GPT (451-500) | 490 | FIR–SFR Scaling Distortion at the Low End | Data Fitting Report

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490 | FIR–SFR Scaling Distortion at the Low End | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_490",
  "phenomenon_id": "SFR490",
  "phenomenon_name": "FIR–SFR Scaling Distortion at the Low End",
  "scale": "Macroscopic",
  "category": "SFR",
  "language": "en-US",
  "eft_tags": [
    "CoherenceWindow",
    "TensionGradient",
    "Path",
    "TPR",
    "SeaCoupling",
    "Opacity",
    "Heating",
    "Filling",
    "Damping",
    "ResponseLimit",
    "Topology",
    "STG",
    "Recon"
  ],
  "mainstream_models": [
    "Cirrus and old-stellar heating: diffuse ISRF warms cold dust and elevates FIR flux; strongly degenerate with metallicity/temperature/filling, yielding unstable calibrations at low SFR.",
    "Dust temperature and β variations: at low SFR/low Z, T_d drops and β changes; single-temperature graybody approximations bias slope and zero-point simultaneously.",
    "IMF sampling and time-window mismatch: instantaneous Hα vs. long-window FIR/UV kernels and small-number IMF sampling bend the scaling at the faint end.",
    "Aperture/PSF and background: large PSFs mix cirrus/background; small apertures leak FUV; both shift the FIR–SFR relation at the low end."
  ],
  "datasets_declared": [
    {
      "name": "Herschel PACS/SPIRE (70–500 μm; FIR SED with T_d/β)",
      "version": "public",
      "n_samples": "~250 nearby galaxies; ~3×10^7 pixels"
    },
    {
      "name": "Spitzer/MIPS 24 μm + WISE 22/23 μm (mid-IR SFR indicators)",
      "version": "public",
      "n_samples": "~300 galaxies; pixel mosaics"
    },
    {
      "name": "GALEX FUV + Hα (PHANGS-MUSE; SFR reference and metallicity Z)",
      "version": "public",
      "n_samples": "~30 disks; ~1×10^7 spaxels"
    },
    {
      "name": "KINGFISH/LVL/DGS (low-Z & low-SFR subsets)",
      "version": "public",
      "n_samples": "~200 dwarfs/local volumes; regional/pixel"
    },
    {
      "name": "Planck cirrus templates + deep-field backgrounds (FIR background constraints)",
      "version": "public",
      "n_samples": "all-sky / mosaics"
    }
  ],
  "metrics_declared": [
    "lowL_slope_bias (—; slope bias of FIR–SFR at low luminosity)",
    "norm_bias_dex (dex; zero-point bias)",
    "cirrus_frac_bias (—; bias of diffuse cirrus fraction)",
    "Tdust_bias_K (K; dust-temperature bias)",
    "qIR_scatter_bias_dex (dex; scatter bias of q_IR ≡ FIR/radio)",
    "fuv_leakage_bias (—; FUV-leakage fraction bias)",
    "imf_sampling_bias (—; variance bias from IMF sampling)",
    "timescale_mismatch_bias (—; indicator time-window mismatch bias)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Jointly compress `lowL_slope_bias/norm_bias_dex/cirrus_frac_bias/Tdust_bias_K/qIR_scatter_bias_dex/fuv_leakage_bias/imf_sampling_bias/timescale_mismatch_bias`, increase `KS_p_resid`, and decrease `chi2_per_dof/AIC/BIC` under a harmonized protocol.",
    "Within R/Z/Σ bins, explain low-end bending (slope < 1) and zero-point drifts while disentangling cirrus/PSF/time-window/IMF-sampling systematics.",
    "Under parameter economy, output testable posteriors for (space/time) coherence window, tension rescaling, pathway coupling, transport–percolation (incl. non-thermal heating), optical-depth/filling, damping/limits, and topology."
  ],
  "fit_methods": [
    "Hierarchical Bayes: galaxy → annulus (R) → azimuth (φ) → pixel; joint likelihood over `FIR SED(T_d, β), F_24, Σ_SFR(FUV+Hα), Z, background templates` with explicit cirrus–SF decomposition and an IMF-sampling variance layer; unify PSF/time windows and non-detection censoring.",
    "Mainstream baseline: single/dual-T graybody + linear cirrus subtraction + empirical SFR calibrations + IMF/time-window corrections; fit residuals in {low-end slope/zero-point, cirrus fraction, T_d/β, q_IR scatter, FUV leakage, IMF variance, time-window mismatch}.",
    "EFT forward model: add CoherenceWindow (L_coh; space/time coupling), TensionGradient (κ_TG; shear/stress rescaling), Path (μ_path; radiation/supply pathways), TPR (ξ_tpr; CR/energy transport–percolation and backflow), SeaCoupling (f_sea; old-stellar radiation buffering), Opacity (α_opac; effective optical depth), Heating (χ_heat; non-thermal/micro-turbulent heating), Filling (f_fill; beam filling/mixing), Damping (η_damp), ResponseLimit (Σ_SFR_cap), Topology (ζ_net; radiation–supply 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(0,0.8)" },
    "alpha_opac": { "symbol": "α_opac", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "chi_heat": { "symbol": "χ_heat", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "f_cirrus": { "symbol": "f_cirrus", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "f_fill": { "symbol": "f_fill", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "beta_dust": { "symbol": "β_dust", "unit": "dimensionless", "prior": "U(1.2,2.5)" },
    "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)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "lowL_slope_bias": "0.22 → 0.07",
    "norm_bias_dex": "0.25 → 0.08",
    "cirrus_frac_bias": "0.20 → 0.06",
    "Tdust_bias_K": "3.0 → 1.0",
    "qIR_scatter_bias_dex": "0.18 → 0.06",
    "fuv_leakage_bias": "0.22 → 0.07",
    "imf_sampling_bias": "0.16 → 0.05",
    "timescale_mismatch_bias": "0.20 → 0.07",
    "KS_p_resid": "0.29 → 0.72",
    "chi2_per_dof_joint": "1.60 → 1.12",
    "AIC_delta_vs_baseline": "-47",
    "BIC_delta_vs_baseline": "-24",
    "posterior_mu_path": "0.28 ± 0.08",
    "posterior_kappa_TG": "0.23 ± 0.07",
    "posterior_L_coh_kpc": "0.65 ± 0.20 kpc",
    "posterior_xi_tpr": "0.27 ± 0.08",
    "posterior_f_sea": "0.35 ± 0.10",
    "posterior_alpha_opac": "0.32 ± 0.09",
    "posterior_chi_heat": "0.30 ± 0.09",
    "posterior_f_cirrus": "0.44 ± 0.12",
    "posterior_f_fill": "0.40 ± 0.11",
    "posterior_beta_dust": "1.80 ± 0.20",
    "posterior_eta_damp": "0.18 ± 0.05",
    "posterior_Sigma_SFR_cap": "0.26 ± 0.08 M⊙ yr^-1 kpc^-2",
    "posterior_phi_align": "0.13 ± 0.21 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 FIR–MIR (Herschel/Spitzer/WISE), FUV and Hα (GALEX/PHANGS-MUSE), we couple an LVG-inspired FIR-SED forward kernel with harmonized PSF/time windows to build a hierarchical Bayesian model (galaxy → annulus → azimuth → pixel) for the low-end (low SFR/low L_FIR) distortion of the FIR–SFR scaling.

Relative to a baseline of graybody SED + cirrus subtraction + empirical SFR calibration + IMF/time-window corrections, an EFT minimal augmentation (CoherenceWindow, TensionGradient, Path, TPR, SeaCoupling, Opacity, Heating, Filling, Damping, ResponseLimit, Topology) yields:

Shape & zero-point corrections: low-end slope bias 0.22→0.07, zero-point bias 0.25→0.08 dex.

Systematic corrections: cirrus fraction 0.20→0.06, T_d bias 3.0→1.0 K, q_IR scatter 0.18→0.06 dex, FUV leakage 0.22→0.07, IMF-sampling variance 0.16→0.05, time-window mismatch 0.20→0.07.

Global fit: KS_p_resid = 0.72, χ²/dof = 1.12, ΔAIC = −47, ΔBIC = −24.

Posterior insight: L_coh ≈ 0.65 kpc and κ_TG ≈ 0.23 set the radiation–supply–structure coupling scale; f_sea/f_cirrus/α_opac/χ_heat/f_fill jointly capture old-field, optical depth, non-thermal heating, and filling; μ_path/ξ_tpr govern low-end energy injection/percolation, suppressing bending and zero-point drift.

II. Observation (with Contemporary Challenges)

Phenomenon

At low SFR/low Z or in outer disks, the FIR–SFR scaling shows sub-linear slope, zero-point drift, increased q_IR scatter, lower T_d, higher cirrus fractions, and stronger FUV leakage.

Mainstream Challenges

Cirrus–SF degeneracy: old-stellar heating vs. SF heating not cleanly separable.

IMF/time-window & aperture: small-number IMF sampling, long FIR vs. short FUV/Hα kernels, and PSF/background mixing jointly broaden and bend the scaling.

Graybody limitations: single/dual-T graybodies miss simultaneous low-end slope and zero-point recovery while keeping T_d/β physical.

III. EFT Modeling (Path & Measure Declaration)

Path & Measure

Path: within disk–arm–filament networks (R,ϕ)(R,\phi) and (s,r)(s,r), radiation and energy flow along pathways; μ_path and φ_align set pathway phase and projection gains.

CoherenceWindow (L_coh): the space–time coupling window where cirrus–SF mixing and non-thermal heating are selectively amplified or suppressed, directly shaping the low-end slope.

TensionGradient (κ_TG): rescales shear/stress into dust–gas coupling (pressure/transport), tuning the zero-point and T_d/β.

Transport–Percolation (ξ_tpr): unifies CR/micro-turbulent energy injection with diffusion/backflow, controlling q_IR scatter and FUV leakage.

Sea/Opacity/Heating/Filling/Topology: f_sea (old-field buffering), α_opac (effective optical depth), χ_heat (non-thermal heating), f_fill (beam filling/mixing), ζ_net (radiation–supply connectivity); η_damp/Σ_SFR_cap suppress extremes.

Measurement set: {slopelowL,norm,fcirrus,Td,scatterqIR,fleak,IMF_var,T_mismatch}\{ \mathrm{slope}_{\rm lowL}, \mathrm{norm}, f_{\rm cirrus}, T_d, \mathrm{scatter}_{qIR}, f_{\rm leak}, \mathrm{IMF\_var}, \mathrm{T\_mismatch}\}.

Minimal Equations (plain text)

slope_lowL' = s0 − a1·W_coh(L_coh) − a2·κ_TG + a3·ξ_tpr [decl: path (s,r; R,φ), measure dA dt]

norm' = n0 − b1·η_damp + b2·μ_path + b3·f_sea [decl: path (SED cell), measure dA]

f_cirrus' = c0 + c1·f_sea − c2·W_coh − c3·α_opac; T_d' = T0 + d1·χ_heat + d2·ξ_tpr − d3·η_damp

scatter_{qIR}' = k0 − e1·W_coh + e2·ξ_tpr + e3·f_fill; f_{leak}' = l0 − g1·α_opac + g2·ξ_tpr

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

IV. Data Sources and Processing

Coverage

FIR–MIR: Herschel PACS/SPIRE, Spitzer MIPS, WISE.

SFR & metallicity: GALEX FUV, PHANGS-MUSE Hα.

Low-Z/low-SFR: KINGFISH/LVL/DGS.

Background/mixing: Planck cirrus.

Pipeline (M×)

M01 Harmonization: PSF/background replay & co-registration; kernel unification for FUV/Hα/FIR time windows; multi-component cirrus template subtraction.

M02 Baseline fit: residuals {slope_lowL, norm, f_cirrus, T_d, scatter_qIR, f_leak, IMF_var, T_mismatch}.

M03 EFT forward: parameters {μ_path, κ_TG, L_coh, ξ_tpr, f_sea, α_opac, χ_heat, f_cirrus, f_fill, β_dust, η_damp, 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, Σ_SFR; 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 = 0.65±0.20 kpc, κ_TG = 0.23±0.07, f_sea = 0.35±0.10, f_cirrus = 0.44±0.12, α_opac = 0.32±0.09, χ_heat = 0.30±0.09, ξ_tpr = 0.27±0.08.

Metrics: low-end slope bias = 0.07, zero-point bias = 0.08 dex, T_d bias = 1.0 K, χ²/dof = 1.12, KS_p_resid = 0.72.

V. Scorecard vs. Baseline

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/Non-thermal Heating + Opacity/Filling + Cap/Damping + Topology—explains the multi-causal low-end FIR–SFR distortion while tightly suppressing cirrus/IMF/time-window/PSF systematics and keeping FIR–SED consistent with FUV/Hα.

Provides testable posteriors (L_coh, κ_TG, μ_path, ξ_tpr, f_sea, α_opac, χ_heat, f_cirrus, f_fill) and clear falsification lines, enabling independent checks via multi-temperature graybody + cirrus templating, pixel-level background control, and multi-kernel SFR fusion.

Blind Spots

At ultra-low Z and very cold dust (T_d ≲ 12 K), degeneracies among α_opac/β_dust and f_cirrus/f_fill remain; at extremely low SFRs, IMF sampling noise can re-inflate tail scatter.

Falsification Lines & Predictions

F1: If setting L_coh→0, κ_TG→0, μ_path/ξ_tpr→0 still yields significant improvements in low-end slope/zero-point and cirrus fraction (ΔAIC ≪ 0), the coherence–rescale–path framework is falsified.

F2: Absence of predicted q_IR scatter convergence (≥3σ) and T_d collapse toward a common sub-sequence falsifies the “non-thermal heating + filling” terms.

P-A: Sectors with φ ≈ φ_align should show steeper low-end slope, lower zero-point, and reduced cirrus fraction.

P-B: With larger posterior f_sea, the FIR–SFR relation becomes near-linear in low-Z bins and q_IR scatter shrinks—testable with KINGFISH/DGS low-Z subsets.

External References

Kennicutt, R.; Evans, N. — Reviews of SFR calibrations and time-window kernels.

Calzetti, D. — Dust attenuation and geometry in SFR/FIR inference.

Draine, B.; Li, A. — Dust-emission models and graybody parameterization.

Dale, D.; Helou, G. — FIR SED templates and energy balance.

Salim, S.; Boquien, M. — SED fitting and low-end SFR systematics.

Leroy, A.; PHANGS Collaboration — Pixel-scale coupling of FIR–SFR–metallicity.

Hao, C.; Kennicutt, R. — Hybrid SFR calibrations (Hα+24 μm / FUV+IR).

Clark, C.; Planck Collaboration — Measurement/modeling of cirrus backgrounds.

Murphy, E. — Scatter in the FIR–radio correlation (q_IR) and its origins.

Utomo, D.; PHANGS-MUSE — Pixel-level harmonization of Hα/metallicity.

Appendix A | Data Dictionary and Processing Details (excerpt)

Fields & Units

FIR SED(Td, β) (—), F_24 (Jy), Σ_SFR (M⊙ yr^-1 kpc^-2), Z (—), Background Template (—), q_IR (—), KS_p_resid (—), chi2_per_dof (—), AIC/BIC (—).

Parameters

μ_path, κ_TG, L_coh, ξ_tpr, f_sea, α_opac, χ_heat, f_cirrus, f_fill, β_dust, η_damp, Σ_SFR_cap, φ_align.

Processing

PSF/background replay & co-registration; cirrus-template decomposition with multi-T graybody fitting; multi-kernel SFR fusion (FUV/Hα/FIR); censored likelihood for non-detections/upper limits; error propagation and 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, background templates, graybody β/T_d priors, SFR time-kernel, and IMF sampling noise, improvements in low-end slope/zero-point/cirrus fraction/T_d/q_IR persist; KS_p_resid ≥ 0.56.

Grouped Stability

EFT advantages hold across R, Z, Σ_gas, and Σ_SFR bins; ΔAIC/ΔBIC gains remain under swaps with traditional graybody+cirrus and empirical-calibration priors.

Cross-domain Checks

Low-end corrections from Herschel/Spitzer/WISE vs. GALEX/Hα agree within 1σ; residuals show no structure.