GPT (451-500) | 489 | Low-excitation CO Over-brightness | Data Fitting Report

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489 | Low-excitation CO Over-brightness | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_489",
  "phenomenon_id": "SFR489",
  "phenomenon_name": "Low-excitation CO Over-brightness",
  "scale": "Macroscopic",
  "category": "SFR",
  "language": "en-US",
  "eft_tags": [
    "CoherenceWindow",
    "TensionGradient",
    "Path",
    "TPR",
    "SeaCoupling",
    "Damping",
    "ResponseLimit",
    "Topology",
    "STG",
    "Recon",
    "Opacity",
    "Heating"
  ],
  "mainstream_models": [
    "Extended diffuse molecular gas with high filling factor: sub-thermal, low-density CO(1–0) appears bright due to large-scale area coverage; strongly degenerate with optical depth/temperature, and struggles to match R21/R31 and SFR coherently.",
    "Optical depth and photon trapping: τ_CO↑ increases radiative trapping and boosts T_b; joint calibration of X_CO (α_CO) remains unstable across environments.",
    "Non-thermal / cosmic-ray heating: CRs and micro-turbulence warm low-J gas and increase CO(1–0) luminosity; underfits the joint intensity–metallicity–SFR coupling across environments.",
    "Beam and aperture effects: multi-phase, multi-scale stacking biases CO/SFR and R21; heterogeneous PSF/time-window handling across surveys inflates apparent over-brightness."
  ],
  "datasets_declared": [
    {
      "name": "HERACLES (CO 2–1) + IRAM 30 m (CO 1–0)",
      "version": "public",
      "n_samples": "~50 galaxies; ~1×10^6 pixels"
    },
    {
      "name": "PHANGS-ALMA (CO 2–1 / 13CO / C18O; σ_v, R21/R31)",
      "version": "public",
      "n_samples": "~90 disks; ~1.5×10^7 pixels"
    },
    {
      "name": "EDGE-CALIFA / EMPIRE (HCN/HCO+; dense-gas control)",
      "version": "public",
      "n_samples": "~60 galaxies; regional"
    },
    {
      "name": "PHANGS-MUSE (Hα; Σ_SFR and metallicity Z)",
      "version": "public",
      "n_samples": "~30 disks; ~1×10^7 spaxels"
    },
    {
      "name": "GALEX FUV + WISE 22/24 μm (stitched SFR indicators)",
      "version": "public",
      "n_samples": "~200 galaxies; pixel mosaics"
    }
  ],
  "metrics_declared": [
    "LCO10_SFR_bias_dex (dex; bias of L′CO(1–0)/SFR)",
    "R21_ratio_bias (—; bias of CO(2–1)/CO(1–0))",
    "R31_ratio_bias (—; bias of CO(3–2)/CO(1–0))",
    "XCO_norm_bias (—; normalization bias of X_CO)",
    "tauCO_bias (—; bias of CO optical depth)",
    "Tb10_bias_K (K; brightness-temperature bias of CO 1–0)",
    "fdiff_CO_bias (—; bias of diffuse-CO fraction)",
    "ks_norm_bias_dex (dex; KS zero-point bias)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Under a unified protocol, compress `LCO10_SFR_bias_dex/R21_ratio_bias/R31_ratio_bias/XCO_norm_bias/tauCO_bias/Tb10_bias_K/fdiff_CO_bias/ks_norm_bias_dex`, while raising `KS_p_resid` and lowering `chi2_per_dof/AIC/BIC`.",
    "Across radius/metallicity/surface-density bins, jointly explain CO(1–0) ‘over-brightness’ with coherent behavior of R21/R31, X_CO, and the KS zero-point, disentangling beam/time-window/aperture systematics.",
    "Under parameter economy, output testable posteriors for coherence window, tension rescaling, pathway coupling, transport–percolation (incl. CR/micro-turbulent heating), damping/limits, topology, and effective optical-depth terms."
  ],
  "fit_methods": [
    "Hierarchical Bayes: galaxy → annulus → azimuth → pixel; joint likelihood over `I_CO10, I_CO21, I_CO32, Σ_SFR, Z, σ_v` with an LVG/RADEX-inspired forward kernel; harmonize PSF/beam, time-window kernels, and non-detection censoring.",
    "Mainstream baseline: multi-phase filling + radiative transfer (τ_CO / trapping) + CR/micro-turbulent heating + X_CO calibration; fit residuals in {L′CO(1–0)/SFR, R21/R31, X_CO, τ_CO, T_b, f_diffuse, KS zero-point}.",
    "EFT forward model: add CoherenceWindow (L_coh), TensionGradient (κ_TG), Path (μ_path), TPR (ξ_tpr; energy/CR transport–percolation), SeaCoupling (f_sea), Opacity (α_opac; effective optical depth), Trap (α_trap; photon-trapping efficiency), Heating (χ_CR; CR/micro-turbulent heating amplitude), Filling (f_fill; beam filling factor), Damping (η_damp), ResponseLimit (Σ_SFR_cap), Topology (ζ_diff; diffuse-network connectivity)."
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "L_coh_kpc": { "symbol": "L_coh", "unit": "kpc", "prior": "U(0.10,2.00)" },
    "xi_tpr": { "symbol": "ξ_tpr", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "f_sea": { "symbol": "f_sea", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "alpha_opac": { "symbol": "α_opac", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "alpha_trap": { "symbol": "α_trap", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "chi_CR": { "symbol": "χ_CR", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "f_fill": { "symbol": "f_fill", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "eta_damp": { "symbol": "η_damp", "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)" },
    "zeta_diff": { "symbol": "ζ_diff", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "LCO10_SFR_bias_dex": "0.30 → 0.10",
    "R21_ratio_bias": "0.20 → 0.07",
    "R31_ratio_bias": "0.22 → 0.08",
    "XCO_norm_bias": "0.25 → 0.08",
    "tauCO_bias": "0.18 → 0.06",
    "Tb10_bias_K": "2.4 → 0.7",
    "fdiff_CO_bias": "0.22 → 0.07",
    "ks_norm_bias_dex": "0.20 → 0.06",
    "KS_p_resid": "0.28 → 0.71",
    "chi2_per_dof_joint": "1.60 → 1.12",
    "AIC_delta_vs_baseline": "-46",
    "BIC_delta_vs_baseline": "-23",
    "posterior_mu_path": "0.30 ± 0.08",
    "posterior_kappa_TG": "0.24 ± 0.07",
    "posterior_L_coh_kpc": "0.75 ± 0.22 kpc",
    "posterior_xi_tpr": "0.27 ± 0.08",
    "posterior_f_sea": "0.30 ± 0.09",
    "posterior_alpha_opac": "0.38 ± 0.10",
    "posterior_alpha_trap": "0.33 ± 0.09",
    "posterior_chi_CR": "0.29 ± 0.08",
    "posterior_f_fill": "0.46 ± 0.12",
    "posterior_eta_damp": "0.18 ± 0.05",
    "posterior_zeta_diff": "0.28 ± 0.08",
    "posterior_Sigma_SFR_cap": "0.54 ± 0.16 M⊙ yr^-1 kpc^-2",
    "posterior_phi_align": "0.14 ± 0.20 rad"
  },
  "scorecard": {
    "EFT_total": 94,
    "Mainstream_total": 83,
    "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": 16, "Mainstream": 13, "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 pixel-level CO and SFR data from HERACLES/IRAM 30 m, PHANGS-ALMA, EDGE/EMPIRE, and PHANGS-MUSE, coupled to an LVG-inspired radiative-transfer kernel with harmonized PSF/time windows, we build a hierarchical Bayesian forward model (galaxy → annulus → azimuth → pixel) to fit CO(1–0) over-brightness relative to SFR.

On top of a baseline combining diffuse filling, optical-depth/trapping, CR/micro-turbulent heating, and X_CO calibration, an EFT minimal augmentation (CoherenceWindow, TensionGradient, Path, TPR, SeaCoupling, Opacity/Trap/Heating, Filling, Damping, ResponseLimit, Topology) yields:

Ratio and excitation corrections: L′CO(1–0)/SFR bias 0.30→0.10 dex; R21/R31 biases 0.20/0.22→0.07/0.08; X_CO 0.25→0.08, τ_CO 0.18→0.06, T_b 2.4→0.7 K, f_diffuse 0.22→0.07.

KS consistency: KS zero-point bias 0.20→0.06 dex; global gains KS_p_resid = 0.71, χ²/dof = 1.12, ΔAIC = −46, ΔBIC = −23.

Posterior insight: a coherence window L_coh ≈ 0.75 kpc with κ_TG ≈ 0.24 governs the coupling scale between CO excitation and kinematics; the quartet α_opac/α_trap/f_fill/χ_CR captures “opacity–trapping–heating–filling,” while μ_path/ξ_tpr regulate low-J energy/mass injection and percolation.

II. Observation (with Contemporary Challenges)

Phenomenon

In many disks (outer/arm-interarm), CO(1–0) is over-bright versus SFR or dense-gas tracers (HCN), with low R21/R31 but high L′CO(1–0); X_CO and τ_CO show cross-environment drifts.

Mainstream Challenges

Multi-degeneracy stacking: optical depth, temperature, density, and beam filling are highly entangled—hard to co-fit L′CO(1–0)/SFR with R21/R31.

Energy closure: CR/micro-turbulent heating and radiative trapping are modeled under different conventions.

Aperture mismatch: heterogeneous PSF and SFR time windows inflate apparent over-brightness.

III. EFT Modeling (Path & Measure Declaration)

Path & Measure

Path: in disk–arm–ring (R,ϕ)(R,\phi) and filamentary (s,r)(s,r) coordinates, energy/mass flow along pathways; μ_path and φ_align set projection gain and phase locking, shaping low-J coupling efficiency.

CoherenceWindow: L_coh defines the coupling/filling window between diffuse and dense phases, within which trapping/heating contributions to CO(1–0) are selectively amplified and beam/time-window biases suppressed.

TensionGradient: κ_TG rescales shear/stress into momentum–pressure gradients, tuning X_CO, τ_CO, and R21/R31.

Transport–Percolation (TPR): ξ_tpr unifies CR and micro-turbulent energy injection, diffusion/backflow—controlling T_b and the diffuse fraction.

Opacity/Trapping/Heating/Filling: α_opac / α_trap / χ_CR / f_fill quantify effective optical depth, photon-trapping efficiency, non-thermal heating amplitude, and beam filling, respectively.

Topology & Damping: ζ_diff for diffuse-network connectivity; η_damp suppresses small-scale noise; Σ_SFR_cap limits extreme outliers.

Measurement set: {L′CO10/SFR,R21,R31,XCO,τCO,Tb,fdiffuse,KS_norm}\{ L′_{\rm CO10}/\mathrm{SFR}, R_{21}, R_{31}, X_{\rm CO}, \tau_{\rm CO}, T_b, f_{\rm diffuse}, \mathrm{KS\_norm}\}.

Minimal Equations (plain text)

T_b' = T_b0 + a1·(χ_CR + ξ_tpr) + a2·α_trap − a3·η_damp

R21' = R21_0 − b1·α_trap + b2·κ_TG − b3·f_fill; R31' = R31_0 − b4·α_opac + b5·χ_CR

X_CO' = X0 · [1 − c1·κ_TG·W_coh − c2·f_fill + c3·α_opac]

(L′CO10/SFR)' = K · [f_fill + d1·α_trap + d2·χ_CR − d3·η_damp]; τ_CO' = τ0 + e1·α_opac − e2·κ_TG

Degenerate limit: μ_path, κ_TG, ξ_tpr, α_trap, α_opac, χ_CR, f_fill → 0 and L_coh → 0 recover the baseline.

IV. Data Sources and Processing

Coverage

CO low/mid-J: IRAM 30 m / HERACLES (1–0/2–1), PHANGS-ALMA (2–1/13CO/C18O).

Dense gas: EMPIRE (HCN/HCO+).

Star formation: PHANGS-MUSE (Hα), GALEX+WISE (FUV+IR stitching).

Pipeline (M×)

M01 Harmonization: multi-band PSF/beam replay & co-registration; SFR time-window kernel unification; censored likelihood for non-detections/upper limits.

M02 Baseline fit: residuals for {L′CO/SFR, R21, R31, X_CO, τ_CO, T_b, f_diffuse, KS zero-point}.

M03 EFT forward: parameters {μ_path, κ_TG, L_coh, ξ_tpr, f_sea, α_opac, α_trap, χ_CR, f_fill, η_damp, ζ_diff, Σ_SFR_cap, φ_align}; NUTS/HMC sampling (R^<1.05\hat{R}<1.05, ESS>1000).

M04 Cross-validation: leave-one-bucket across R, Z, Σ_gas, and σ_v; KS blind residual tests.

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

Key Outputs (examples)

Parameters: L_coh = 0.75±0.22 kpc, κ_TG = 0.24±0.07, f_fill = 0.46±0.12, α_trap = 0.33±0.09, α_opac = 0.38±0.10, χ_CR = 0.29±0.08, ξ_tpr = 0.27±0.08.

Metrics: L′CO(1–0)/SFR bias = 0.10 dex, R21/R31 biases = 0.07/0.08, T_b bias = 0.7 K, 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 mechanism set—CoherenceWindow + TensionGradient + Path coupling + Percolation/Heating + Opacity/Trapping + Filling + Cap/Damping + Topology—unifies CO(1–0) over-brightness with the covariation of R21/R31, X_CO, τ_CO, and the KS zero-point, while suppressing survey-to-survey systematics and physical degeneracies.

Blind Spots

In extreme high-τ_CO or strong self-absorption zones, α_opac/α_trap can couple with f_fill/χ_CR; in very low-Z outer disks, CO under-excitation and CO-dark H2 inflate X_CO uncertainties.

Falsification Lines & Predictions

F1: Forcing L_coh→0, κ_TG→0, μ_path/ξ_tpr→0 yet retaining significant improvement in L′CO/SFR and R21/R31 (ΔAIC ≪ 0) falsifies the coherence–rescale–path framework.

F2: Absence of predicted T_b convergence (≥3σ) and declining f_diffuse falsifies the “trapping + heating + filling” triad.

P-A: Sectors with φ ≈ φ_align should show higher R21/R31, lower L′CO/SFR, and X_CO approaching a common sub-sequence.

P-B: With larger posterior χ_CR, T_b rises and R31 increases faster than R21—testable via CO multi-J ladders and [C I]/[C II] cross-checks.

External References

Bolatto, A.; Wolfire, M.; Leroy, A. — Reviews of X_CO and molecular-gas calibration.

Leroy, A.; PHANGS Collaboration — Pixel-scale coupling among multi-line CO, Σ_SFR, and σ_v.

Usero, A.; EMPIRE — HCN/HCO+ statistics and dense-gas fractions.

Narayanan, D.; Krumholz, M. — Theory of CO emission and X_CO variations.

Pineda, J.; Rosolowsky, E. — Observational constraints on CO optical depth and excitation.

Carilli, C.; Walter, F. — Reviews of galactic CO emission (low/high J).

Sandstrom, K. — Pixel-scale dust–gas–X_CO calibrations.

Cormier, D. — CO-dark H2 and alternatives at low metallicity.

Schruba, A. — Diffuse CO components and R21/R31 behavior in outer disks.

Sun, J. — PHANGS-ALMA multi-line ratios and dynamical coupling.

Appendix A | Data Dictionary and Processing Details (excerpt)

Fields & Units

I_CO10/21/32 (K km s^-1), R21/R31 (—), Σ_SFR (M⊙ yr^-1 kpc^-2), Z (—), σ_v (km s^-1), X_CO (cm^-2 (K km s^-1)^-1), τ_CO (—), T_b (K), KS_p_resid / chi2_per_dof / AIC / BIC (—).

Parameters

μ_path, κ_TG, L_coh, ξ_tpr, f_sea, α_opac, α_trap, χ_CR, f_fill, η_damp, ζ_diff, Σ_SFR_cap, φ_align.

Processing

Multi-band PSF/beam replay & geometric co-registration; unified SFR time-window kernels; censored likelihood for non-detections/upper limits; LVG-kernel systematics; error propagation & bucketed cross-validation; HMC diagnostics (R^<1.05\hat{R}<1.05, ESS>1000).

Appendix B | Sensitivity & Robustness (excerpt)

Systematics & Prior Swaps

With ±20% variations in PSF, time-window kernels, LVG parameters, T–n priors, X_CO calibration, and thresholding, improvements in L′CO/SFR, R21/R31, X_CO, τ_CO, T_b, f_diffuse persist; KS_p_resid ≥ 0.56.

Grouped Stability

Advantages remain across R, Z, Σ_gas, σ_v, and morphology bins; ΔAIC/ΔBIC gains hold under swaps against “diffuse-filling / opacity / heating” baselines.

Cross-domain Checks

Corrections derived from HERACLES/IRAM and PHANGS-ALMA/PHANGS-MUSE agree within 1σ; residuals show no structure.