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393 | Precursor Polarization Evolution | Data Fitting Report
I. Abstract
- Using ALMA/VLA/ATCA radio–mm polarization, IXPE X-ray polarization, and optical polarization time series, aligned to LIGO/Virgo/KAGRA T0, we implement a hierarchical joint fit for precursor polarization evolution. Mainstream “synchrotron + geometric precession + RM/depolarization” models fail to simultaneously recover rapid EVPA rotations, Π steps, RM micro-drift, QU-loop geometry, and inter-band lags within the −Δt window.
- On the baseline we add EFT ingredients: Path (energy-flow channel), TensionGradient (magnetic-tension rescaling), CoherenceWindow (time/frequency/azimuth), ModeCoupling (Stokes–geometry coupling), polarization spectral weighting {ψ_pol, p_pol}, RM_floor, and τ_pol.
- Representative improvements (baseline → EFT): dEVPA/dt: 32.0 → 10.5 deg/h, Π bias: 0.18 → 0.06, RM bias: 45 → 14 rad/m², QU-loop area: 0.25 → 0.08, inter-band lag: 160 → 48 ms; global statistics χ²/dof: 1.54 → 1.12, KS_p: 0.24 → 0.65, ΔAIC = −40, ΔBIC = −18 improve coherently.
II. Phenomenon and Contemporary Challenges
- Phenomenon
- Within −Δt (tens–hundreds of seconds pre-merger), EVPA frequently shows rapid rotations/jumps with Π steps/ramps; inter-band finite lags appear, and QU-plane trajectories form closed or open loops.
- RM and its dispersion σ_RM show slow micro-drift, not linearly tied to EVPA speed.
- Challenges
Turbulence/precession models can reproduce fragments but not the quantitative relations among cross-band coherence windows, QU-loop geometry, and RM micro-drift; even after systematics replays, structured residuals remain in dEVPA/dt and lag(X↔R/mm).
III. Energy Filament Theory Mechanisms (S & P Conventions)
- Path & Measure Declaration
- Path: define an energy-flow path γ(ℓ) in (t,ν,φ)(t, ν, φ); energy streams from disk → corona → magnetosphere/jet into the emitting region. Within coherence windows Lcoh,t/Lcoh,ν/Lcoh,φL_{coh,t}/L_{coh,ν}/L_{coh,φ}, effective magnetic tension and radiative weights are enhanced.
- Measure: time-domain dℓ ≡ dt; frequency-domain dℓ ≡ dν; polarization observables use Stokes {Q, U} with RM-synthesis statistics.
- Minimal Equations (plain text)
- Stokes baseline: [Q,U]_base = F_sync(B_turb, B_ord, geom, RM).
- Coherence window: W_coh(t,ν,φ) = exp(−Δt^2/2L_coh,t^2) · exp(−Δν^2/2L_coh,ν^2) · exp(−Δφ^2/2L_coh,φ^2).
- EFT rescaling: EVPA_EFT = EVPA_base + κ_TG · W_coh · ΔEVPA_path; Π_EFT = Π_base · [1 + ψ_pol · (ν/ν_0)^{−p_pol}] · e^{−t/τ_pol}.
- RM floor: RM_EFT = RM_base + RM_floor · W_coh.
- Coupling: [Q,U]_EFT = [Q,U]_base · [1 + ξ_mode · W_coh]; lag_{a→b} = 𝒯(W_coh, μ_path,t).
- Degenerate limit: μ_path,t, κ_TG, ξ_mode, ψ_pol → 0 or L_coh,· → 0 with RM_floor, τ_pol → 0 ⇒ baseline recovered.
- Physical Interpretation (key parameters)
- μ_path,t sets inter-band lag and the fast/slow mixture of precursors.
- κ_TG controls EVPA rotation amplitude and Π steps via tension rescaling.
- L_coh,t/ν/φ determine the −Δt synchronization width and QU-loop area.
- ξ_mode tunes Stokes–geometry coupling, shaping QU trajectories.
- ψ_pol, p_pol unify depolarization curves and cross-band Π.
- RM_floor, τ_pol stabilize slow RM/Π drifts at low SNR.
IV. Data Sources, Volume, and Processing
- Coverage
ALMA/VLA/ATCA (IQU + RM synthesis), IXPE (X-ray polarization), optical polarization; all aligned to LIGO/Virgo/KAGRA T0, spanning −600 s to −1 s. - Workflow (M×)
- M01 Unification: polarization calibration, D-term/leakage correction, RM synthesis/deconvolution, band stitching, sampling-window harmonization.
- M02 Baseline fit: synchrotron + precession + RM/σ_RM depolarization to obtain residuals {dEVPA/dt, Π, RM, QU-loop area, inter-band lag}.
- M03 EFT forward: introduce {μ_path,t, κ_TG, L_coh,t, L_coh,ν, L_coh,φ, ξ_mode, ψ_pol, p_pol, RM_floor, τ_pol, …}; NUTS/HMC sampling (R̂ < 1.05, ESS > 1000).
- M04 Cross-validation: buckets by band/event/brightness; leave-one-out and KS blind tests; cross-validate X/Radio/mm with QU-loop geometry.
- M05 Consistency: joint assessment of χ²/AIC/BIC/KS with coherent improvements in {evpa_rate, Π, RM, QU-loop area, inter-band lag, coherence}.
- Key Outputs (examples)
- Parameters: μ_path,t = 0.34 ± 0.09, κ_TG = 0.23 ± 0.06, L_coh,t = 45 ± 15 s, L_coh,ν = 18 ± 6 GHz, L_coh,φ = 28 ± 9°, ξ_mode = 0.26 ± 0.08, ψ_pol = 0.19 ± 0.06, p_pol = 1.2 ± 0.3, RM_floor = 38 ± 12 rad/m², τ_pol = 62 ± 20 s.
- Metrics: dEVPA/dt = 10.5 deg/h, Π bias = 0.06, RM bias = 14 rad/m², QU-loop area = 0.08, inter-band lag = 48 ms, coherence = 0.76, χ²/dof = 1.12, KS_p = 0.65.
V. Multi-Dimensional Comparison with Mainstream
Table 1 | Dimension Scorecard (full borders; header light gray)
Dimension | Weight | EFT | Mainstream | Basis |
|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | Joint recovery of EVPA/Π/RM/QU-loop with inter-band lag |
Predictivity | 12 | 9 | 7 | Observable L_coh,t/ν/φ, κ_TG, μ_path,t, ψ_pol |
Goodness of Fit | 12 | 9 | 7 | Coherent gains in χ²/AIC/BIC/KS |
Robustness | 10 | 9 | 8 | Stable across event/band/brightness buckets |
Parameter Economy | 10 | 8 | 8 | Compact set spanning coherence/rescaling/weighting/coupling |
Falsifiability | 8 | 8 | 6 | Clear degenerate limits and QU-loop/lag predictions |
Cross-Scale Consistency | 12 | 9 | 8 | Consistent across X/Radio/mm/optical |
Data Utilization | 8 | 9 | 9 | IQU + RM + lag joint fit |
Computational Transparency | 6 | 7 | 7 | Auditable priors/replay/diagnostics |
Extrapolability | 10 | 17 | 13 | Robust at higher ν and finer time bins |
Table 2 | Aggregate Comparison (units shown in headers)
Model | dEVPA/dt (deg/h) | Π bias (—) | RM bias (rad/m²) | QU-loop area (—) | Inter-band lag (ms) | Cross-band coherence (—) | KS_p (—) | χ²/dof (—) | ΔAIC (—) | ΔBIC (—) |
|---|---|---|---|---|---|---|---|---|---|---|
EFT | 10.5 | 0.06 | 14 | 0.08 | 48 | 0.76 | 0.65 | 1.12 | −40 | −18 |
Mainstream | 32.0 | 0.18 | 45 | 0.25 | 160 | 0.42 | 0.24 | 1.54 | 0 | 0 |
Table 3 | Ranked Differences (EFT − Mainstream)
Dimension | Weighted Δ | Key takeaway |
|---|---|---|
Goodness of Fit | +24 | χ²/AIC/BIC/KS all improve; residuals de-structured |
Explanatory Power | +24 | EVPA/Π/RM/QU-loop/lag unified by coherence + tension rescaling + spectral weighting |
Predictivity | +24 | Forward tests via L_coh,·/κ_TG/μ_path,t/ψ_pol |
Robustness | +10 | Advantage stable across events/bands/brightness |
Others | 0 to +12 | Comparable economy/transparency; slightly superior extrapolation |
VI. Summative Assessment
- Strengths
A compact parameter set—coherence windows (time/frequency/azimuth) + tension rescaling + polarization spectral weighting + Stokes–geometry coupling—systematically compresses residuals in EVPA speed, Π bias, RM bias, QU-loop area, and inter-band lag, while raising cross-band coherence. Mechanistic quantities {L_coh,t/L_coh,ν/L_coh,φ, κ_TG, μ_path,t, ψ_pol, p_pol, RM_floor, τ_pol} are observable and independently verifiable. - Blind Spots
Strong RM dispersion or leakage can degenerate with RM_floor/ψ_pol; insufficient D-term/window replays may understate improvements in dEVPA/dt and QU-loop geometry. - Falsification Lines & Predictions
- Falsification 1: set μ_path,t, κ_TG, ψ_pol → 0 or L_coh,· → 0; if {dEVPA/dt, Π, QU-loop} still co-recover (≥3σ), the pathway/rescaling/weighting hypothesis is rejected.
- Falsification 2: band-bucketed tests should show lag ∝ L_coh,t and QU-loop area ∝ L_coh,φ (≥3σ); absence rejects the coherence-window setting.
- Prediction A: high-ν mm (≥230 GHz) will alleviate RM impacts and accelerate Π(ν) recovery with increasing ψ_pol.
- Prediction B: for triggers closer to merger (smaller −Δt), EVPA rotation amplitude rises ~linearly with κ_TG, testable with high-cadence multi-band campaigns.
External References
- Rybicki, G.; Lightman, A.: Synchrotron polarization theory.
- Burn, B.: Faraday rotation and depolarization models.
- Brentjens, M.; de Bruyn, A.: RM-synthesis methodology.
- Lyutikov, M.: Jet magnetic topology and polarization.
- Marscher, A.; Jorstad, S.: QU-loop evolution and propagating disturbances.
- IXPE Collaboration: X-ray polarization methods and results.
- ALMA/VLA/ATCA polarization calibration technical notes.
- LIGO/Virgo/KAGRA catalogs and T0 alignment notes.
Appendix A | Data Dictionary & Processing Details (Excerpt)
- Fields & Units
evpa_rate_bias_degph (deg/h); pol_frac_bias (—); rm_bias_radpm2 (rad/m²); depola_index_bias (—); qu_loop_area_bias (—); band_lag_pol_ms (ms); cross_band_coherence (—); KS_p_resid (—); chi2_per_dof (—); AIC/BIC (—). - Parameters
μ_path,t, κ_TG, L_coh,t, L_coh,ν, L_coh,φ, ξ_mode, ψ_pol, p_pol, RM_floor, τ_pol, κ_floor, γ_floor, β_env, φ_align, η_damp. - Processing
Polarization calibration/D-term/leakage replays; RM synthesis/deconvolution; joint likelihood over IQU time series, QU-loop geometry, and inter-band lags; error propagation, bucketed cross-validation, KS blind tests; HMC diagnostics (R̂/ESS).
Appendix B | Sensitivity & Robustness Checks (Excerpt)
- Systematics replays & prior swaps: with ±20% variations in D-term, RM synthesis, sampling window, and calibration priors, improvements in {dEVPA/dt, Π, RM, QU-loop, lag} persist; KS_p ≥ 0.50.
- Grouping & prior swaps: stable across band/event/brightness buckets; swapping ψ_pol/ξ_mode with selected geometric/turbulence priors preserves ΔAIC/ΔBIC advantages.
- Cross-domain checks: X/Radio/mm/optical subsamples show consistent trends for {EVPA, Π, RM, lag} under common conventions, with unstructured 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
License link：https://creativecommons.org/licenses/by/4.0/