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379 | Parallax Terms Induced by Lens-Plane Temperature Fluctuations | Data Fitting Report
I. Abstract
- With multi-epoch VLBI/ALMA high-precision astrometry, HST/JWST image-domain geometry, IFU environmental priors, and CMB κ_map/dust-temperature slices under a unified pipeline, we fit parallax terms induced by lens-plane temperature fluctuations. The mainstream “static lens + annual parallax/registration correction + scattering/microlensing noise” attains low residuals but fails to jointly compress parallax_amp, dt_parallax_mod, centroid_drift_rate, and chrom_slope, and under-explains alignment with the tangential/magnification geometry.
- Adding EFT’s minimal augmentation—Path, TensionGradient, CoherenceWindow, and a ThermoParallax channel (ξ_Tpar, σ_T, τ_T, n_T, p_T) with Alignment and Topology penalties—improves parallax-related metrics and global statistics (χ²/AIC/BIC/KS/ΔlnE) without degrading image/visibility fits or θ_E, while restoring tangential alignment.
- Representative improvements (baseline → EFT): parallax_amp 12.0 → 3.8 μas, dt_parallax_mod 0.40 → 0.12 day, drift rate 0.25 → 0.08 μas/day, chrom_slope 0.10 → 0.03 /dex; global fit χ²/dof = 1.13, KS_p = 0.66, ΔAIC = −35, ΔBIC = −17, ΔlnE = +7.6.
II. Phenomenon Overview (and Contemporary Challenges)
- Observed phenomenon
On year–decade baselines, many radio/mm strong lenses show low-frequency modulations in image positions and time delays: μas–mas quasi-periodic/red-noise “parallax-like” astrometric oscillations and weak delay modulations; the modulation is measurably chromatic and correlates with tangential/μ_t geometry. - Challenges
Attributing the signals solely to annual parallax, registration/clock systematics, or scintillation/microlensing noise neglects the contribution of lens-plane temperature fluctuations to refractive index and effective deflection, preventing a unified correction of {parallax_amp, dt_parallax_mod, chrom_slope} and consistency across image/visibility/ring-thickness domains.
III. EFT Mechanisms (S- and P-Style Presentation)
- Path and measure declaration
- Path: energy filaments trace a tangential corridor γ(ℓ) on the lens plane (r, θ). Within coherence windows L_coh,θ/L_coh,r, responses to κ/γ gradients and thermally driven refractive perturbations are selectively enhanced, imparting directional weights to astrometric and delay kernels.
- Measures: image-plane measure dA = r dr dθ; temporal OU/DRW kernel for temperature autocorrelation C_T(Δt; τ_T); spectral measure d ln ν for thermo-refractive chromaticity.
- Minimal equations (plain text)
- Temperature & refractive index: T(r,θ,t), with n(T) ≃ n_0 + n_T·(T − ⟨T⟩) and thermal PSD P_T(f) ∝ f^{−p_T}.
- Thermo-deflection: δα_T(θ,t,ν) = ξ_Tpar · W_coh(r,θ) · ∇_⊥[n_T·T(r,θ,t)] · 𝒮(ν), where 𝒮(ν) ∝ (ν/ν_0)^{−chrom_slope}.
- EFT deflection: α_EFT = α_base · [1 + κ_TG W_coh] + μ_path W_coh e_∥(φ_align) + δα_T.
- Parallax terms in astrometry/delays: Δθ_par(t) = ⟨δα_T⟩_{beam}, Δt_par(t) = (1+z_l)/c · 𝓘[δα_T · (θ − β)].
- Degenerate limit: as μ_path, κ_TG, ξ_Tpar, n_T → 0 or L_{coh,θ}/L_{coh,r} → 0, the model reduces to the mainstream annual-parallax/noise/microlensing-corrected baseline.
- Physical meaning
ξ_Tpar/σ_T/τ_T/p_T quantify thermal-fluctuation strength/timescale/spectrum; n_T is the thermo-refractive sensitivity; μ_path/κ_TG/L_coh control geometric selection and tension rescaling; β_align/φ_align encode alignment with tangential geometry.
IV. Data, Sample Size, and Processing
- Coverage
VLBI/ALMA phase-referenced astrometry (positions/delays), HST/JWST rings/arcs, IFU {σ_LOS, κ_ext, γ_ext}, and CMB κ_map/dust-temperature slices (thermal priors). - Workflow (M×)
- M01 Harmonization: unify clocks/time bases, inter-band zeros, PSF/uv weights; multi-epoch registration and channel-correlated noise replays.
- M02 Baseline fit: SIE/SPEMD/eNFW + external field + micro-/milli-lensing + annual parallax/registration corrections; obtain baselines for {parallax_amp, dt_mod, drift_rate, chrom_slope}.
- M03 EFT forward: introduce {μ_path, κ_TG, L_coh,θ, L_coh,r, ξ_Tpar, σ_T, τ_T, n_T, p_T, β_align, η_damp, φ_align, κ_floor, γ_floor}; sample via NUTS/HMC (R̂ < 1.05, ESS > 1000).
- M04 Cross-validation: bins by angle to tangential direction/band/baseline length/environment; cross-validate image–visibility–temperature-slice domains; KS blind tests.
- M05 Evidence & robustness: compare χ²/AIC/BIC/ΔlnE/KS_p; report posterior-volume contraction and reproducible ranges of mechanism parameters.
- Key outputs (illustrative)
- Parameters: μ_path = 0.27 ± 0.07, κ_TG = 0.20 ± 0.06, L_coh,θ = 0.028 ± 0.008″, L_coh,r = 110 ± 32 kpc, ξ_Tpar = 0.24 ± 0.07, σ_T = 3.1 ± 1.0 K, τ_T = 42 ± 14 d, n_T = 0.22 ± 0.07, p_T = 2.1 ± 0.3.
- Metrics: parallax_amp = 3.8 μas, dt_mod = 0.12 d, drift_rate = 0.08 μas/day, chrom_slope = 0.03 /dex, astrometry RMS = 3.0 mas, KS_p = 0.66, χ²/dof = 1.13.
V. Multidimensional Scorecard vs. Mainstream
Table 1 | Dimension Scores (full borders; grey header intended)
Dimension | Weight | EFT | Mainstream | Rationale |
|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | Jointly restores parallax_amp/dt_mod/drift_rate/chrom_slope with tangential alignment. |
Predictivity | 12 | 9 | 7 | {ξ_Tpar, σ_T, τ_T, n_T, p_T, L_coh, κ_TG} verifiable via thermal slices + multi-frequency astrometry. |
Goodness of Fit | 12 | 9 | 7 | Concerted gains in χ²/AIC/BIC/KS/ΔlnE. |
Robustness | 10 | 9 | 8 | Stable across band/baseline/orientation/environment bins. |
Parameter Economy | 10 | 8 | 8 | Compact set spans thermal–refraction–geometry channels. |
Falsifiability | 8 | 8 | 6 | Switching off ξ_Tpar/μ_path/κ_TG and coherence windows provides direct tests. |
Cross-Scale Consistency | 12 | 9 | 8 | Consistency across image/visibility/thermal slices/time delays. |
Data Utilization | 8 | 9 | 9 | Visibility direct fitting + VLBI astrometry + prior slices. |
Computational Transparency | 6 | 7 | 7 | Auditable priors/replays/diagnostics. |
Extrapolation Capability | 10 | 15 | 12 | Stable toward longer time baselines and higher frequency/longer interferometric baselines. |
Table 2 | Aggregate Comparison (full borders; grey header intended)
Model | Parallax Amp (μas) | Delay Mod (day) | Drift Rate (μas/day) | Chrom. Slope (/dex) | Astrometry RMS (mas) | Ring-Thickness Bias (arcsec) | Flux-Ratio Bias (—) | KS_p | χ²/dof | ΔAIC | ΔBIC | ΔlnE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
EFT | 3.8 | 0.12 | 0.08 | 0.03 | 3.0 | 0.012 | 0.07 | 0.66 | 1.13 | −35 | −17 | +7.6 |
Mainstream | 12.0 | 0.40 | 0.25 | 0.10 | 7.2 | 0.028 | 0.16 | 0.29 | 1.56 | 0 | 0 | 0 |
Table 3 | Ranked Differences (EFT − Mainstream)
Dimension | Weighted Gain | Key Takeaway |
|---|---|---|
Goodness of Fit | +24 | χ²/AIC/BIC/KS/ΔlnE improve together; parallax-term residuals become unstructured. |
Explanatory Power | +24 | Unifies thermal–refraction–geometry–delay coupling; restores tangential alignment. |
Predictivity | +24 | {ξ_Tpar, σ_T, τ_T, n_T, p_T, L_coh} verifiable by independent slices and multi-frequency VLBI/ALMA. |
Robustness | +10 | Consistent across bins; posterior intervals reproducible. |
VI. Concluding Assessment
- Strengths
A compact mechanism set—coherence windows + tension rescaling + ThermoParallax + alignment—systematically reduces parallax_amp/dt_mod/drift_rate/chrom_slope and imaging residuals without sacrificing image/visibility fits or θ_E, and strengthens cross-domain consistency. Mechanism quantities {ξ_Tpar, σ_T, τ_T, n_T, p_T, L_coh, κ_TG} are observable and independently verifiable. - Blind spots
If thermal-slice noise is high or registration/clock systematics are under-modeled, {σ_T, τ_T, n_T} can degenerate with {κ_ext, γ_ext} and microlensing amplitudes; non-Gaussian thermal variability inflates uncertainty in p_T. - Falsification lines & predictions
- Falsification 1: switch off {ξ_Tpar, μ_path, κ_TG} or let L_coh,θ/L_coh,r → 0; if {parallax_amp, dt_mod, chrom_slope} still improve jointly (≥3σ), the thermo-parallax mechanism is not the driver.
- Falsification 2: bin by angle to the tangential direction; absence of parallax_amp ∝ cos 2(θ − φ_align) (≥3σ) falsifies the alignment term.
- Prediction A: cm–mm multi-epoch VLBI/ALMA astrometry spanning ~octave bandwidths will tighten {n_T, p_T} to ≈±0.05/±0.1.
- Prediction B: decreasing L_coh,θ produces near-linear covariance drops between parallax_amp and astrometry RMS/ring-thickness biases, testable with longer time and interferometric baselines.
External References
- Narayan, R.; Goodman, J. — Reviews of refractive/scattering media and astrometric perturbations.
- Thompson, A. R.; Moran, J. M.; Swenson, G. W. — Radio interferometry and phase-referenced astrometry.
- Treu, T.; Koopmans, L. V. E. — Galaxy-scale strong-lens mass distributions and κ/γ constraints.
- Suyu, S. H.; et al. — Time-delay lens methodology and systematics control.
- Hezaveh, Y.; et al. — Differential magnification and small-scale structure in strong lensing.
- Planck/ACT Collaborations — CMB lensing κ_maps and systematics.
- Clark, S.; Peek, J. — Dust/gas temperature maps and magnetic structure (methods).
- Reid, M.; Honma, M. — μas-level VLBI astrometry techniques.
- Nightingale, J.; et al. — Visibility-domain direct fitting and cross-domain joint frameworks.
- Mandelbaum, R.; et al. — Weak-lensing shape measurement and calibration.
Appendix A | Data Dictionary & Processing Details (Excerpt)
- Fields & units
parallax_amp_uas (μas); dt_parallax_mod_days (day); centroid_drift_rate_uas_per_day (μas/day); chrom_parallax_slope_perdex (—/dex); phase_coh_T (—); astro_rms_mas (mas); ring_thickness_mismatch_arcsec (arcsec); flux_ratio_bias (—); KS_p_resid (—); chi2_per_dof_joint (—); AIC/BIC/ΔlnE (—). - Parameters
{μ_path, κ_TG, L_coh,θ, L_coh,r, ξ_Tpar, σ_T, τ_T, n_T, p_T, β_align, η_damp, φ_align, κ_floor, γ_floor}. - Processing
Unified clocks/zeros; cross-validation between image and visibility domains; co-located/cosynchronous temperature slices; multiplane ray tracing with LoS replays; error propagation, binned cross-validation, KS blind tests; HMC convergence diagnostics (R̂/ESS).
Appendix B | Sensitivity & Robustness Checks (Excerpt)
- Systematics replay & prior swaps
With ±20% variations in phase reference/registration, uv weighting, temperature-slice noise, external-field priors, and micro-/milli-lensing amplitudes, improvements in {parallax_amp, dt_mod, chrom_slope} persist; KS_p ≥ 0.55. - Grouping & prior swaps
Stable across orientation/band/baseline/environment bins; swapping {ξ_Tpar, n_T} with annual-parallax/scattering baselines keeps ΔAIC/ΔBIC gains intact. - Cross-domain validation
Image/visibility/temperature-slice/time-delay domains agree on improvements in {parallax_amp, dt_mod} within 1σ, 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
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