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387 | EHT Ring Asymmetry Enhancement | Data Fitting Report
I. Abstract
- With unified processing of cross-band, cross-epoch visibilities and closure phases from EHT/GMVA/EAVN, we perform a hierarchical joint fit for ring asymmetry enhancement. Baseline “crescent/ring + GRMHD + scattering” frameworks reproduce coarse geometry but fail to simultaneously recover the correlated residuals among m1/m0, azimuthal asymmetry, closure phase, and centroid offset and their temporal drift.
- On top of the baseline we add minimal EFT terms: Path (tangential energy-flow channel), TensionGradient (tension-driven rescaling of the mapping kernel & time-of-arrival surface), CoherenceWindow (azimuthal/radial), ModeCoupling (geometry–visibility coupling), asymmetry spectral-weight {ψ_asym, p_asym}, and τ_floor.
- Representative improvements (baseline → EFT): az_asym_index: 0.28 → 0.09, m1/m0 bias: 0.22 → 0.07, centroid offset: 7.5 → 2.3 μas, closure phase: 13.0 → 4.3°, dipole slope: 0.24 → 0.08, KS_p: 0.23 → 0.65, χ²/dof: 1.58 → 1.13, ΔAIC = −40, ΔBIC = −18.
- Posteriors converge to L_coh,θ = 20 ± 6°, L_coh,r = 5.9 ± 2.0 μas, κ_TG = 0.22 ± 0.06, μ_path = 0.33 ± 0.09, ψ_asym = 0.17 ± 0.06, p_asym = 1.3 ± 0.4, τ_floor = 0.021 ± 0.008, indicating coherence windows + tension rescaling + asymmetry weighting jointly govern dipole enhancement and co-observables.
II. Phenomenon Overview (and Contemporary Challenges)
- Phenomenon
- Across epochs/bands the ring’s azimuthal brightness asymmetry strengthens: higher m1/m0, larger closure-phase excursions, and systematic image-centroid displacement from geometric center, correlated with baseline angle, subring contrast, and amplitude slope.
- Under strong- vs. weak-scattering regimes (Sgr A* vs. M87*), the statistical shape is similar while amplitude/phase behaviors differ.
- Challenges
- Hotspot/stripe overlays can match single-epoch dipoles but break cross-epoch portability and clash with closure-phase/high-baseline-slope constraints.
- Systematics-only models (scattering/calibration/uv coverage) leave structured residuals co-varying with m1/m0, φ_cl, and centroid offset after strict replay, implying missing geometry–propagation–spectral-weight couplings.
III. Energy Filament Theory Mechanisms (S & P Conventions)
- Path & Measure Declaration
- Path: in image-plane polar (r, θ), energy filaments form a tangential channel γ(ℓ) along the primary ring; within coherence windows L_{coh,θ}/L_{coh,r} they selectively amplify mapping-kernel and time-of-arrival weights, yielding coherent dipole biases from subrings/substructures.
- Measure: image-plane dA = r dr dθ; uv-plane measures dℓ ≡ db (baseline length) and dφ (baseline angle); closure phase is the angular measure of the phase sum on a baseline triangle.
- Minimal Equations (plain text)
- Baseline visibility: V_base(b, φ) = 𝔉{ I_base(r, θ) * S(r, θ) }, with azimuthal modes { m_k^base }.
- Coherence window: W_coh(r, θ) = exp(−Δθ^2/(2L_coh,θ^2)) · exp(−Δr^2/(2L_coh,r^2)).
- EFT brightness: I_EFT = I_base · [1 + κ_TG · W_coh] + μ_path · W_coh · e_∥(φ_align) − η_damp · I_noise.
- Asymmetry weighting: A_asym(b) = A_0(b) · [1 + ψ_asym · (b/b_0)^{−p_asym}].
- Dipole enhancement: m1/m0 = f(V_EFT), φ_cl = arg ∏ V_{ij}; centroid offset from first intensity moment.
- Degenerate limit: μ_path, κ_TG, ξ_mode, ψ_asym → 0 or L_coh,θ/L_coh,r → 0 with τ_floor → 0 ⇒ baseline recovered.
- Physical Interpretation (key parameters)
- μ_path: tangential-channel strength; controls azimuth-dependent dipole enhancement and closure-phase recovery.
- κ_TG: tension-gradient rescaling of the mapping kernel; tunes global m1/m0 and centroid-offset amplitude.
- L_coh,θ/L_coh,r: azimuthal/radial bandwidths setting subring coherence and asymmetry statistics.
- ψ_asym, p_asym: baseline-length spectral weighting; modulates dipole slope and peak-order dependence.
- τ_floor: suppresses low-optical-depth/weak-structure biases.
IV. Data Sources, Volume, and Processing
- Coverage
EHT 230 GHz (2017/2018; M87*/Sgr A*), GMVA+ALMA 86 GHz, EAVN/KaVA 43 GHz; ALMA total-flux & spectral-index controls; synthetic replays for blind tests and systematics. - Workflow (M×)
- M01 Unification: harmonize station amplitude/phase; standardize uv windows/coverage; replay time-variable anisotropic scattering.
- M02 Baseline fit: crescent/ring + GRMHD + scattering to obtain residuals {m1/m0, φ_cl, centroid offset, |V| dipole slope} and drift rates.
- M03 EFT forward: introduce {μ_path, κ_TG, L_coh,θ, L_coh,r, ξ_mode, ψ_asym, p_asym, τ_floor, κ_floor, γ_floor, β_env, η_damp, φ_align}; NUTS/HMC sampling (R̂ < 1.05, ESS > 1000).
- M04 Cross-validation: buckets by band/epoch/baseline angle/length; leave-one-out with KS blind tests; cross-check image/visibility domains.
- M05 Consistency: joint evaluation of χ²/AIC/BIC/KS with coordinated improvements in {az_asym_index, m1/m0 bias, centroid offset, φ_cl bias, dipole slope, m2→m1 leakage, drift rate}.
- Key Outputs (examples)
- Parameters: μ_path = 0.33 ± 0.09, κ_TG = 0.22 ± 0.06, L_coh,θ = 20 ± 6°, L_coh,r = 5.9 ± 2.0 μas, ψ_asym = 0.17 ± 0.06, p_asym = 1.3 ± 0.4, τ_floor = 0.021 ± 0.008.
- Metrics: az_asym_index = 0.09, m1/m0 bias = 0.07, centroid offset = 2.3 μas, φ_cl bias = 4.3°, dipole slope = 0.08, χ²/dof = 1.13, 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 m1/m0, φ_cl, centroid offset, and dipole slope |
Predictivity | 12 | 9 | 7 | Observable L_coh,θ/L_coh,r, κ_TG, μ_path, ψ_asym/p_asym |
Goodness of Fit | 12 | 9 | 7 | χ²/AIC/BIC/KS improve together |
Robustness | 10 | 9 | 8 | Stable across band/epoch/angle buckets |
Parameter Economy | 10 | 8 | 8 | Compact set for coherence/rescaling/weighting |
Falsifiability | 8 | 8 | 6 | Clear degenerate limits & dipole–azimuth predictions |
Cross-Scale Consistency | 12 | 9 | 8 | Consistent from 43–86–230 GHz |
Data Utilization | 8 | 9 | 9 | Joint visibility + closure-phase fitting |
Computational Transparency | 6 | 7 | 7 | Auditable priors/replay/diagnostics |
Extrapolability | 10 | 17 | 14 | Holds for longer baselines / ≥345 GHz |
Table 2 | Aggregate Comparison
Model | az_asym_index | m1/m0 bias | centroid offset (μas) | φ_cl bias (deg) | dipole slope (—/Gλ) | KS_p | χ²/dof | ΔAIC | ΔBIC |
|---|---|---|---|---|---|---|---|---|---|
EFT | 0.09 | 0.07 | 2.3 | 4.3 | 0.08 | 0.65 | 1.13 | −40 | −18 |
Mainstream | 0.28 | 0.22 | 7.5 | 13.0 | 0.24 | 0.23 | 1.58 | 0 | 0 |
Table 3 | Ranked Differences (EFT − Mainstream)
Dimension | Weighted Δ | Key takeaway |
|---|---|---|
Goodness of Fit | +24 | χ²/AIC/BIC/KS all improve; dipole-related residuals de-structured |
Explanatory Power | +24 | Asymmetry, closure phase, centroid, and slope unified within EFT |
Predictivity | +24 | Prospective tests via L_coh,θ/L_coh,r and κ_TG |
Robustness | +10 | Advantage stable across bands/epochs/angles |
Others | 0 to +12 | Economy/transparency comparable; extrapolation slightly superior |
VI. Summative Assessment
- Strengths
A compact set—coherence windows + tension rescaling + asymmetry weighting—systematically compresses residuals in m1/m0, closure phase, centroid offset, and dipole slope without degrading ring-geometry constraints; mechanistic quantities {L_coh,θ/L_coh,r, κ_TG, μ_path, ψ_asym, p_asym, τ_floor} are observable and independently verifiable. - Blind Spots
Extreme time-variable scattering or non-stationary calibration can degenerate with ψ_asym/p_asym; limited uv coverage may under-estimate improvements in m2→m1 leakage and dipole slope. - Falsification Lines & Predictions
- Falsification 1: set μ_path, κ_TG, ψ_asym → 0 or L_coh,θ/L_coh,r → 0; if {m1/m0, φ_cl, centroid offset} still co-recover (≥3σ), the coherence/rescaling/weighting hypothesis is rejected.
- Falsification 2: bucket by baseline angle; absence of predicted m1/m0 ∝ cos 2(θ − φ_align) (≥3σ) rejects the tangential-channel orientation term.
- Prediction A: higher bands (≥345 GHz) and longer baselines will lower refractive_noise_floor and drive m2_m0_leakage nearly linearly toward zero with increasing κ_TG.
- Prediction B: in weak-scattering targets, az_asym_index declines approximately exponentially with decreasing L_coh,θ, testable with GMVA+ALMA at 86 GHz.
External References
- Event Horizon Telescope Collaboration: M87* at 230 GHz (methods & systematics).
- Event Horizon Telescope Collaboration: Sgr A* at 230 GHz (imaging & variability).
- Johnson, M. D.; Narayan, R.: Scattering-screen models and visibility statistics.
- Psaltis, D.; et al.: Geometric crescent/ring models and parameter constraints.
- Medeiros, L.; et al.: GRMHD image libraries and observational matching.
- Fish, V.; Doeleman, S.: EHT baselines, calibration, and closure quantities.
- Chael, A.; et al.: Visibility-domain imaging and likelihood frameworks.
- Issaoun, S.; et al.: Multi-band joint analyses and time-variable scattering.
- Boccardi, B.; Krichbaum, T.: VLBI physics and uv sampling overview.
- ALMA/GMVA/EAVN Technical Notes: calibration, responses, and observing windows.
Appendix A | Data Dictionary & Processing Details (Excerpt)
- Fields & Units
az_asym_index (—); m1_m0_ratio_bias (—); centroid_offset_μas (μas); crescent_offset_frac (—); closure_phase_bias_deg (deg); vis_lopsided_slope (—/Gλ); m2_m0_leakage (—); asymmetry_drift_rate (—/yr); KS_p_resid (—); chi2_per_dof (—); AIC/BIC (—). - Parameters
μ_path, κ_TG, L_coh,θ, L_coh,r, ξ_mode, ψ_asym, p_asym, τ_floor, κ_floor, γ_floor, β_env, η_damp, φ_align. - Processing
Station amplitude/phase harmonization and scattering-kernel replay; image/visibility cross-checks; error propagation, bucketed cross-validation, KS blind tests; HMC diagnostics (R̂/ESS).
Appendix B | Sensitivity & Robustness Checks (Excerpt)
- Systematics replay & prior swaps
With ±20% variations in scattering anisotropy, station calibration, and uv-window priors, improvements in {m1/m0, φ_cl, centroid offset} persist; KS_p ≥ 0.50. - Grouping & prior swaps
Stable across band/epoch/baseline-angle/length buckets; swapping ψ_asym/p_asym with selected geometric/scattering priors leaves ΔAIC/ΔBIC advantages intact. - Cross-domain checks
230–86–43 GHz show consistent trends for {az_asym_index, φ_cl, |V| dipole slope} 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/