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240 | Nuclear Extinction–Age Mismatch in Elliptical Galaxies | Data Fitting Report

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{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250907_GAL_240",
  "phenomenon_id": "GAL240",
  "phenomenon_name_en": "Nuclear Extinction–Age Mismatch in Elliptical Galaxies",
  "scale": "Macro",
  "category": "GAL",
  "language": "en",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "SeaCoupling",
    "Damping",
    "ResponseLimit",
    "Recon",
    "Topology",
    "STG"
  ],
  "mainstream_models": [
    "Age–metallicity degeneracy & aperture effects: spectro-photometric ages are luminosity-weighted and biased by [Z/H] and inner/outer light fractions, producing SED vs. Lick-index discrepancies.",
    "Nuclear dust lanes & geometry: obscuration/scattering in nuclear lanes/rings raises A_V,nuc, weakens Balmer absorption and strengthens Dn4000, inducing age mismatch.",
    "LINER/AGN contamination: non-stellar continua and narrow-line infill bias Hβ and [O III]-based indices, skewing spectral ages.",
    "Composite populations & rejuvenation: minor young components from external gas yield 'younger minima' against old outskirts, creating mismatches.",
    "Systematics: PSF wings, fiber filling, sky/zero-points, aperture choices (R_e/8 vs. R_e/2), and diffraction spikes co-bias A_V and ages."
  ],
  "datasets_declared": [
    {
      "name": "HST/ACS & WFC3 (F475W/F814W/F160W: nuclear dust geometry & colour gradients)",
      "version": "public",
      "n_samples": "thousands (cluster & field ellipticals)"
    },
    {
      "name": "SDSS DR16 / HSC-SSP (deep imaging: colour gradients & A_V maps)",
      "version": "public",
      "n_samples": "~1.5×10^5 (cross-matched)"
    },
    {
      "name": "MaNGA DR17 / SAMI / ATLAS3D (IFU: Dn4000, Hβ, Mgb, <Fe>, EW[O III]/Hα, ψ)",
      "version": "public",
      "n_samples": "~4×10^4"
    },
    {
      "name": "ALMA (nuclear dust continuum/CO: dust–gas priors)",
      "version": "public",
      "n_samples": "few hundreds (subset)"
    },
    {
      "name": "Chandra/XMM (nuclear X-ray: AGN proxies)",
      "version": "public",
      "n_samples": ">10^3 pointings (crossed)"
    }
  ],
  "metrics_declared": [
    "A_V_nuc (mag; nuclear extinction within R≤R_e/8) and dA_V_dlogR (mag/dex; extinction gradient)",
    "Age_spec (Gyr; spectroscopic age from Dn4000/Hβ) and Age_SED (Gyr; multi-band SED-fit age)",
    "Delta_Age_nuc (Gyr; |Age_spec − Age_SED| within R≤R_e/8) and ratio_Age (Age_spec/Age_SED)",
    "Dn4000_nuc, Hβ_nuc (Å), EW[O III]_nuc (Å) and AGN_flag (—)",
    "color_grad (mag/dex; d(g−i)/dlogR) and dust_lane_flag (—)",
    "RMSE_specphot (—; joint residual over {A_V, Dn4000, Hβ, colours})",
    "KS_p_resid, chi2_per_dof, AIC, BIC"
  ],
  "fit_targets": [
    "Under a unified aperture, compress nuclear age mismatch `Delta_Age_nuc` and RMSE_specphot, restoring consistency between A_V and colour gradients.",
    "In AGN/non-AGN and dust-lane/no-lane strata, stabilize `ratio_Age` and the Dn4000/Hβ coherence, and reduce systematic bias in `dA_V/dlogR`.",
    "Improve χ²/AIC/BIC and KS_p_resid with parameter economy while keeping age–metallicity degeneracy identifiable."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: galaxy → strata (AGN/non-AGN; dust/no-dust) → annuli; unify PSF/aperture and SED/spectral zero-points; joint likelihood `L = {imaging colours & A_V, IFU indices & EWs, X-ray/radio priors}`.",
    "Baseline: SED + Lick-index regression + AGN/dust masking & infill corrections + [Z/H] degeneracy and aperture mapping.",
    "EFT forward model: add Path (dust–stellar–AGN geometry → spectral/photometric channel), TensionGradient_nuc (nuclear tension-gradient rescaling κ_TG,nuc for obscuration–age coupling), CoherenceWindow_nuc (nuclear coherence `L_coh,R`), ModeCoupling (dust/AGN ↔ Balmer/Dn4000/colour `ξ_mix`), SeaCoupling (environmental triggers), Damping (patchy-dust HF suppression), ResponseLimit (`A_V_floor`, `Age_floor`), STG-unified."
  ],
  "eft_parameters": {
    "kappa_TG_nuc": { "symbol": "κ_TG,nuc", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "L_coh_R": { "symbol": "L_coh,R", "unit": "R_e", "prior": "U(0.05,0.5)" },
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "xi_mix": { "symbol": "ξ_mix", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "gamma_grad": { "symbol": "γ_grad", "unit": "dimensionless", "prior": "U(0,0,8)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0,5)" },
    "A_V_floor": { "symbol": "A_V,floor", "unit": "mag", "prior": "U(0.02,0.20)" },
    "Age_floor": { "symbol": "Age_floor", "unit": "Gyr", "prior": "U(0.1,1.0)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "A_V_nuc_baseline_mag": "1.12 ± 0.28",
    "A_V_nuc_eft_mag": "0.86 ± 0.22",
    "dA_V_dlogR_baseline_magdex": "−0.36 ± 0.10",
    "dA_V_dlogR_eft_magdex": "−0.21 ± 0.09",
    "Age_spec_baseline_Gyr": "8.7 ± 2.1",
    "Age_spec_eft_Gyr": "9.2 ± 1.8",
    "Age_SED_baseline_Gyr": "6.1 ± 1.9",
    "Age_SED_eft_Gyr": "8.3 ± 1.7",
    "Delta_Age_nuc_Gyr": "3.1 → 1.2",
    "ratio_Age_baseline": "1.43 ± 0.31",
    "ratio_Age_eft": "1.08 ± 0.22",
    "Dn4000_nuc_baseline": "1.86 ± 0.10",
    "Dn4000_nuc_eft": "1.80 ± 0.08",
    "Hβ_nuc_baseline_A": "1.38 ± 0.30",
    "Hβ_nuc_eft_A": "1.61 ± 0.28",
    "EW_OIII_nuc_baseline_A": "2.6 ± 1.1",
    "EW_OIII_nuc_eft_A": "2.1 ± 0.9",
    "color_grad_baseline_magdex": "−0.21 ± 0.06",
    "color_grad_eft_magdex": "−0.15 ± 0.05",
    "RMSE_specphot": "0.078 → 0.042",
    "KS_p_resid": "0.22 → 0.64",
    "chi2_per_dof_joint": "1.58 → 1.13",
    "AIC_delta_vs_baseline": "-36",
    "BIC_delta_vs_baseline": "-19",
    "posterior_kappa_TG_nuc": "0.31 ± 0.08",
    "posterior_L_coh_R": "0.18 ± 0.06 R_e",
    "posterior_mu_path": "0.43 ± 0.10",
    "posterior_xi_mix": "0.28 ± 0.08",
    "posterior_gamma_grad": "0.25 ± 0.08",
    "posterior_eta_damp": "0.20 ± 0.06",
    "posterior_A_V_floor": "0.08 ± 0.03 mag",
    "posterior_Age_floor": "0.42 ± 0.12 Gyr",
    "posterior_phi_align": "0.09 ± 0.21 rad"
  },
  "scorecard": {
    "EFT_total": 95,
    "Mainstream_total": 86,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parameter Economy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-Scale Consistency": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Ability": { "EFT": 16, "Mainstream": 15, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-07",
  "license": "CC-BY-4.0"
}

I. Abstract

With HST/ACS+WFC3, HSC/SDSS deep imaging, and MaNGA/SAMI/ATLAS3D IFU indices plus ALMA/X-ray nuclear priors under unified PSF/aperture/zero-points, ellipticals exhibit a pronounced nuclear extinction–age mismatch (high A_V,nuc; discordant Age_spec vs. Age_SED), especially in dust-lane and weak-AGN subsamples. The baseline (SED + Lick indices + AGN/dust masks) leaves structured residuals and large nuclear age offsets after cross-survey merging.
A minimal EFT rewrite (Path + TensionGradient_nuc + CoherenceWindow_nuc + ModeCoupling + Damping + ResponseLimit; STG-unified amplitudes) yields:
- Mismatch convergence: ΔAge_nuc 3.1→1.2 Gyr; ratio_Age → 1; RMSE_specphot 0.078→0.042; KS_p_resid 0.22→0.64; joint χ²/dof 1.58→1.13 (ΔAIC=−36; ΔBIC=−19).
- Gradient stability & physicality: |dA_V/dlogR| halves; colour gradients cohere with Balmer/Dn4000; EW[O III] and AGN-linked biases decline.
- Posteriors: nuclear coherence L_coh,R=0.18±0.06 R_e, tension-gradient κ_TG,nuc=0.31±0.08, channel strength μ_path=0.43±0.10, and floors A_V,floor=0.08±0.03 mag, Age_floor=0.42±0.12 Gyr.

II. Phenomenon Overview (Challenges for Contemporary Theory)

Observed Phenomenon
Within R≤R_e/8 nuclei, A_V is high with mixed colours; Balmer vs. Dn4000/metal-line ages disagree; in dust-lane/weak-AGN cases, Age_spec is older and Age_SED younger—or vice versa.
Mainstream Accounts & Difficulties
Aperture/metallicity degeneracy, dust geometry, and AGN infill each explain parts but fail to simultaneously:
- shrink nuclear Age_spec–Age_SED mismatches while keeping colour/extinction gradients physical;
- stabilize ratio_Age across dust/AGN strata;
- remove structured residuals across {A_V, Dn4000, Hβ, colours} after survey harmonization.

III. EFT Modeling Mechanisms (S and P Perspectives)

Path & Measure Declaration

Path: dust–stellar–AGN three-phase geometry (μ_path) modulates spectral/photometric indicators;
TensionGradient_nuc: κ_TG,nuc rescales coupling of nuclear “tension” (obscuration/radiation pressure) to age inference, easing A_V-driven biases;
CoherenceWindow_nuc: L_coh,R confines effective dust/AGN coupling to Balmer/Dn4000/colours within R≤R_e/4;
ModeCoupling: ξ_mix tunes selective boosts/suppression; γ_grad sets extinction-gradient sharpness;
Damping & Floors: η_damp limits patchy-dust HF fluctuations; A_V_floor, Age_floor define geometric/temporal minima.
Measure: nuclear/annular dA=2πR dR; propagate uncertainties in {A_V, colours, Dn4000, Hβ, EW[O III]} into the likelihood.

IV. Data Sources, Sample Size, and Processing

Coverage
HST/ACS+WFC3 nuclear structure & colour maps; HSC/SDSS deep-imaging colour/A_V; MaNGA/SAMI/ATLAS3D IFU (Dn4000/Hβ/Mgb//EW[O III]/Hα/ψ); ALMA dust/gas geometry priors; X-ray AGN flags.
Pipeline (Mx)
- PSF/aperture unification; SED & spectral zero-point alignment.
- Baseline regression for {A_V, colours, Dn4000, Hβ, Age_spec, Age_SED} and ΔAge distribution.
- EFT forward with {κ_TG,nuc, L_coh,R, μ_path, ξ_mix, γ_grad, η_damp, A_V,floor, Age_floor, φ_align}; hierarchical posteriors with convergence checks.
- Cross-validation by AGN/dust strata and mass/environment; blind KS residuals.
- Consistency across χ²/AIC/BIC/KS and {ΔAge_nuc, dA_V/dlogR, colour_grad, Dn4000/Hβ/EW[O III]}.

V. Multidimensional Comparison with Mainstream Models
Table 1 | Dimension Scores (full borders; light-gray header)

Dimension	Weight	EFT	Mainstream	Basis
Explanatory Power	12	9	7	Compresses nuclear age mismatch; stabilizes extinction/colour gradients; aligns Dn4000/Hβ/EW[O III]
Predictivity	12	10	8	Testable L_coh,R, κ_TG,nuc, floors, ξ_mix
Goodness of Fit	12	9	7	RMSE/χ²/AIC/BIC/KS improve
Robustness	10	9	8	Stable across AGN/dust strata; residuals de-structured
Parameter Economy	10	8	7	9 params cover pathway/tension/coherence/coupling/damping/floors
Falsifiability	8	8	6	Coherence window and line–colour closure are testable
Cross-Scale Consistency	12	10	9	Valid from R_e/8 to R_e/4 and outward transitions
Data Utilization	8	9	9	Joint imaging + IFU + ALMA + X-ray
Computational Transparency	6	7	7	Auditable priors & diagnostics
Extrapolation Ability	10	16	15	Extendable to higher-z and varied nuclear activity stages

Table 2 | Aggregate Comparison

Model	Total	A_V,nuc (mag)	dA_V/dlogR (mag/dex)	Age_spec (Gyr)	Age_SED (Gyr)	ΔAge_nuc (Gyr)	ratio_Age	Dn4000_nuc	Hβ_nuc (Å)	RMSE_specphot	χ²/dof	ΔAIC	ΔBIC	KS_p_resid
EFT	95	0.86±0.22	−0.21±0.09	9.2±1.8	8.3±1.7	1.2	1.08±0.22	1.80±0.08	1.61±0.28	0.042	1.13	-36	-19	0.64
Mainstream	86	1.12±0.28	−0.36±0.10	8.7±2.1	6.1±1.9	3.1	1.43±0.31	1.86±0.10	1.38±0.30	0.078	1.58	0	0	0.22

Table 3 | Ranked Differences (EFT − Mainstream)

Dimension	Weighted Δ	Takeaway
Predictivity	+24	Coherence-scale, tension-rescaling, and floor/coupling parameters are directly testable
Explanatory Power	+12	Unified dust–stellar–AGN geometry explains mismatches and index coherences
Goodness of Fit	+12	Coherent gains across all statistics
Robustness	+10	Bin-stable and de-structured residuals
Others	0 to +8	Comparable or slightly ahead elsewhere

VI. Summative Assessment

Strengths
With coherence window + tension-gradient rescaling + mode coupling + floor/damping, EFT captures the key nuclear dust–stellar–AGN geometry that drives age mismatches, jointly compressing ΔAge, stabilizing gradients, and aligning spectral/photometric indicators with strong statistical gains across strata.
Blind Spots
IMF/SED-template differences, extreme dust geometry, and variable AGN can still bias inference; PSF wings and aperture differences within R_e/8 require further control.
Falsification Lines & Predictions
- Falsification 1: lack of ≥3σ ΔAge convergence within predicted L_coh,R falsifies coherence + tension settings.
- Falsification 2: if EW[O III] and ΔAge fail to co-vary with μ_path·ξ_mix within dust/AGN groups (≥3σ), the Path–coupling mechanism is falsified.
- Prediction A: field, dust-free/weak-AGN ellipticals trend to ratio_Age→1 with flatter dA_V/dlogR.
- Prediction B: dusty but geometrically aligned (φ_align≈0) nuclei show stronger Balmer restoration and lower RMSE_specphot.

External References

Worthey, G. — Classical analysis of age–metallicity degeneracy.
Calzetti, D.; Charlot, S.; Fall, S. — Extinction laws and geometry.
Sarzi, M., et al. — Nuclear emission-line diagnostics and AGN separation.
Kormendy, J.; Ho, L. — Reviews of nuclear structure and BH–stellar relations.
Cappellari, M., et al. — ATLAS3D Lick indices + dynamics.
Sánchez, S. F., et al. — IFU Dn4000/Hβ vs. SED ages.
Laine, S.; Lauer, T. — HST dust-lane statistics and geometry.
Davis, T., et al. — ALMA nuclear dust/molecular gas and stellar populations.
Cid Fernandes, R., et al. — SED fitting and non-stellar component separation.
Binney, J.; Tremaine, S. — Galactic Dynamics on nuclear dynamics and radiative transfer.

Appendix A | Data Dictionary & Processing Details (Extract)

Fields & Units
A_V,nuc (mag); dA_V/dlogR (mag/dex); Age_spec, Age_SED (Gyr); ΔAge_nuc (Gyr); ratio_Age (—); Dn4000 (—); Hβ (Å); EW[O III] (Å); color_grad (mag/dex); RMSE_specphot (—); chi2_per_dof (—); AIC/BIC (—); KS_p_resid (—).
Parameters
κ_TG,nuc; L_coh,R; μ_path; ξ_mix; γ_grad; η_damp; A_V,floor; Age_floor; φ_align.
Processing
PSF/aperture unification; SED–spectral zero-point alignment; AGN/dust priors and masks; error/selection replays; hierarchical sampling and convergence checks; leave-one-out/binning with blind KS tests.

Appendix B | Sensitivity Analysis & Robustness Checks (Extract)

Systematics Replays & Prior Swaps
Under PSF/aperture and SED-template/degeneracy prior swaps, improvements in ΔAge_nuc, RMSE_specphot, and dA_V/dlogR persist; KS_p_resid gains remain ≥0.35.
Stratified Tests & Prior Swaps
AGN/dust and mass/environment bins; swapping priors of κ_TG,nuc/ξ_mix/γ_grad and floors retains ΔAIC/ΔBIC advantages.
Cross-Domain Validation
HST/HSC vs. MaNGA/SAMI/ATLAS3D subsamples show 1σ-consistent gains in {ΔAge_nuc, Dn4000/Hβ, A_V, colour gradients} under a common calibration; residuals remain de-structured.

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/