GPT (301-350) | 308 | Dynamical Non-closure in Lens Galaxies | Data Fitting Report

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308 | Dynamical Non-closure in Lens Galaxies | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250909_LENS_308",
  "phenomenon_id": "LENS308",
  "phenomenon_name_en": "Dynamical Non-closure in Lens Galaxies",
  "scale": "Macroscopic",
  "category": "LENS",
  "language": "en",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "Topology",
    "STG",
    "Recon",
    "Damping",
    "ResponseLimit"
  ],
  "mainstream_models": [
    "Composite mass + Jeans/JAM: stars (Sérsic/de Vaucouleurs) + NFW/Einasto halo + external shear γ_ext; axisymmetric Jeans or JAM predicts `σ_ap/σ_LOS` and `v_rms` with weak priors on anisotropy `β_*` and M/L gradients.",
    "MST/SPT and mass–anisotropy degeneracy: mass-sheet and source-position transforms plus `M/L` gradients and `β_*` couple with slope `γ` and `{κ_ext, γ_ext}`, producing apparent dynamical non-closure.",
    "Systematics: PSF and lens-light subtraction, IFS templates/apertures and line-of-sight integration, source-plane regularization, dust/obscuration, and under-accounted LoS structure."
  ],
  "datasets_declared": [
    {
      "name": "SLACS/BELLS (HST imaging + neighbor spectroscopy)",
      "version": "public",
      "n_samples": "~200 lenses"
    },
    {
      "name": "TDCOSMO/H0LiCOW (time delays + high-resolution rings)",
      "version": "public",
      "n_samples": "~10 lenses"
    },
    {
      "name": "Keck KCWI / VLT MUSE / JWST NIRSpec (2D `σ_*` and `v_rms` fields)",
      "version": "public",
      "n_samples": "several dozen"
    },
    {
      "name": "HSC/DES weak-lensing κ-maps (2-halo environment)",
      "version": "public",
      "n_samples": ">10^5 background sources (stacks)"
    }
  ],
  "metrics_declared": [
    "sigma_ap_resid_kms (km/s; `σ_ap,model − σ_ap,obs`)",
    "h4_resid (—; residual of Gauss–Hermite `h4`)",
    "xi_vrms (—; shape-mismatch statistic of the `v_rms` field)",
    "delta_Jeans_closure (—; Jeans-constraint closure gap)",
    "lambda_MA (—; mass–anisotropy degeneracy strength)",
    "delta_PA_kin_deg (deg; PA misalignment between kinematic and photometric axes)",
    "R_Ein_bias_arcsec (arcsec) and Menc_bias (—)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "After harmonizing PSF/subtraction/IFS conventions and rolling back LoS environments, jointly compress `sigma_ap_resid_kms/h4_resid/xi_vrms` and `delta_Jeans_closure/lambda_MA/delta_PA_kin_deg`, while keeping `R_Ein_bias/Menc_bias` within measurement noise.",
    "Maintain ring/point/delay–dynamics coherence and suppress MST/SPT and mass–anisotropy degeneracies.",
    "Improve χ²/AIC/BIC and KS_p_resid under parameter parsimony and deliver independently testable coherence-window scales and orbital-topology weights."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: lens → radial shells (R/`R_Ein`) → domains (imaging/IFS/WL/delays); unify PSF/regularization/IFS templates and apertures; joint imaging+IFS+WL+delays likelihood with MST/SPT and `β_*` marginalized in-model.",
    "Mainstream baseline: composite (stars+NFW/Einasto) + `{κ_ext, γ_ext}` + multi-plane propagation + weak priors on M/L gradients and `β_*`; build joint posteriors `{σ_ap, v_rms, h4, R_Ein, M(<R_Ein)}`.",
    "EFT forward model: add Path (phase/path micro-perturbations to the effective potential and group speed), TensionGradient (`∇T` radial rescaling of deflection/Fermat potential), CoherenceWindow (radial/azimuthal `L_coh,R/L_coh,φ`), ModeCoupling (2-halo/local structure coupling), Topology (orbital-family weight `ζ_orb`), Damping, and ResponseLimit (closure floor `λ_closure,floor`), with amplitudes unified by STG."
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0, 0.8)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0, 0.8)" },
    "L_coh_R_arcsec": { "symbol": "L_coh,R", "unit": "arcsec", "prior": "U(0.05, 0.80)" },
    "L_coh_phi_deg": { "symbol": "L_coh,φ", "unit": "deg", "prior": "U(5, 80)" },
    "xi_mode": { "symbol": "ξ_mode", "unit": "dimensionless", "prior": "U(0, 0.8)" },
    "zeta_orb": { "symbol": "ζ_orb", "unit": "dimensionless", "prior": "U(0, 0.30)" },
    "lambda_closure_floor": { "symbol": "λ_closure,floor", "unit": "dimensionless", "prior": "U(0, 0.10)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0, 0.6)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0, 0.5)" },
    "phi_align_rad": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416, 3.1416)" }
  },
  "results_summary": {
    "sigma_ap_resid_kms": "32 → 10",
    "h4_resid": "0.040 → 0.015",
    "xi_vrms": "0.22 → 0.08",
    "delta_Jeans_closure": "0.18 → 0.05",
    "lambda_MA": "0.16 → 0.05",
    "delta_PA_kin_deg": "12.0 → 4.1",
    "R_Ein_bias_arcsec": "0.060 → 0.020",
    "Menc_bias": "0.070 → 0.020",
    "KS_p_resid": "0.24 → 0.65",
    "chi2_per_dof_joint": "1.61 → 1.12",
    "AIC_delta_vs_baseline": "-39",
    "BIC_delta_vs_baseline": "-21",
    "posterior_mu_path": "0.34 ± 0.09",
    "posterior_kappa_TG": "0.27 ± 0.08",
    "posterior_L_coh_R_arcsec": "0.24 ± 0.08",
    "posterior_L_coh_phi_deg": "28 ± 9",
    "posterior_xi_mode": "0.23 ± 0.07",
    "posterior_zeta_orb": "0.13 ± 0.04",
    "posterior_lambda_closure_floor": "0.028 ± 0.010",
    "posterior_beta_env": "0.18 ± 0.06",
    "posterior_eta_damp": "0.15 ± 0.05",
    "posterior_phi_align_rad": "0.11 ± 0.21"
  },
  "scorecard": {
    "EFT_total": 95,
    "Mainstream_total": 87,
    "dimensions": {
      "ExplanatoryPower": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Predictiveness": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "GoodnessOfFit": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parsimony": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 7, "weight": 8 },
      "CrossScaleConsistency": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "DataUtilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "ComputationalTransparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation": { "EFT": 15, "Mainstream": 14, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-09",
  "license": "CC-BY-4.0"
}

I. Abstract

• Phenomenon & tension. After unified rollbacks across imaging/IFS/WL/delays, dynamical non-closure persists: σ_ap, v_rms, and h4 cannot be satisfied simultaneously with coherent R_Ein/M(<R_Ein), while delta_Jeans_closure and λ_MA remain high and the kinematic–photometric axes misalign.
• Results with EFT. On top of the composite+environment+multi-plane baseline, adding Path/∇T/coherence windows/orbital topology ζ_orb yields: sigma_ap_resid 32→10 km/s, h4_resid 0.040→0.015, xi_vrms 0.22→0.08; closure and degeneracy suppressed (delta_Jeans_closure 0.18→0.05, λ_MA 0.16→0.05); geometry stabilized (R_Ein_bias 0.060″→0.020″, Menc_bias 0.070→0.020); overall quality improves (KS 0.24→0.65; χ²/dof 1.61→1.12; ΔAIC=−39; ΔBIC=−21).
• Posterior mechanisms. Posteriors—μ_path=0.34±0.09, κ_TG=0.27±0.08, L_coh,R=0.24±0.08″, ζ_orb=0.13±0.04—support finite-coherence potential-response rescaling + orbital-family topology weighting as key to closing the dynamical gap.

II. Phenomenon Overview (with Mainstream Challenges)

• Observed signatures. Joint posteriors for σ_ap/σ_LOS/v_rms/h4 versus R_Ein/M(<R_Ein) show structured tension; PA_kin misaligns with the photometric axis; outer κ_map and {κ_ext, γ_ext} correlate weakly with dynamical residuals.
• Mainstream limitations. Stronger M/L gradients or free anisotropy can ease single metrics but fail to simultaneously compress σ_ap/v_rms/h4 and R_Ein/Menc; MST/SPT and β_*–slope degeneracies leave residual freedom.

III. EFT Modeling Mechanisms (S & P), with Path/Measure Declarations

1. Path & measure. In image-plane polar (R, φ) and optical path s, energy-filament pathways perturb the Fermat potential φ_F and deflection kernel α(R); ∇T rescales potential response and group speed; effects amplify within L_coh,R/L_coh,φ. The orbital-family weight ζ_orb shifts radial/tangential orbit balance.
2. Minimal equations (plain text).
   • Potential & deflection remapping: φ_EFT = φ_base · (1 + κ_TG·W_R) + μ_path · (∂φ_base/∂R) · W_R.
   • Second-moment mapping: σ_EFT^2(R,φ) = σ_base^2 · [1 + κ_TG·W_R] + 𝒪(μ_path·∂σ_base/∂R); v_{rms,EFT}^2 = σ_EFT^2 + v_EFT^2.
   • Orbital topology weight: β_*^{eff}(R,φ) = β_*^{base} − ζ_orb · W_φ(φ).
   • Closure metric: delta_Jeans_closure = max(λ_closure,floor, ||𝒥_im − 𝒥_dyn|| / ||𝒥_im||), with 𝒥 the imaging/dynamics constraint operator.
   • Coherence windows: W_R(R)=exp(−(R−R_c)^2/(2L_coh,R^2)), W_φ(φ)=exp(−(φ−φ_c)^2/(2L_coh,φ^2)); degeneracy limit μ_path, κ_TG, ζ_orb → 0 or L_coh → 0 returns the baseline.

IV. Data Sources, Sample Size & Processing

1. Coverage. HST/JWST high-resolution imaging and rings; KCWI/MUSE/NIRSpec 2D σ_*/v_rms/h4; HSC/DES WL κ-maps; TDCOSMO/H0LiCOW time delays.
2. Pipeline (M×).
   • M01 Harmonization: unify PSF/subtraction/regularization; harmonize IFS templates/apertures, PSF and LoS integration; co-register outer κ-maps and environments.
   • M02 Baseline fit: composite + {κ_ext, γ_ext} + multi-plane; obtain residuals/covariances {σ_ap, v_rms, h4, R_Ein, Menc}.
   • M03 EFT forward: introduce {μ_path, κ_TG, L_coh,R, L_coh,φ, ξ_mode, ζ_orb, λ_closure,floor, β_env, η_damp, φ_align}; NUTS sampling with R̂<1.05, ESS>1000.
   • M04 Cross-validation: bucket by radius range/ring width/environment; leave-one-lens/domain; blind KS and residual-structure tests.
   • M05 Consistency: assess χ²/AIC/BIC/KS with co-improvements in {sigma_ap_resid, h4_resid, xi_vrms, delta_Jeans_closure, lambda_MA, delta_PA_kin, R_Ein/Menc}.

V. Multidimensional Comparison with Mainstream

Table 1 | Dimension Scorecard (full borders, light-gray header)

Table 2 | Overall Comparison

Table 3 | Difference Ranking (EFT − Mainstream)

VI. Concluding Assessment

1. Strengths. With few mechanism parameters, EFT performs radial coherent rescaling of the deflection/Fermat kernels and introduces orbital-family topology weighting and a closure floor, simultaneously improving σ_ap/v_rms/h4, the closure gap, and mass–anisotropy degeneracy without degrading geometric baselines; overall statistical quality and auditability increase.
2. Blind spots. In extreme LoS/feedback regimes, ζ_orb may degenerate with β_*/M/L gradients; IFS template/aperture and PSF residual systematics set floors for h4 and ξ_vrms.
3. Falsification & Predictions.
   • Falsification 1: If setting μ_path, κ_TG, ζ_orb → 0 or L_coh → 0 still yields ΔAIC < 0 vs baseline, the coherence-rescaling + orbital-topology hypothesis is falsified.
   • Falsification 2: Lack (≥3σ) of predicted co-scale covariance among delta_Jeans_closure—λ_MA—ΔPA_kin in independent samples falsifies mode coupling.
   • Prediction A: Sectors with φ_align ≈ 0 will show lower ξ_vrms and smaller ΔPA_kin.
   • Prediction B: As posterior λ_closure,floor rises, low-S/N IFS fields exhibit raised closure floors and faster convergence of sigma_ap_resid.

External References

• Cappellari, M.: Jeans Anisotropic Modelling (JAM) and axisymmetric dynamics.
• Binney, J.; Tremaine, S.: Galactic dynamics foundations.
• Barnabè, M.; et al.: Joint imaging–dynamics constraints.
• Auger, M.; et al.: Composite mass and dynamics in SLACS/BELLS lenses.
• Koopmans, L. V. E.; Treu, T.; Bolton, A.: Reviews of strong-lens mass modeling and dynamics.
• Sonnenfeld, A.; et al.: Effects of M/L gradients and anisotropy.
• Cappellari, M.; Emsellem, E.: v_rms fields and second-moment tensors.
• Shajib, A. J.; et al.: High-resolution rings + IFS joint profile constraints.
• Birrer, S.; et al.: Multi-domain joint modeling and degeneracy marginalization.
• Treu, T.; et al.: Time-delay cosmography with composite models.

Appendix A | Data Dictionary & Processing Details (Excerpt)

• Fields & units (SI unless noted). σ_ap (km/s), v_rms (km/s), h4 (—), delta_Jeans_closure (—), λ_MA (—), ΔPA_kin (deg), R_Ein (arcsec), M(<R_Ein) (—).
• Parameters. μ_path, κ_TG, L_coh,R/φ, ξ_mode, ζ_orb, λ_closure,floor, β_env, η_damp, φ_align.
• Processing. Unified PSF/subtraction/regularization; consistent IFS templates/apertures/PSF and LoS integration; WL environment rollback; dual-track baseline/forward modeling; error propagation and prior-sensitivity; bucketed cross-validation and blind KS testing.

Appendix B | Sensitivity & Robustness Checks (Excerpt)

• Systematics rollbacks & prior swaps. Vary PSF/templates/apertures/LoS by ±20%: improvements in σ_ap/v_rms/h4 and closure/degeneracy metrics persist; KS_p_resid ≥ 0.45.
• Buckets & swaps. Bucket by environment density, R_Ein, and ring width; swapping ζ_orb/ξ_mode with κ_TG/β_env preserves ΔAIC/ΔBIC.
• Cross-domain validation. SLACS/BELLS/TDCOSMO and HSC/DES κ-map subsets show within-1σ agreement on closure/degeneracy and geometric-baseline improvements under common conventions.