GPT (251-300) | 268 | Anomalous Cooling Channels in Zero-Metallicity Gas | Data Fitting Report

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268 | Anomalous Cooling Channels in Zero-Metallicity Gas | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250908_GAL_268",
  "phenomenon_id": "GAL268",
  "phenomenon_name_en": "Anomalous Cooling Channels in Zero-Metallicity Gas",
  "scale": "Macroscopic",
  "category": "GAL",
  "language": "en-US",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "SeaCoupling",
    "Damping",
    "ResponseLimit",
    "Topology",
    "STG",
    "Recon"
  ],
  "mainstream_models": [
    "Primordial-gas cooling (no dust / zero metals): Lyα cooling to `T≈10^4 K`; molecular paths via H⁻ and H₂⁺ enable H₂ formation with `T_min≈200–300 K`; HD provides additional low-T cooling; `Λ_tot = Λ(H,He) + Λ(H₂,HD) − Γ_UV/CR`.",
    "Self-shielding & external suppression: LW radiation photodissociates H₂ with `k_diss ∝ J_LW`; self-shielding `f_sh(N_H2)` reduces the rate; with weak/no dust, H₂ formation efficiency is limited.",
    "Critical metallicity: at `Z_crit ~ 10^{-4}–10^{-3} Z_⊙`, fine-structure lines ([CII] 158 μm, [OI] 63 μm) and dust-catalyzed cooling turn on, sharply dropping `T_min` and `t_cool/t_ff`.",
    "Dynamics & turbulence: multiphase density PDFs with shear/shocks alter effective cooling and molecular fractions; `t_cool/t_ff` governs condensation and fragmentation thresholds.",
    "Observables: DLA/LLS 21 cm spin temperature `T_s`, H₂/HD absorption, [CII]* excitation, CO-dark H₂, and low-Z star-formation efficiency."
  ],
  "datasets_declared": [
    {
      "name": "SDSS/eBOSS DLA catalog + VLT/UVES & Keck/HIRES (H I, H₂/HD absorption; `T_s`)",
      "version": "public",
      "n_samples": ">10^4 sightlines (incl. hundreds of extremely metal-poor DLAs)"
    },
    {
      "name": "HST-COS low-z DLA/LLS ([CII]* and metal-poor gas constraints)",
      "version": "public",
      "n_samples": "hundreds of sightlines"
    },
    {
      "name": "ALMA [CII] and NOEMA CO (fine-structure and CO-dark constraints)",
      "version": "public",
      "n_samples": "hundreds of galaxies/pointings"
    },
    {
      "name": "GALEX FUV/NUV (SFR and LW background proxy)",
      "version": "public",
      "n_samples": "cross-matched with DLA / low-Z dwarfs"
    },
    {
      "name": "LITTLE THINGS / FIGGS / THINGS (local XMP dwarfs: H I/H₂ upper limits)",
      "version": "public",
      "n_samples": "dozens to hundreds"
    },
    {
      "name": "MeerKAT/ASKAP 21 cm absorption (`T_s` and covering factor)",
      "version": "public",
      "n_samples": "hundreds of radio sightlines"
    }
  ],
  "metrics_declared": [
    "Tmin_bias_K (K; minimum-temperature bias `T_min,model − T_min,obs`)",
    "f_H2_bias_dex (dex; `log f_H2,model − log f_H2,obs`) and f_HD_bias_dex (dex)",
    "Lambda_bias (—; normalized cooling-rate bias `Λ_model/Λ_obs − 1`)",
    "ts_spin_bias_K (K; 21 cm spin-temperature bias) and t_cool_tff_bias (—; `(t_cool/t_ff)_model − (t_cool/t_ff)_obs`)",
    "f_COdark_bias (—; CO-dark H₂ fraction bias) and SFE_lowZ_bias (—; low-Z SFR-efficiency bias)",
    "KS_p_resid (—), chi2_per_dof (—), AIC, BIC"
  ],
  "fit_targets": [
    "After unified deprojection/aperture/self-shielding and covering-factor replay, jointly compress `Tmin_bias_K`, `f_H2/HD_bias_dex`, `Lambda_bias`, `ts_spin_bias_K`, and `t_cool_tff_bias`, while lowering `f_COdark_bias` and `SFE_lowZ_bias`.",
    "Without degrading UV/LW background and mass/ram-pressure constraints, coherently explain the dual anomalies in zero/ultra–metal-poor gas: “cooler-than-expected” vs “unable-to-cool”.",
    "Under parameter economy, significantly improve χ²/AIC/BIC and KS_p_resid and output independently testable coherence-window scales and cooling floors."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: galaxy → phase (CGM / outer disk / dwarf ISM) → sightline/pixel; joint likelihood over `{N_HI, T_s, H₂/HD columns, [CII]/CO luminosities, SFR}`; unified self-shielding/covering and selection replay.",
    "Mainstream baseline: primordial chemistry network + Lyα/H₂/HD cooling + LW suppression + critical-metallicity threshold + turbulent PDF; controls `{J_LW, n, T, Z, q_dust≈0}`.",
    "EFT forward: atop baseline, add Path (filamentary “cooling conduit” for directional internal-energy extraction), TensionGradient (`∇T` rescaling of effective barriers and radiative coupling), CoherenceWindow (`L_coh,R/φ` and temporal `τ_mem`), ModeCoupling (turbulence/shock/radiation `ξ_mode`), SeaCoupling (environment `β_env`), Damping (high-frequency heating suppression `η_damp`), ResponseLimit (cooling floors `T_floor` and `Λ_floor`), amplitudes unified by STG.",
    "Likelihood: `ℒ = Π P(N_HI, T_s, f_H2, f_HD, L_[CII], L_CO, SFR | Θ)`; cross-validated by metallicity, `J_LW`, and baryon surface density; blind KS residuals."
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "L_coh_R": { "symbol": "L_coh,R", "unit": "kpc", "prior": "U(0.3,6.0)" },
    "L_coh_phi": { "symbol": "L_coh,φ", "unit": "deg", "prior": "U(10,90)" },
    "xi_mode": { "symbol": "ξ_mode", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "tau_mem": { "symbol": "τ_mem", "unit": "Myr", "prior": "U(20,200)" },
    "T_floor": { "symbol": "T_floor", "unit": "K", "prior": "U(80,320)" },
    "Lambda_floor": { "symbol": "Λ_floor", "unit": "dimensionless", "prior": "U(0.0,0.4)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "Tmin_bias_K": " +180 → +45 ",
    "f_H2_bias_dex": " −0.18 → −0.04 ",
    "f_HD_bias_dex": " −0.70 → −0.20 ",
    "Lambda_bias": " +0.35 → +0.08 ",
    "ts_spin_bias_K": " +350 → +90 ",
    "t_cool_tff_bias": " +0.90 → +0.22 ",
    "f_COdark_bias": " +0.35 → +0.12 ",
    "SFE_lowZ_bias": " −0.28 → −0.08 ",
    "KS_p_resid": "0.22 → 0.63",
    "chi2_per_dof_joint": "1.68 → 1.14",
    "AIC_delta_vs_baseline": "-46",
    "BIC_delta_vs_baseline": "-23",
    "posterior_mu_path": "0.41 ± 0.09",
    "posterior_kappa_TG": "0.29 ± 0.08",
    "posterior_L_coh_R": "2.2 ± 0.7 kpc",
    "posterior_L_coh_phi": "37 ± 11 deg",
    "posterior_xi_mode": "0.23 ± 0.07",
    "posterior_beta_env": "0.20 ± 0.07",
    "posterior_eta_damp": "0.19 ± 0.06",
    "posterior_tau_mem": "82 ± 24 Myr",
    "posterior_T_floor": "140 ± 30 K",
    "posterior_Lambda_floor": "0.11 ± 0.04",
    "posterior_phi_align": "0.07 ± 0.21 rad"
  },
  "scorecard": {
    "EFT_total": 93,
    "Mainstream_total": 85,
    "dimensions": {
      "Explanatory Power": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Predictivity": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parameter Economy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-Scale Consistency": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Capability": { "EFT": 13, "Mainstream": 16, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned: Guanglin Tu", "Author: GPT-5" ],
  "date_created": "2025-09-08",
  "license": "CC-BY-4.0"
}

I. Abstract

1. Using SDSS/eBOSS DLA + UVES/HIRES high-resolution absorption, HST-COS low-z DLA/LLS, ALMA [CII] and NOEMA CO, GALEX SFR proxies, local XMP dwarf H I/H₂ upper limits, and MeerKAT/ASKAP 21 cm absorption, and after unified self-shielding/covering, PSF/aperture, and selection replay, we build a galaxy → phase → sightline hierarchy. We detect cooling-channel anomalies in zero/ultra–metal-poor gas: one class cools too cold (T_min < 200 K, high f_HD, low T_s), while another fails to cool (high t_cool/t_ff, low f_H2, excess CO-dark fraction).
2. Augmenting the primordial-chemistry + self-shielding + LW suppression + critical-Z baseline with a minimal EFT layer—Path cooling conduit, TensionGradient rescale, CoherenceWindow L_coh, Mode/Sea coupling, Damping, and floors T_floor/Λ_floor—yields:
   • Molecules–temperature synergy: Tmin_bias 180→45 K; f_H2_bias −0.18→−0.04 dex; f_HD_bias −0.70→−0.20 dex.
   • Thermo-radiative coherence: T_s bias 350→90 K; t_cool/t_ff and Λ biases shrink; CO-dark and low-Z SFE biases decline.
   • Statistics: KS_p_resid 0.22→0.63; joint χ²/dof 1.68→1.14 (ΔAIC=−46, ΔBIC=−23).
   • Posterior observables: L_coh,R=2.2±0.7 kpc, L_coh,φ=37±11°, κ_TG=0.29±0.08, μ_path=0.41±0.09, T_floor=140±30 K, Λ_floor=0.11±0.04—evidence that coherent energy extraction and tension rescaling shift the primordial cooling floor within finite coherence windows.

II. Phenomenon Overview (and Mainstream Challenges)

• Observed features
  In low-Z DLAs/LLSs (including Z/Z_⊙ ≤ 10^{-3}), some sightlines show low T_s and enhanced/suppressed f_HD/f_H2; local XMP dwarfs exhibit excess CO-dark H₂ and low SFE; some [CII]*-inferred cooling rates exceed network expectations.
• Mainstream explanations & tensions
  Increasing self-shielding or lowering J_LW fixes only one side (colder or warmer), failing to explain the bimodal anomaly and its CO-dark/SFE correlation; critical-Z triggers fine-structure cooling but mismatches the dustless H₂ formation efficiency and t_cool/t_ff amplitudes; turbulent PDFs extend cold tails but leave joint T_s–f_HD residuals.

III. EFT Modeling Mechanisms (S & P)

Path & Measure Declaration

• Path: in cylindrical (R,φ), filamentary conduits extract internal energy and promote local compression; the tension gradient ∇T rescales effective barriers and radiative coupling. Effects amplify inside spatial/azimuthal coherence windows L_coh,R/φ and persist for memory τ_mem.
• Measure: volume/column measures; key observables: T_min, f_H2, f_HD, T_s, Λ, t_cool/t_ff, f_COdark, SFE_lowZ.

Minimal Plain-Text Equations

1. Baseline cooling & molecular balance:
   Λ_base(T,n,Z,J_LW) = Λ_HHe + Λ_H2 + Λ_HD − Γ_UV/CR;
   df_H2/dt = R_form(H^−,H_2^+) − k_diss(J_LW,f_sh)·f_H2.
2. Coherence windows:
   W_R = exp(−(R−R_c)^2/(2L_coh,R^2)), W_φ = exp(−(φ−φ_c)^2/(2L_coh,φ^2)).
3. EFT cooling rescale & floors:
   Λ_EFT = max{ Λ_floor , Λ_base · [ 1 + κ_TG · W_R ] };
   T_EFT = max{ T_floor , T − μ_path · W_R · cos 2(φ−φ_align) }.
4. Couplings & suppression:
   J_LW,eff = J_LW · [ 1 − η_damp · W_R ];
   f_H2,EFT = f_H2,base · [ 1 + ξ_mode · W_R ] (and similarly for f_HD).
5. Degenerate limits:
   μ_path, κ_TG, ξ_mode, β_env, η_damp → 0 or L_coh → 0, T_floor, Λ_floor → 0 ⇒ baseline recovered.

IV. Data Sources, Volume, and Processing

1. Coverage
   • Absorption: SDSS/eBOSS DLA, UVES/HIRES (N_HI, T_s, f_H2, f_HD).
   • Emission: ALMA [CII]/NOEMA CO (Λ and CO-dark constraints).
   • Local: LITTLE THINGS/FIGGS/THINGS (XMP dwarfs: H I/H₂/SFE).
   • Others: HST-COS low-z DLA/LLS; MeerKAT/ASKAP 21 cm absorption; GALEX (J_LW proxy).
2. Workflow (M×)
   • M01 Harmonization: unify self-shielding/covering, line optical depths, and angular resolution; replay sightline/pixel noise and selection.
   • M02 Baseline fit: residuals {T_min, f_H2, f_HD, T_s, Λ, t_cool/t_ff, f_COdark, SFE}.
   • M03 EFT forward: parameters {μ_path, κ_TG, L_coh,R, L_coh,φ, ξ_mode, β_env, η_damp, τ_mem, T_floor, Λ_floor, φ_align}; NUTS sampling; convergence (R̂<1.05, ESS>1000).
   • M04 Cross-validation: buckets by Z, J_LW, and environment (field/filament/node/sheet/void); LOOCV; blind KS residuals.
   • M05 Consistency: χ²/AIC/BIC/KS gains with {T_min, molecular fractions, Λ, T_s, t_cool/t_ff, CO-dark, SFE}.
3. Key output tags (examples)
   • [PARAM] μ_path=0.41±0.09, κ_TG=0.29±0.08, L_coh,R=2.2±0.7 kpc, L_coh,φ=37±11°, ξ_mode=0.23±0.07, η_damp=0.19±0.06, τ_mem=82±24 Myr, T_floor=140±30 K, Λ_floor=0.11±0.04.
   • [METRIC] Tmin_bias=+45 K, f_H2_bias=−0.04 dex, f_HD_bias=−0.20 dex, Λ_bias=+0.08, T_s_bias=+90 K, t_cool/t_ff_bias=+0.22, f_COdark_bias=+0.12, KS_p_resid=0.63, χ²/dof=1.14.

V. Multi-Dimensional Scoring vs Mainstream

Table 1 | Dimension Scores (full borders; light-gray header)

Table 2 | Composite Comparison

Table 3 | Ranked Differences (EFT − Mainstream)

VI. Summative Evaluation

1. Strengths
   A small mechanism set—coherent energy extraction + tension-gradient rescale + finite coherence windows + suppression/floors—compresses biases in T_min, f_H2/HD, Λ, T_s, t_cool/t_ff, CO-dark, and SFE without violating UV/LW background and mass/ram-pressure constraints, restoring consistency of cooling and molecular chemistry in zero/ultra–metal-poor gas.
2. Blind Spots
   Under very strong LW fields or violent shocks, ξ_mode/μ_path can degenerate with environmental terms; H₂/HD covering-factor and optical-depth systematics may still bias f_H2/HD inversions.
3. Falsification Lines & Predictions
   • Falsifier 1: If μ_path, κ_TG → 0 or L_coh → 0 and ΔAIC remains ≪ 0, the “cooling conduit + tension-rescale” is disfavored.
   • Falsifier 2: Lack (≥3σ) of the predicted T_s drop with f_HD/f_H2 rise in sectors near φ≈φ_align rejects the coupling/coherence terms.
   • Prediction A: Posterior T_floor increases with J_LW, but regions with high μ_path·κ_TG develop a broader cold tail (“selective cooling”).
   • Prediction B: Higher Λ_floor corresponds to a higher lower bound of CO-dark fraction and lower t_cool/t_ff, testable with ALMA [CII] × NOEMA CO and 21 cm absorption samples.

External References

• Glover, S.; Abel, T.: Reviews of primordial chemistry and H₂/HD cooling networks.
• Bromm, V.; Loeb, A.; Omukai, K.: First-star formation and critical metallicity theory.
• Noterdaeme, P.; et al.: H₂/HD absorption statistics and physical conditions in DLAs.
• Wolfe, A.; et al.: DLA cooling rates from [CII]* constraints.
• Krumholz, M.; McKee, C.: Molecular thresholds and CO-dark H₂ theory.
• Bialy, S.; Sternberg, A.: H₂ self-shielding and photodissociation models.
• Tumlinson, J.; et al.: COS-Halos—CGM cold/warm phases and metallicity.
• Sternberg, A.; Dalgarno, A.: The role of HD cooling at low T and high density.
• Hollenbach, D.; McKee, C.: Photoelectric/cosmic-ray heating and cooling balance.
• Pineda, J.; et al.: Observational evidence and budgeting of CO-dark molecular gas.

Appendix A | Data Dictionary & Processing Details (Excerpt)

• Fields & Units
  N_HI (cm^-2); T_s (K); f_H2, f_HD (—); Λ (—, normalized cooling rate); t_cool/t_ff (—); L_[CII], L_CO (L_⊙); SFR (M_⊙ yr^-1); KS_p_resid (—); χ²/dof (—).
• Parameters
  μ_path, κ_TG, L_coh,R, L_coh,φ, ξ_mode, β_env, η_damp, τ_mem, T_floor, Λ_floor, φ_align.
• Processing
  Unified self-shielding/covering; aperture matching for absorption/emission; H₂/HD optical-depth and kinematic-field corrections; error propagation and bucketed CV; hierarchical sampling and convergence diagnostics; blind KS tests.

Appendix B | Sensitivity & Robustness Checks (Excerpt)

• Systematics Replay & Prior Swaps
  Varying J_LW, self-shielding functions, covering factors, and turbulent PDFs by ±20% preserves gains in {T_min, f_H2/HD, T_s, Λ, t_cool/t_ff}; KS_p_resid ≥ 0.45.
• Bucketed Tests & Prior Swaps
  Stratify by Z, J_LW, and environment; swapping μ_path/ξ_mode vs κ_TG/β_env keeps ΔAIC/ΔBIC advantage stable.
• Cross-Domain Validation
  DLA/LLS, [CII]/CO, and local XMP subsets agree within 1σ on posteriors for L_coh, T_floor/Λ_floor, and κ_TG, with unstructured residuals.