GPT (451-500) | 478 | Star Formation Efficiency Bias in Low-Metallicity Environments | Data Fitting Report

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478 | Star Formation Efficiency Bias in Low-Metallicity Environments | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_478",
  "phenomenon_id": "SFR478",
  "phenomenon_name": "Star Formation Efficiency Bias in Low-Metallicity Environments",
  "scale": "Macroscopic",
  "category": "SFR",
  "language": "en-US",
  "eft_tags": [
    "CoherenceWindow",
    "TensionGradient",
    "Path",
    "SeaCoupling",
    "TPR",
    "Damping",
    "ResponseLimit",
    "Topology",
    "STG",
    "Recon"
  ],
  "mainstream_models": [
    "Metallicity-controlled molecular formation and shielding: lower dust-to-gas ratio increases shielding length, reduces H2 formation efficiency, and raises the CO-dark fraction; requires empirical X_CO(Z) calibration with strong parameter degeneracy.",
    "Kennicutt–Schmidt law extrapolated across metallicity: Σ_SFR–Σ_gas/Σ_H2 slope/zero-point systematically drift at low Z; impacted by CO selection thresholds and Hα/FUV calibration differences.",
    "Free-fall/turbulence–regulated SFE: variations in free-fall or turbulent support timescales explain τ_dep shifts; underfits joint behavior of CO-dark H2 and shielding topology.",
    "Toomre Q and shear: stability thresholds vary in low-Z disks and can lengthen τ_dep; struggles to simultaneously match indicator differences and the unified X_CO–Z slope bias."
  ],
  "datasets_declared": [
    {
      "name": "DGS (Dwarf Galaxy Survey; Herschel multi-band)",
      "version": "public",
      "n_samples": "~50 dwarf galaxies; ~2×10^6 pixels"
    },
    {
      "name": "LITTLE THINGS (VLA HI) + SHIELD (low-Z dwarfs)",
      "version": "public",
      "n_samples": "~70 galaxies; ~8×10^6 pixels"
    },
    {
      "name": "xCOLD GASS / ALLSMOG low-Z subsamples (CO / molecular gas)",
      "version": "public",
      "n_samples": "~250 galaxies; measurement level"
    },
    {
      "name": "PHANGS-MUSE subset (Hα; SFR and metallicity Z)",
      "version": "public",
      "n_samples": "~30 disks; ~10^7 spaxels"
    },
    {
      "name": "GALEX FUV + WISE 22/24 μm (stitched SFR indicators)",
      "version": "public",
      "n_samples": "~200 galaxies; pixel mosaics"
    }
  ],
  "metrics_declared": [
    "sfe_bias_dex (dex; log SFE bias)",
    "tau_dep_bias_gyr (Gyr; H2 depletion-time bias)",
    "XCO_Z_slope_bias (—; slope bias of X_CO–Z)",
    "f_COdark_bias (—; CO-dark H2 fraction bias)",
    "SFR_calib_bias (—; Hα/FUV/IR cross-calibration bias)",
    "KS_slope_bias (—; slope bias of Σ_SFR–Σ_gas/Σ_H2)",
    "Qeff_bias (—; effective Q bias)",
    "clumping_factor_bias (—; CNM clumping-factor bias)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Jointly compress `sfe_bias_dex/tau_dep_bias_gyr/XCO_Z_slope_bias/f_COdark_bias/SFR_calib_bias/KS_slope_bias/Qeff_bias/clumping_factor_bias`, raise `KS_p_resid`, and lower `chi2_per_dof/AIC/BIC` under a unified aperture/resolution protocol.",
    "Provide a unified account of SFE bias, τ_dep extension, X_CO–Z slope, and the CO-dark H2 fraction for low-Z (including extremely metal-poor) samples while remaining consistent across SFR indicators.",
    "Under parameter economy, output testable posteriors for coherence window, tension re-scaling, path coupling, transport–percolation (TPR), damping/caps, and shielding topology."
  ],
  "fit_methods": [
    "Hierarchical Bayes: galaxy → environment bins (by Z/G_0/DGR) → pixels; joint likelihood over `Σ_SFR, Σ_HI, Σ_H2 (latent), Z, G_0, DGR, CO` with censoring for CO non-detections; harmonized PSF/beam and indicator stitching.",
    "Mainstream baseline: KS law + X_CO(Z) + free-fall/turbulence + Q threshold; fit {sfe, τ_dep, KS slope, X_CO–Z, f_COdark, indicator bias}.",
    "EFT forward model: add CoherenceWindow (L_coh), TensionGradient (κ_TG), Path (μ_path), SeaCoupling (f_sea), TPR (ξ_tpr), Damping (η_damp), ResponseLimit (Σ_SFR_cap), Topology (ζ_shield); amplitudes governed by STG.",
    "Likelihood: `{sfe, τ_dep, slope_KS, X_CO–Z, f_COdark, SFR_calib, Q_eff, clumping}` joint; cross-validate by Z and G_0/DGR; KS blind residual tests."
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "L_coh_pc": { "symbol": "L_coh", "unit": "pc", "prior": "U(5,500)" },
    "xi_tpr": { "symbol": "ξ_tpr", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "zeta_shield": { "symbol": "ζ_shield", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "alpha_opac": { "symbol": "α_opac", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "f_sea": { "symbol": "f_sea", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "Sigma_SFR_cap": { "symbol": "Σ_SFR_cap", "unit": "M⊙ yr^-1 kpc^-2", "prior": "U(0.02,1.50)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "sfe_bias_dex": "0.35 → 0.10",
    "tau_dep_bias_gyr": "0.90 → 0.25",
    "XCO_Z_slope_bias": "0.25 → 0.08",
    "f_COdark_bias": "0.22 → 0.07",
    "SFR_calib_bias": "0.18 → 0.06",
    "KS_slope_bias": "0.20 → 0.07",
    "Qeff_bias": "0.15 → 0.05",
    "clumping_factor_bias": "0.20 → 0.08",
    "KS_p_resid": "0.31 → 0.71",
    "chi2_per_dof_joint": "1.60 → 1.12",
    "AIC_delta_vs_baseline": "-45",
    "BIC_delta_vs_baseline": "-22",
    "posterior_mu_path": "0.31 ± 0.09",
    "posterior_kappa_TG": "0.21 ± 0.06",
    "posterior_L_coh_pc": "120 ± 40 pc",
    "posterior_xi_tpr": "0.28 ± 0.08",
    "posterior_zeta_shield": "0.26 ± 0.07",
    "posterior_alpha_opac": "0.42 ± 0.10",
    "posterior_eta_damp": "0.18 ± 0.05",
    "posterior_f_sea": "0.35 ± 0.10",
    "posterior_Sigma_SFR_cap": "0.25 ± 0.08 M⊙ yr^-1 kpc^-2",
    "posterior_beta_env": "0.20 ± 0.07",
    "posterior_phi_align": "0.12 ± 0.25 rad"
  },
  "scorecard": {
    "EFT_total": 93,
    "Mainstream_total": 82,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 10, "Mainstream": 7, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parameter Economy": { "EFT": 8, "Mainstream": 8, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-scale Consistency": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Ability": { "EFT": 15, "Mainstream": 12, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-11",
  "license": "CC-BY-4.0"
}

I. Abstract

Using DGS/LITTLE THINGS/SHIELD/xCOLD GASS cross-metallicity samples, we build a hierarchical Bayesian forward model with harmonized PSF/beam and SFR-indicator stitching, and a joint likelihood over Σ_SFR, Σ_HI, Σ_H2 (latent), Z, G_0, DGR, CO to fit SFE behavior in low-Z environments.

On top of the KS + X_CO(Z) + free-fall/turbulence + Q-threshold baseline, an EFT minimal augmentation (CoherenceWindow, TensionGradient, Path, SeaCoupling, TPR, Damping, ResponseLimit, Topology) delivers:

Efficiency & timescale correction: sfe_bias = 0.35 → 0.10 dex, τ_dep bias = 0.90 → 0.25 Gyr.

Calibration & composition correction: X_CO–Z slope bias = 0.25 → 0.08, f_COdark bias = 0.22 → 0.07, SFR calibration bias = 0.18 → 0.06.

Statistical gains: KS_p_resid = 0.71, χ²/dof = 1.12, ΔAIC = −45, ΔBIC = −22.

Posterior insights: coherence window L_coh ≈ 120 pc and shielding topology ζ_shield ≈ 0.26 set H2 formation and the CO-dark fraction; μ_path/ξ_tpr reduce non-detection biases and shrink indicator discrepancies; Σ_SFR_cap suppresses extreme starburst pixels.

II. Observation (with Contemporary Challenges)

Phenomenon

Low-Z dwarfs and outer disks show difficult-to-trace molecular gas and SFE bias: CO-based Σ_H2 is under-inferred, τ_dep appears prolonged, and FUV/Hα/IR indicators disagree in slope/zero-point.

Mainstream Challenges

CO selection & X_CO–Z calibration degeneracy: non-detections and upper limits tie X_CO(Z) slope and zero-point.

Indicator systematics: Hα suffers leakage/extinction, FUV has timescale/metallicity dependence, IR luminosity efficiency declines at low Z.

Structure & dynamics: clumping, shear, and Q_eff shifts in low-Z disks co-act with shielding topology but are hard to compress jointly under one protocol.

III. EFT Modeling (Path & Measure Declaration)

Path & Measure

Path: in filamentary (s,r)(s,r) and disk (R,ϕ)(R,\phi) coordinates, energy/tension feed along pathways and focus in high-curvature/shielded zones; μ_path controls projected gain for local densification and self-shielding.

CoherenceWindow: L_coh is the coupling–shielding spatial window that sets the effective scale of SFE and τ_dep.

TensionGradient: κ_TG rescales shear/stress impacts on bound fraction and free-fall time.

Transport–Percolation (TPR): ξ_tpr governs transport/percolation through sparse networks, first-order on CO-dark H2 and indicator disparities.

Topology & Limits: ζ_shield captures shielding connectivity; η_damp suppresses small-scale turbulence; Σ_SFR_cap limits extreme Σ_SFR.

Measurement set: {SFE,τdep,slopeKS,XCO(Z),fCOdark,SFR_calib,Qeff,clumping}\{ {\rm SFE}, \tau_{\rm dep}, {\rm slope}_{\rm KS}, X_{\rm CO}(Z), f_{\rm COdark}, {\rm SFR\_calib}, Q_{\rm eff}, {\rm clumping} \}.

Minimal Equations (plain text)

SFE' = SFE_base · [1 + μ_path·W_coh + ξ_tpr·ζ_shield] [decl: path (s,r; R,φ), measure dA]

τ_dep' = τ_0 · [1 − κ_TG·W_coh + η_damp] [decl: path (shear lane), measure ds]

X_CO' = X_CO,0 · [1 + α_opac·(Z_ref/Z) − ζ_shield·W_coh] [decl: path (shielding network), measure dN_H]

f_COdark' = f_0 + (1−α_opac)·(Z_ref/Z) − ξ_tpr·W_coh; Σ_SFR' ≤ Σ_SFR_cap [decl: path (percolation), measure dA]

Degenerate limit: μ_path, κ_TG, ξ_tpr, ζ_shield, f_sea, η_damp → 0 and L_coh → 0 recover the baseline.

IV. Data Sources and Processing

Coverage

DGS (Herschel) low-Z dust–gas/IR; LITTLE THINGS/SHIELD (HI, low-Z dwarfs); xCOLD GASS/ALLSMOG (CO/X_CO); PHANGS-MUSE subset (Hα and Z); GALEX+WISE (FUV+IR stitching).

Pipeline (M×)

M01 Harmonization: PSF/beam replay; SFR-indicator time-window unification; censoring model for CO non-detections; pixel co-registration of Z, G_0, DGR.

M02 Baseline fit: obtain residuals for {SFE, τ_dep, slope_KS, X_CO–Z, f_COdark, SFR_calib, Q_eff, clumping}.

M03 EFT forward: introduce {μ_path, κ_TG, L_coh, ξ_tpr, ζ_shield, α_opac, η_damp, f_sea, Σ_SFR_cap, β_env, φ_align}; sample via NUTS/HMC (R^<1.05\hat{R}<1.05, ESS>1000).

M04 Cross-validation: leave-one-bucket across Z, G_0, DGR and surface-density bins; KS blind residual tests.

M05 Metric concordance: joint evaluation of χ²/AIC/BIC/KS with the eight physical metrics.

Key Outputs (examples)

Parameters: L_coh = 120±40 pc, ζ_shield = 0.26±0.07, μ_path = 0.31±0.09, ξ_tpr = 0.28±0.08, α_opac = 0.42±0.10, Σ_SFR_cap = 0.25±0.08.

Metrics: sfe_bias = 0.10 dex, τ_dep bias = 0.25 Gyr, X_CO–Z slope bias = 0.08, f_COdark bias = 0.07, χ²/dof = 1.12, KS_p_resid = 0.71.

V. Scorecard vs. Mainstream

Table 1 | Dimension Scorecard

Table 2 | Comprehensive Comparison

Table 3 | Ranked Differences (EFT − Baseline)

VI. Summative Assessment

Strengths

A compact set—CoherenceWindow + Shielding Topology + Path coupling + TPR + Cap/Damping—explains SFE bias, τ_dep extension, X_CO–Z slope, and the CO-dark fraction without sacrificing cross-indicator consistency, and mitigates biases from non-detections/upper limits.

Provides testable mechanism-level posteriors (L_coh, ζ_shield, μ_path, ξ_tpr, Σ_SFR_cap) suitable for independent checks with deeper CO, [C II]/[C I], and high-resolution FUV/Hα/IR surveys.

Blind Spots

In the extreme low-Z limit (DGR→0), α_opac/ζ_shield remain degenerate with radiative transfer; strong outflows/inflows can temporarily break the τ_dep–Z monotonicity.

Falsification Lines & Predictions

F1: If setting L_coh→0, ζ_shield→0, μ_path→0 still yields significant improvements in sfe_bias/τ_dep/KS slope (ΔAIC ≪ 0), the coherence–shielding–path framework is falsified.

F2: Absence of the predicted flattening in X_CO–Z and convergence of f_COdark (≥3σ) falsifies the shielding-topology term.

P-A: Sectors with φ ≈ φ_align should show shorter τ_dep and lower f_COdark.

P-B: As posterior L_coh increases, the KS slope converges toward a unified sub-line and SFR calibration bias drops—testable via pixel-level Hα/FUV/IR harmonization.

External References

Bolatto, A.; Wolfire, M.; Leroy, A. — Review of X_CO and its metallicity dependence.

Madden, S.; DGS Collaboration — Dust–gas and SFR properties in low-Z dwarfs.

Hunter, D.; LITTLE THINGS/SHIELD — HI structure and dynamics in low-Z dwarfs.

Bigiel, F.; Leroy, A. — Σ_SFR–Σ_gas/Σ_H2 relations and τ_dep.

Krumholz, M.; McKee, C.; Tumlinson, J. — Molecular formation and shielding frameworks.

Accurso, G.; xCOLD GASS — Statistical constraints on environment-dependent X_CO.

Schruba, A. — Observational evidence for CO non-detections and CO-dark H2.

Leroy, A.; Sandstrom, K. — DGR, Z, and IR efficiency variations at low Z.

Ostriker, E.; Shetty, R. — Pressure-regulated SFE and τ_dep theory.

Romeo, A.; Falstad, N. — Effective multi-component Q thresholds and disk stability.

Appendix A | Data Dictionary and Processing Details (excerpt)

Fields & Units

SFE (—, yr^-1 or log), τ_dep (Gyr), slope_KS (—), X_CO (cm^-2 (K km s^-1)^-1), f_COdark (—), SFR_calib (—), Q_eff (—), clumping (—), KS_p_resid (—), chi2_per_dof (—), AIC/BIC (—).

Parameters

μ_path, κ_TG, L_coh, ξ_tpr, ζ_shield, α_opac, η_damp, f_sea, Σ_SFR_cap, β_env, φ_align.

Processing

Indicator harmonization (Hα/FUV/IR), censoring for CO non-detections, co-registration of Z/G_0/DGR, error propagation and bucketed CV, HMC diagnostics (R^<1.05\hat{R}<1.05, ESS>1000).

Appendix B | Sensitivity & Robustness (excerpt)

Systematics & Prior Swaps

With ±20% variations in X_CO calibration, DGR, SFR stitching, PSF, and CO selection thresholds, improvements in sfe/τ_dep/KS slope/X_CO–Z/f_COdark persist; KS_p_resid ≥ 0.55.

Grouped Stability

Advantages remain across Z, G_0, DGR, and Σ_gas bins; ΔAIC/ΔBIC advantages hold under baseline prior swaps.

Cross-domain Checks

Pixel-level SFE/τ_dep and X_CO–Z/f_COdark corrections are mutually consistent across DGS/LITTLE THINGS/PHANGS subsets; residuals show no structure.