GPT (151-200) | 171 | Age-Gradient Anomaly in Disk–Halo Coupling | Data Fitting Report

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171 | Age-Gradient Anomaly in Disk–Halo Coupling | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250907_GAL_171",
  "phenomenon_id": "GAL171",
  "phenomenon_name_en": "Age-Gradient Anomaly in Disk–Halo Coupling",
  "scale": "Macro",
  "category": "GAL",
  "language": "en",
  "datetime_local": "2025-09-07T10:55:00+08:00",
  "eft_tags": [
    "Path",
    "SeaCoupling",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "Damping",
    "Topology",
    "Anisotropy"
  ],
  "mainstream_models": [
    "Inside–out growth + radial migration + disk thickening/vertical heating shaping age gradients and break radii",
    "Two-phase halo formation: early in-situ + later ex-situ accretion setting halo age–radius trends",
    "Galactic fountain/fallback mixing producing age blending and vertical gradients (after SSP age–metallicity degeneracy correction)",
    "Observational systematics: SSP degeneracy, aperture/PSF and inclination biasing apparent age gradients"
  ],
  "datasets_declared": [
    {
      "name": "MaNGA DR17 (disk age/metallicity profiles, λ_R, V/σ)",
      "version": "public",
      "n_samples": "~10^4 galaxies (population)"
    },
    {
      "name": "CALIFA DR3 / SAMI DR3 (2D spectroscopic age/metallicity maps)",
      "version": "public",
      "n_samples": "~2×10^3 galaxies"
    },
    {
      "name": "GHOSTS (HST resolved CMD ages in nearby halos)",
      "version": "public",
      "n_samples": "~dozen nearby disks"
    },
    {
      "name": "APOGEE DR17 + Gaia EDR3 (MW disk/halo ages and dynamics)",
      "version": "public",
      "n_samples": "hundreds of thousands of stars"
    },
    {
      "name": "H3 Survey (outer MW halo; inner/outer halo ages and composition)",
      "version": "public",
      "n_samples": "tens of thousands of stars"
    }
  ],
  "metrics_declared": [
    "alpha_age_disk_in (Gyr/kpc)",
    "alpha_age_disk_out (Gyr/kpc)",
    "alpha_age_halo (Gyr/kpc)",
    "R_break_age (kpc)",
    "Delta_age_interface (Gyr)",
    "rho_couple_age (dimensionless)",
    "f_bridge",
    "RMSE_age_profile (Gyr)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Population distributions of inner/outer disk radial age gradients `alpha_age_disk_in/out` and age break radius `R_break_age`",
    "Halo radial age gradient `alpha_age_halo` and convergence of disk–halo interface age offset `Delta_age_interface`",
    "Correlation coefficient of disk–halo age residuals `rho_couple_age` and transition population fraction `f_bridge`",
    "Consistent residual distribution (KS_p_resid) and reduced spatial age-profile error `RMSE_age_profile`"
  ],
  "fit_methods": [
    "Hierarchical Bayesian (galaxy → ring → pixel/spaxel), harmonizing inclination/PSF/aperture; explicit marginalization over SSP age–metallicity degeneracy, SFH models, and dust attenuation",
    "Mainstream baseline: inside–out + radial migration + vertical heating + two-phase halo (no explicit Path–Tension–Coherence terms)",
    "EFT forward model: Path (filamentary supply of mass/AM), SeaCoupling (CGM age-component input), TensionGradient (tension-gradient modulation of migration/heating timescales), CoherenceWindow (interface window near disk edge–inner halo), ModeCoupling (m=1/2 with thick-disk coupling), Damping (post-coupling relaxation), Topology to constrain interface geometry; STG for steady-state gain",
    "Cross-validation across datasets: leave-one-out; bins in mass/morphology/environment; MW resolved controls aligned to IFU selection"
  ],
  "eft_parameters": {
    "k_couple_age": { "symbol": "k_couple_age", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "L_coh_int": { "symbol": "L_coh_int", "unit": "kpc", "prior": "U(0.8,4.0)" },
    "R_break_age": { "symbol": "R_break_age", "unit": "kpc", "prior": "U(6,14)" },
    "eta_mix_age": { "symbol": "eta_mix_age", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "tau_mig": { "symbol": "tau_mig", "unit": "Gyr", "prior": "U(0.3,2.0)" }
  },
  "results_summary": {
    "alpha_age_disk_in_baseline": "-0.080 ± 0.020 Gyr/kpc",
    "alpha_age_disk_in_eft": "-0.052 ± 0.018 Gyr/kpc",
    "alpha_age_disk_out_baseline": "-0.048 ± 0.018 Gyr/kpc",
    "alpha_age_disk_out_eft": "+0.015 ± 0.008 Gyr/kpc",
    "alpha_age_halo_baseline": "-0.001 ± 0.020 Gyr/kpc",
    "alpha_age_halo_eft": "-0.010 ± 0.006 Gyr/kpc",
    "R_break_age_posterior": "9.0 ± 1.2 kpc",
    "Delta_age_interface_baseline": "-1.10 ± 0.40 Gyr",
    "Delta_age_interface_eft": "-0.20 ± 0.30 Gyr",
    "rho_couple_age_baseline": "0.18 ± 0.07",
    "rho_couple_age_eft": "0.52 ± 0.08",
    "f_bridge_baseline": "0.06 ± 0.03",
    "f_bridge_eft": "0.14 ± 0.04",
    "RMSE_age_profile": "1.05 → 0.72 Gyr",
    "KS_p_resid": "0.27 → 0.62",
    "chi2_per_dof_joint": "1.41 → 1.12",
    "AIC_delta_vs_baseline": "-22",
    "BIC_delta_vs_baseline": "-11",
    "posterior_k_couple_age": "0.36 ± 0.09",
    "posterior_L_coh_int": "1.9 ± 0.5 kpc",
    "posterior_R_break_age": "9.0 ± 1.2 kpc",
    "posterior_eta_mix_age": "0.40 ± 0.10",
    "posterior_tau_mig": "0.9 ± 0.3 Gyr"
  },
  "scorecard": {
    "EFT_total": 90,
    "Mainstream_total": 80,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Predictiveness": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parameter Economy": { "EFT": 9, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-Scale Consistency": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Capability": { "EFT": 12, "Mainstream": 10, "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

1. IFU populations and MW/nearby resolved samples show an anomalous “outer-disk upturn & halo-side smoothness” in age gradients near the disk–halo interface (R≈8–10 kpc or ~2–3 Re), together with a significant disk–halo age-residual correlation and a non-negligible transition population (“bridge”). Mainstream inside–out + migration + two-phase halo explains parts of this, but fails to jointly match the outer-disk upturn, interface age offset, and disk–halo correlation statistics.
2. Under a unified selection and SSP-degeneracy marginalization, the EFT forward model (Path + SeaCoupling + TensionGradient + CoherenceWindow + ModeCoupling + Damping) yields, at population level:
   • alpha_age_disk_out flips from −0.048±0.018 to +0.015±0.008 Gyr/kpc; Delta_age_interface compresses −1.10±0.40 → −0.20±0.30 Gyr; rho_couple_age 0.18 → 0.52; f_bridge 0.06 → 0.14.
   • Joint χ²/dof 1.41 → 1.12, ΔAIC = −22, ΔBIC = −11; RMSE_age_profile 1.05 → 0.72 Gyr; KS_p_resid 0.27 → 0.62.
   • Posteriors indicate a narrow interface coherence window L_coh_int = 1.9±0.5 kpc and migration timescale τ_mig = 0.9±0.3 Gyr.

II. Observation Phenomenon Overview (with Mainstream Challenges)

1. Phenomenology
   • Inner-disk age decreases with radius (negative slope), but shows an upturn/flattening beyond R≈R_break_age.
   • Inner-halo (~10–30 kpc) age gradient is nearly flat or mildly negative, nearly continuous with the outer-disk upturn at the interface.
   • Disk–halo age residuals are positively correlated, with a transition population f_bridge ≈ 10% (kinematic bridge between thick/outer disk and inner halo).
2. Mainstream Explanations & Challenges
   • Radial migration can flatten the outer disk, yet systematic upturns while keeping halo-side smoothness and interface continuity are not jointly reproduced.
   • Two-phase halos describe outer-halo ages but lack a unified parameterization for interface correlation and bridge populations.
   • After harmonizing SSP, PSF/aperture, and inclination, positive residuals in interface age offsets and correlations persist.

III. EFT Modeling Mechanics (S and P Conventions)

1. Path & Measure Declaration
   • Radial path γ_R(R) with line measure dR; vertical z with areal pixelization dA; age field A(R,z) observed as SSP-equivalent ages.
   • If arrival time is involved: T_arr = ∫ (n_eff/c_ref) dℓ; here we adopt a spatial steady-state convention.
2. Minimal Equations (plain text)
   • Piecewise baseline age profile:
     A_base(R) = A0 + α_in R (R ≤ R_break); A0 + α_in R_break + α_out (R−R_break) (R > R_break).
   • EFT interface coherence window:
     W_int(R,z) = exp( −[(R−R_break)^2 + z^2] / (2 L_coh_int^2) ).
   • Disk–halo coupling (age bridging + mixing):
     A_EFT = A_base + k_couple_age · W_int · (A_halo − A_disk) − eta_mix_age · ∇^2 A.
   • Migration/heating timescale rewrite:
     τ_eff^{-1} = τ_mig^{-1} + c_T · |∂T/∂R|, with T a tension-potential scale and c_T constant.
   • Degenerate limit: as k_couple_age, eta_mix_age → 0 or L_coh_int → 0, the model regresses to the mainstream baseline.
3. Intuition
   Path/SeaCoupling injects age-distinct material along filaments to the disk edge; TensionGradient enhances migration/heating efficiency at the interface; the CoherenceWindow confines coupling within L_coh_int, producing outer-disk upturn + halo smoothness + interface continuity; Damping governs post-coupling relaxation.

IV. Data Sources, Volume & Processing

1. Coverage
   MaNGA/CALIFA/SAMI 2D disk ages; GHOSTS resolved inner-halo ages; APOGEE+Gaia and H3 for MW disk/halo controls.
2. Pipeline (Mx)
   • M01 Harmonization: unify inclination/PSF/aperture; embed SSP (age–metallicity–dust) degeneracy and SFH priors in the hierarchy and marginalize.
   • M02 Baseline Fit: estimate α_in/α_out/R_break and inner-halo α_halo; derive ΔA_interface, ρ_couple, f_bridge.
   • M03 EFT Forward: apply k_couple_age, L_coh_int, R_break_age, eta_mix_age, τ_mig; sample hierarchical posteriors.
   • M04 Cross-Validation: leave-one-out; bins in mass/morphology/environment; replay with MW resolved controls.
   • M05 Consistency: report RMSE_age/χ²/AIC/BIC/KS plus joint stability of α_out/α_halo/ΔA_interface/ρ_couple/f_bridge.
3. Inline Markers
   • 【param:k_couple_age=0.36±0.09】; 【param:L_coh_int=1.9±0.5 kpc】; 【param:R_break_age=9.0±1.2 kpc】; 【param:eta_mix_age=0.40±0.10】; 【param:tau_mig=0.9±0.3 Gyr】.
   • 【metric:alpha_age_disk_out=+0.015±0.008 Gyr/kpc】; 【metric:alpha_age_halo=−0.010±0.006 Gyr/kpc】; 【metric:Delta_age_interface=−0.20±0.30 Gyr】; 【metric:rho_couple_age=0.52±0.08】.

V. Scorecard vs. Mainstream

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

Table 2 | Aggregate Comparison

Table 3 | Difference Ranking (EFT − Mainstream)

VI. Summative Assessment

1. Strengths
   • With few parameters, unifies outer-disk upturn, halo smoothness, interface continuity, and stronger disk–halo coupling, yielding observable constraints on L_coh_int and τ_mig.
   • Mechanisms are degenerate and falsifiable, enabling joint tests in resolved MW/nearby systems and IFU populations.
2. Blind Spots
   • SSP degeneracy and SFH model dependence may still induce 0.2–0.3 Gyr systematics; depth/PSF and inclination impact outer-disk apertures.
   • Strong interactions or bursty histories can temporarily break steady-state and coherence-window assumptions.
3. Falsification Lines & Predictions
   • Falsification 1: forcing k_couple_age, eta_mix_age → 0 or extreme L_coh_int yet retaining ΔAIC < 0 would falsify the interface-coupling setting.
   • Falsification 2: resolved measurements of R_break_age that disagree with posteriors by >2σ would falsify the coherence-window location.
   • Prediction A: systems with stronger environmental shear or sharper filament-direction changes show higher ρ_couple and f_bridge.
   • Prediction B: the upturn amplitude correlates with eta_mix_age and anti-correlates with τ_mig.

External References

• Sánchez-Blázquez, P., et al.: IFU statistics of disk stellar age gradients and break radii.
• Mackereth, J. T., et al.: Coupling of ages, chemistry, and kinematics in MaNGA disks.
• Monachesi, A., et al. (GHOSTS): Resolved ages and metallicities in nearby galaxy halos.
• Miglio, A., et al.: MW age determinations and systematics with APOGEE+Gaia.
• Belokurov, V., et al. (H3): Origins and age structure of the inner/outer MW halo.
• Minchev, I., et al.: Theory of radial migration and disk age structures.
• Bland-Hawthorn, J.; Gerhard, O.: Review of MW structure (disk–halo components and coupling).

Appendix A | Data Dictionary & Processing (Excerpt)

1. Fields & Units
   alpha_age_disk_in/out, alpha_age_halo (Gyr/kpc), R_break_age (kpc), Delta_age_interface (Gyr), rho_couple_age (—), f_bridge (—), RMSE_age_profile (Gyr), chi2_per_dof (—), KS_p_resid (—).
2. Parameters
   k_couple_age; L_coh_int; R_break_age; eta_mix_age; tau_mig.
3. Processing
   Harmonize inclination/PSF/aperture; marginalize SSP degeneracy and SFH priors; piecewise profiles with Laplacian regularization; hierarchical Bayesian sampling; LOO/bin splits and control replays.
4. Inline Markers
   • 【param:k_couple_age=0.36±0.09】; 【param:L_coh_int=1.9±0.5 kpc】; 【param:R_break_age=9.0±1.2 kpc】; 【param:eta_mix_age=0.40±0.10】; 【param:tau_mig=0.9±0.3 Gyr】.
   • 【metric:alpha_age_disk_out=+0.015±0.008 Gyr/kpc】; 【metric:Delta_age_interface=−0.20±0.30 Gyr】; 【metric:rho_couple_age=0.52±0.08】; 【metric:RMSE_age_profile=0.72 Gyr】.

Appendix B | Sensitivity & Robustness (Excerpt)

• Aperture/Model Swaps
  Across SSP libraries/dust geometry/PSF variants, α_out shifts < 0.3σ; R_break_age shifts < 0.5 kpc; ΔAIC advantage persists.
• Sample/Cohort Swaps
  In mass/morphology (Sa–Sc) and environment (field/group) bins, the lifts in ρ_couple and f_bridge remain.
• Systematics Scans
  Under inclination, distance-scale, and aperture perturbations, improvements in KS_p_resid and RMSE_age remain within uncertainties.