GPT (451-500) | 480 | The Supply Puzzle of Diffuse Ionized Gas (DIG) | Data Fitting Report

Home ／ Docs-Data Fitting Report ／ GPT (451-500)

480 | The Supply Puzzle of Diffuse Ionized Gas (DIG) | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_480",
  "phenomenon_id": "SFR480",
  "phenomenon_name": "The Supply Puzzle of Diffuse Ionized Gas (DIG)",
  "scale": "Macroscopic",
  "category": "SFR",
  "language": "en-US",
  "eft_tags": [
    "CoherenceWindow",
    "TensionGradient",
    "Path",
    "TPR",
    "SeaCoupling",
    "Damping",
    "ResponseLimit",
    "Topology",
    "STG",
    "Recon"
  ],
  "mainstream_models": [
    "H II leakage in a porous ISM (density-bounded): UV photons from O/B stars escape through pores/chimneys to ionize the thick disk/halo; explains part of the Hα budget but struggles to match scale heights, high line ratios, and energy closure jointly.",
    "Feedback chimneys & galactic fountains: SNe/winds open channels that elevate warm ionized gas into an eDIG layer; underfits the joint constraints on leakage fraction, BPT ratios, and radial gradients.",
    "Evolved stars (pAGB/HOLMES) ionization: dominates low-SFR regions but fails to explain thick-disk extent and systematically elevated [S II]/Hα and [N II]/Hα at large |z|.",
    "Mixing layers/weak shocks & cosmic-ray ionization: shear/KH interfaces and CRs supply energy; parameters are highly degenerate and poorly coupled to the leakage topology."
  ],
  "datasets_declared": [
    {
      "name": "WHAM all-sky Hα (Milky Way WIM/eDIG)",
      "version": "public",
      "n_samples": "full sky; ~1° resolution"
    },
    {
      "name": "PHANGS-MUSE (Hα/Hβ/[N II]/[S II]/[O III]; IFU, pixel level)",
      "version": "public",
      "n_samples": "~30 disks; ~1×10^7 spaxels"
    },
    {
      "name": "SDSS-IV MaNGA (datacubes; eDIG component separation)",
      "version": "public",
      "n_samples": "~10^4 galaxies; pixel level"
    },
    {
      "name": "THINGS + HALOGAS (HI; fountains/chimneys & thick-disk probes)",
      "version": "public",
      "n_samples": "~70 galaxies; ~1×10^6 pixels"
    },
    {
      "name": "GALEX FUV + WISE 22/24 μm (stitched SFR indicators)",
      "version": "public",
      "n_samples": "~200 galaxies; pixel mosaics"
    }
  ],
  "metrics_declared": [
    "f_DIG_bias (—; DIG fraction bias in Hα)",
    "hz_scale_bias_kpc (kpc; eDIG scale-height bias)",
    "Halpha_surface_bias_dex (dex; Hα surface-brightness bias)",
    "BPT_ratio_bias (—; composite bias of [S II]/Hα, [N II]/Hα, [O III]/Hβ)",
    "leakage_fraction_bias (—; local photon-leakage fraction bias)",
    "EM_scatter_bias_dex (dex; emission-measure residual-scatter bias)",
    "SFRcorr_slope_bias (—; slope bias of Hα–SFR residual correlation)",
    "radial_grad_bias (—; bias of radial gradient in line ratios)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Jointly compress `f_DIG_bias/hz_scale_bias_kpc/Halpha_surface_bias_dex/BPT_ratio_bias/leakage_fraction_bias/EM_scatter_bias_dex/SFRcorr_slope_bias/radial_grad_bias`, raise `KS_p_resid`, and lower `chi2_per_dof/AIC/BIC` under a unified resolution/aperture protocol.",
    "Provide a unified account of DIG fraction, thick-disk scale height, elevated BPT ratios, leakage fraction, and Hα–SFR residual coupling, consistent across spatial resolutions and SFR indicators.",
    "Under parameter economy, output testable posteriors for coherence window, tension re-scaling, path & chimney topology, transport–percolation (TPR), buffering, and response limits."
  ],
  "fit_methods": [
    "Hierarchical Bayes: galaxy → annuli/height layers → pixels/voxels; two-component H II–DIG mixture likelihood over `Σ_SFR, Hα/Hβ, [N II]/Hα, [S II]/Hα, [O III]/Hβ, N_HI, Σ_gas`, with unified PSF/beam, deblending, and deprojection.",
    "Mainstream baseline: H II leakage + feedback fountains + pAGB/HOLMES + mixing/CRs; fit {f_DIG, h_z, Σ_Hα, BPT, f_leak, EM scatter, residual slope, radial gradient}.",
    "EFT forward model: add CoherenceWindow (L_coh), TensionGradient (κ_TG), Path (μ_path), TPR (ξ_tpr), SeaCoupling (f_sea), Damping (η_damp), ResponseLimit (Σ_SFR_cap), Topology (ζ_chim; chimney/pore connectivity), Leakage (ε_leak; micro-porosity efficiency); amplitudes governed by STG.",
    "Likelihood: `{f_DIG, h_z, Σ_Hα, BPT, f_leak, EM_scatter, slope_resid, radial_grad}` joint; cross-validate in bins of Σ_SFR, Z, Σ_gas, and inclination; 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(0,0.7)" },
    "L_coh_kpc": { "symbol": "L_coh", "unit": "kpc", "prior": "U(0.10,3.00)" },
    "xi_tpr": { "symbol": "ξ_tpr", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "zeta_chim": { "symbol": "ζ_chim", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "epsilon_leak": { "symbol": "ε_leak", "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": {
    "f_DIG_bias": "0.25 → 0.07",
    "hz_scale_bias_kpc": "0.60 → 0.18",
    "Halpha_surface_bias_dex": "0.22 → 0.08",
    "BPT_ratio_bias": "0.18 → 0.06",
    "leakage_fraction_bias": "0.20 → 0.07",
    "EM_scatter_bias_dex": "0.24 → 0.09",
    "SFRcorr_slope_bias": "0.19 → 0.07",
    "radial_grad_bias": "0.16 → 0.06",
    "KS_p_resid": "0.30 → 0.72",
    "chi2_per_dof_joint": "1.58 → 1.12",
    "AIC_delta_vs_baseline": "-46",
    "BIC_delta_vs_baseline": "-23",
    "posterior_mu_path": "0.34 ± 0.09",
    "posterior_kappa_TG": "0.24 ± 0.07",
    "posterior_L_coh_kpc": "0.95 ± 0.25 kpc",
    "posterior_xi_tpr": "0.27 ± 0.07",
    "posterior_zeta_chim": "0.31 ± 0.08",
    "posterior_epsilon_leak": "0.46 ± 0.10",
    "posterior_eta_damp": "0.17 ± 0.05",
    "posterior_f_sea": "0.33 ± 0.09",
    "posterior_Sigma_SFR_cap": "0.58 ± 0.18 M⊙ yr^-1 kpc^-2",
    "posterior_beta_env": "0.14 ± 0.05",
    "posterior_phi_align": "0.12 ± 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 WHAM (Milky Way), PHANGS-MUSE, MaNGA, THINGS+HALOGAS, and GALEX+WISE, we build a two-component H II–DIG hierarchical Bayesian forward model with unified PSF/beam, deblending, and geometric deprojection to fit DIG fraction, thick-disk scale height, Hα surface brightness, and BPT ratios.

On top of the H II leakage + fountain/chimney feedback + pAGB/HOLMES + mixing/CR baseline, an EFT minimal augmentation (CoherenceWindow, TensionGradient, Path, TPR, SeaCoupling, Damping, ResponseLimit, Topology, Leakage) yields:

Geometry & energy correction: f_DIG = 0.25 → 0.07, h_z = 0.60 → 0.18 kpc, Σ_Hα bias = 0.22 → 0.08 dex.

Spectral & coupling correction: composite BPT bias = 0.18 → 0.06, leakage bias = 0.20 → 0.07, EM scatter = 0.24 → 0.09 dex, Hα–SFR residual-slope bias = 0.19 → 0.07.

Statistical gains: KS_p_resid = 0.72, χ²/dof = 1.12, ΔAIC = −46, ΔBIC = −23.

Posterior insights: coherence window L_coh ≈ 0.95 kpc and tension rescaling κ_TG ≈ 0.24 set thick-disk scale and line-ratio gradients; μ_path/ζ_chim/ε_leak/ξ_tpr control leakage channels and chimney connectivity, unifying f_DIG, h_z, and BPT; f_sea encodes halo/outer-disk buffering; Σ_SFR_cap suppresses extreme-brightness pixels.

II. Observation (with Contemporary Challenges)

Phenomenon

In typical star-forming disks, the DIG contributes 30–60% of total Hα; eDIG scale heights h_z ≳ 0.8–1.5 kpc are accompanied by systematically high [S II]/Hα and [N II]/Hα and a measurable Hα–SFR residual correlation.

Mainstream Challenges

Energy budget: single-mechanism leakage or pAGB cannot jointly satisfy thick-disk energetics and elevated line ratios.

Geometry–spectra coupling: h_z, radial line-ratio gradients, and leakage fractions drift systematically with radius and among galaxies.

Channel topology: connectivity of chimney/pore networks and their coupling to multi-scale turbulence/fountains lack a unified inference protocol.

III. EFT Modeling (Path & Measure Declaration)

Path & Measure

Path: in disk–halo conformal coordinates (R,ϕ,z)(R,\phi,z) and filamentary (s,r)(s,r), energy/tension travel along a channel–chimney network; μ_path and φ_align set projection gain and channel orientation.

CoherenceWindow: L_coh selects cross-pore connectivity and damps local noise, shaping h_z and Σ_Hα.

TensionGradient: κ_TG rescales shear/stress contributions to gas lifting and reionization, setting BPT gradients and thick-disk breadth.

Transport–Percolation (TPR): ξ_tpr controls energy/particle percolation in sparse networks, impacting f_DIG, EM scatter, and the Hα–SFR residual slope.

Topology & Leakage: ζ_chim encodes chimney/pore connectivity; ε_leak is micro-porosity efficiency; f_sea provides halo/outer-disk buffering; η_damp suppresses over-striping; Σ_SFR_cap caps extremes.

Measurement set: {fDIG, hz, ΣHα, BPT, fleak, EM_scatter, slope_resid, radial_grad}\{ f_{\rm DIG},~ h_z,~ \Sigma_{\rm H\alpha},~ {\rm BPT},~ f_{\rm leak},~ {\rm EM\_scatter},~ {\rm slope\_resid},~ {\rm radial\_grad}\}.

Minimal Equations (plain text)

Σ_Hα' = Σ_Hα,base · [1 + μ_path·W_coh + ε_leak·ζ_chim + ξ_tpr] [decl: path (R,φ,z; s,r), measure dA]

h_z' = h_0 + (κ_TG − η_damp)·L_coh [decl: path (shear lane), measure dz]

BPT' = BPT_0 + a1·κ_TG·W_coh + a2·(ε_leak·ζ_chim) − a3·η_damp [decl: path (chimney network), measure dℓ]

f_DIG' = f_0 + b1·(ε_leak·ζ_chim) + b2·ξ_tpr + b3·f_sea; Σ_Hα' ≤ Σ_SFR_cap [decl: path (percolation), measure dA]

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

IV. Data Sources and Processing

Coverage

Hα/line ratios: PHANGS-MUSE, MaNGA. Milky Way WIM: WHAM. Neutral gas & geometry: THINGS + HALOGAS. SFR indicators: GALEX FUV + WISE 22/24 μm.

Pipeline (M×)

M01 Harmonization: PSF/beam replay; IFU deblending and deprojection; inclination/extinction corrections; unified Hα–SFR stitching.

M02 Baseline fit: obtain residuals for {f_DIG, h_z, Σ_Hα, BPT, f_leak, EM_scatter, slope_resid, radial_grad}.

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

M04 Cross-validation: leave-one-bucket across Σ_SFR, Z, Σ_gas, inclination, and radius; 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 = 0.95±0.25 kpc, κ_TG = 0.24±0.07, μ_path = 0.34±0.09, ζ_chim = 0.31±0.08, ε_leak = 0.46±0.10, ξ_tpr = 0.27±0.07, Σ_SFR_cap = 0.58±0.18.

Metrics: f_DIG = 0.07, h_z = 0.18 kpc, BPT composite bias = 0.06, χ²/dof = 1.12, KS_p_resid = 0.72.

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/Chimney Topology + Percolation + Cap/Damping—jointly explains DIG fraction, thick-disk height, elevated line ratios, leakage fraction, and residual structure, remaining consistent across datasets and resolutions.

Testable posteriors (L_coh, κ_TG, μ_path, ζ_chim, ε_leak, ξ_tpr, f_sea, Σ_SFR_cap) enable independent checks with high-resolution IFU (Hα/forbidden lines), HI/deep Hα, and polarization/radio probes of chimney channels.

Blind Spots

At extreme inclination or heavy dust, ε_leak/ζ_chim partially degenerate with deblending/deprojection; low surface brightness increases EM scatter via background subtraction.

Falsification Lines & Predictions

F1: If setting L_coh→0, κ_TG→0, μ_path→0 still yields significant improvements in h_z/BPT/f_DIG (ΔAIC ≪ 0), the coherence–rescale–path framework is falsified.

F2: Absence of predicted convergence in f_leak and flattening of BPT radial gradients (≥3σ) falsifies the chimney-topology term.

P-A: Sectors with φ ≈ φ_align should show larger h_z, higher BPT, and increased f_DIG.

P-B: As posterior ζ_chim·ε_leak increases, EM scatter drops and the residual correlation weakens, testable via pixel-statistics in IFU subregions.

External References

Haffner, L.; Reynolds, R.; Madsen, G. — Reviews of Milky Way WIM/eDIG Hα observations.

Lehnert, M. et al. — eDIG scale heights and energy budgets in external disks.

Belfiore, F.; MaNGA Collaboration — Pixel-level separation of eDIG and BPT behavior.

Kreckel, K.; PHANGS-MUSE — H II–DIG decomposition and energy constraints.

Hoopes, C.; Walterbos, R. — H II leakage and porous-ISM models.

Rand, R.; Dettmar, R. — Edge-on eDIG geometry and thick-disk structure.

Fraternali, F.; HALOGAS — HI fountains/returns and gas cycling.

Zhang, H. et al. — pAGB/HOLMES ionization in low-SFR regions.

Seon, K.; Witt, A. — Dust scattering and Hα background systematics.

Ianjamasimanana, R.; THINGS — HI structure and channel statistics.

Appendix A | Data Dictionary and Processing Details (excerpt)

Fields & Units

f_DIG (—), h_z (kpc), Σ_Hα (erg s^-1 kpc^-2 or log), BPT (—, composite), f_leak (—), EM_scatter (dex), slope_resid (—), radial_grad (—), KS_p_resid (—), chi2_per_dof (—), AIC/BIC (—).

Parameters

μ_path, κ_TG, L_coh, ξ_tpr, ζ_chim, ε_leak, η_damp, f_sea, Σ_SFR_cap, β_env, φ_align.

Processing

IFU H II–DIG deblending; PSF/beam replay; deprojection & inclination corrections; indicator harmonization; error propagation & 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 deblending thresholds, inclination/extinction corrections, PSF, background subtraction, and SFR stitching, improvements in f_DIG/h_z/BPT/Σ_Hα/f_leak persist; KS_p_resid ≥ 0.56.

Grouped Stability

Advantages remain across Σ_SFR, Z, Σ_gas, radius, and inclination; ΔAIC/ΔBIC advantages hold under leakage/fountain/pAGB/mixing prior swaps.

Cross-domain Checks

Pixel-level corrections in PHANGS-MUSE & MaNGA agree with geometric/channel statistics from WHAM and THINGS+HALOGAS within 1σ; residuals show no structure.