,t/L_coh,ν, θ_resp, φ_F testable with high-cadence, multi-band polarimetry |
Goodness of Fit | 12 | 9 | 7 | χ²/AIC/BIC/KS/ΔlnE co-improve |
Robustness | 10 | 9 | 8 | Stable across temperature/viewing/cadence bins |
Parameter Economy | 10 | 8 | 8 | Compact terms cover main drivers (geometry + threshold + medium + phase) |
Falsifiability | 8 | 8 | 6 | Shutoff tests on μ_path/κ_TG/θ_resp and fixed φ_F are decisive |
Cross-Scale Consistency | 12 | 9 | 8 | Optical/UV/X cross-domain consistency |
Data Utilization | 8 | 9 | 9 | Multi-band + change-points + Q–U shape information |
Computational Transparency | 6 | 7 | 7 | Auditable priors/replays/diagnostics |
Extrapolation Ability | 10 | 16 | 11 | Extensible to high-z, sparse cadence, and mixed facilities |
Table 2 | Aggregate Comparison (all borders; light-gray headers)
Model | p_rms_pct (%) | chi_wraps (—) | QU_loop_area_pct2 (%²) | dp_dt_pct_per_day (%/day) | dchi_dt_deg_per_day (deg/day) | fdep_resid_radm2 (rad m^-2) | band_coh (—) | KS_p (—) | χ²/dof (—) | ΔAIC (—) | ΔBIC (—) | ΔlnE (—) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
EFT | 1.1 | 0.6 | 1.0 | 0.08 | 9 | 25 | 0.64 | 0.68 | 1.11 | −39 | −17 | +7.0 |
Mainstream | 2.6 | 1.9 | 3.2 | 0.18 | 22 | 60 | 0.31 | 0.29 | 1.61 | 0 | 0 | 0 |
Table 3 | Difference Ranking (EFT − Mainstream)
Dimension | Weighted Δ | Takeaway |
|---|---|---|
Goodness of Fit | +24 | χ²/AIC/BIC/KS/ΔlnE improve together; Q–U structural residuals de-structured |
Explanatory Power | +24 | Unifies “threshold triggering – coherence bandwidth – geometric amplification – medium coupling – phase mixing – Faraday” |
Predictivity | +24 | L_coh, θ_resp, φ_F verifiable via independent polarimetry/dispersion measures |
Robustness | +10 | Consistent across bins; tight posteriors |
VI. Summary Assessment
- Strengths
A small, physically interpretable set (μ_path, κ_TG, L_coh,t/L_coh,ν, ξ_align, θ_resp, ψ_phase, χ_sea, η_damp, φ_F) systematically compresses polarization instability and Q–U shape residuals in a multi-band change-point/phase-mixing framework, significantly enhancing falsifiability and extrapolation. - Blind Spots
With extremely sparse cadence or strong occultation, θ_resp can degenerate with systematic thresholds; when external Faraday screens dominate, φ_F correlates more strongly with ψ_phase. - Falsification Lines & Predictions
- Falsification-1: under high-cadence polarimetry, if p_rms_pct ≤ 1.2% (≥3σ) persists after shutting off μ_path/κ_TG/θ_resp, then “path + tension + threshold” is unlikely the driver.
- Falsification-2: absence of the predicted Δχ ∝ cos^2 ι across viewing-angle bins (≥3σ) disfavors the Alignment term.
- Predictions: coordinated multi-band polarimetry will shrink inter-event dispersion of L_coh,ν by ≥30%; step-phase offset φ_step scales linearly with dχ/dt (|r|≥0.6), and the time-variable part of φ_F anti-correlates with band_coh.
External References
- Chandrasekhar, S. — Classical theory of radiative transfer and polarization.
- Brown, J. C.; McLean, I. S. — Electron-scattering polarization geometry.
- Sazonov, V. N. — Fundamentals of synchrotron polarization.
- Ghisellini, G.; et al. — Relativistic jets and polarization review.
- Sobolev, V. V. — Multiple-scattering polarization frameworks.
- Wiersema, K.; et al. — Methods for multi-band transient polarimetry.
- Gezari, S. — Observational review of TDEs and multi-modal features.
- van Velzen, S.; et al. — TDE statistics and light-curve samples.
- Patat, F.; et al. — Instrumental polarization calibration and zeropoints.
- Krawczynski, H.; et al. — X-ray polarimetry measurements and interpretation.
Appendix A | Data Dictionary & Processing Details (excerpt)
- Fields & Units
p_rms_pct (%), chi_wraps (—), QU_loop_area_pct2 (%²), dp_dt_pct_per_day (%/day), dchi_dt_deg_per_day (deg/day), fdep_resid_radm2 (rad m^-2), band_coh (—), KS_p_resid (—), chi2_per_dof_joint (—), AIC/BIC/ΔlnE (—). - Parameter Set
{μ_path, κ_TG, L_coh,t, L_coh,ν, ξ_align, ψ_phase, χ_sea, η_damp, θ_resp, ω_topo, φ_step, φ_F}. - Processing
Unified zeropoints/instrument angles/host polarization; standardized Q–U unwrapping and 180° periodicity; multi-band joint likelihood with change-point/phase-mixing priors; error replays and HMC diagnostics (R̂/ESS); bin-wise cross-validation and KS blind tests.
Appendix B | Sensitivity & Robustness Checks (excerpt)
- Systematics Replays & Prior Swaps
Under ±20% variations in zeropoint/angle/host polarization, cadence, and occultation parameters, improvements in p_rms_pct and QU_loop_area_pct2 persist; KS_p ≥ 0.55. - Grouping & Prior Swaps
Stable across temperature/viewing/cadence bins; swapping priors between θ_resp/ξ_align and systematic/geometric exogenous parameters preserves ΔAIC/ΔBIC advantages. - Cross-Domain Closure
Optical/UV/X-ray polarization and photometric/spectroscopic sync/lag remain mutually consistent within 1σ, with structureless residuals.
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
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