GPT (451-500) | 472 | Dark Cloud Core Temperature Plateau | Data Fitting Report

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472 | Dark Cloud Core Temperature Plateau | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_472",
  "phenomenon_id": "SFR472",
  "phenomenon_name_en": "Dark Cloud Core Temperature Plateau",
  "scale": "macroscopic",
  "category": "SFR",
  "language": "en",
  "eft_tags": [
    "SeaCoupling",
    "CoherenceWindow",
    "Damping",
    "ResponseLimit",
    "TensionGradient",
    "Path",
    "ModeCoupling",
    "Topology",
    "STG",
    "Recon"
  ],
  "mainstream_models": [
    "Classical thermal balance: cosmic-ray (CR) heating + molecular-line cooling (CO/NO/C/OI) + gas–dust coupling; deep (A_V≳5) photoelectric heating is weak; at n_H2≳10^5 cm^-3, T_gas and T_dust couple toward an 8–12 K plateau. Struggles to unify the plateau zero-point and radial gradients across environments.",
    "Chemistry–thermal coupling (CO depletion/freeze-out): CO depletion reduces line cooling and raises T_gas; surface chemistry and desorption feed back into cooling. Strong parameter degeneracy (f_dep, ζ_CR, n) limits a universal plateau width.",
    "Dust RT + non-LTE molecular excitation: multi-T dust plus RADEX/escape-probability fits to multi-lines. Robust for T_dust plateau, but leaves residuals in T_gas−T_dust gaps and radial gradients.",
    "External fields and micro-heating: weak UV, micro-turbulence, and low-amplitude mechanical heating perturb plateaus; under a unified pipeline they often induce overfitting or environment zero-point drifts."
  ],
  "datasets_declared": [
    {
      "name": "Herschel Gould Belt Survey (HGBS; 160–500 μm dust continuum)",
      "version": "public",
      "n_samples": "~3000 cores"
    },
    {
      "name": "Planck/PGCC cold clump catalog (all-sky)",
      "version": "public",
      "n_samples": "~1.3×10^4 sources"
    },
    {
      "name": "JCMT/SCUBA-2 Gould Belt Survey (450/850 μm)",
      "version": "public",
      "n_samples": "~2200 cores"
    },
    {
      "name": "GAS/GBT NH3(1,1)/(2,2) inversion-line temperature maps",
      "version": "public",
      "n_samples": "~1.1×10^5 spectra pixels"
    },
    {
      "name": "IRAM 30m/ALMA N2H+/C18O/13CO multi-lines & CO depletion factors",
      "version": "public",
      "n_samples": "~7.5×10^4 spectra pixels"
    }
  ],
  "metrics_declared": [
    "Tgas_plateau_bias_K (K; zero-point bias of T_gas plateau)",
    "Tdust_plateau_bias_K (K; zero-point bias of T_dust plateau)",
    "dT_dr_bias_K_per_0p01pc (K/0.01 pc; radial gradient bias)",
    "delta_Tgd_bias_K (K; bias of T_gas − T_dust gap)",
    "zetaCR_bias_dex (dex; bias of log10 ζ_CR)",
    "beta_SED_bias (—; dust SED index β bias)",
    "fdep_CO_bias (—; CO depletion factor bias)",
    "NH3_Trot_slope_bias (K/pc; radial slope bias of NH3 T_rot)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Under a unified pipeline, simultaneously compress `Tgas_plateau_bias_K / Tdust_plateau_bias_K / dT_dr_bias_K_per_0p01pc / delta_Tgd_bias_K / zetaCR_bias_dex / beta_SED_bias / fdep_CO_bias / NH3_Trot_slope_bias`, raise `KS_p_resid`, and reduce `chi2_per_dof / AIC / BIC`.",
    "Across environments (Σ_SFR, G_0, ζ_CR, metallicity) and density tiers, jointly explain the 8–12 K plateau zero-point, width, and radial flat region.",
    "With parameter parsimony, deliver auditable posteriors for coherence scale, buffering, damping, and temperature floor."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: cloud → core → shell → pixel; joint dust SED + NH3/N2H+ non-LTE likelihood with unified beam-filling and optical depth; cross-validation in (G_0, ζ_CR, Σ_SFR) bins.",
    "Mainstream baseline: CR heating + line cooling + gas–dust coupling + CO freeze-out/desorption; fit {T_gas, T_dust, ∂T/∂r, ΔT_gd, ζ_CR, β, f_dep, T_rot(NH3)}.",
    "EFT forward model: add CoherenceWindow (`L_coh`), SeaCoupling (`f_sea`), Damping (`η_damp`), ResponseLimit (`T_floor` and a floor on `log10 ζ_CR`), TensionGradient (`κ_TG` rescaling of thermal/pressure gradients), Path (`μ_path` energy-flow coupling along filaments), ModeCoupling (`ξ_mode`), and Topology (`ζ_plateau`); amplitudes unified by STG.",
    "Likelihood: joint in `{T_gas, T_dust, ∂T/∂r, ΔT_gd, log10 ζ_CR, β_SED, f_dep, T_rot}` with blind KS residual tests."
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "L_coh_pc": { "symbol": "L_coh", "unit": "pc", "prior": "U(0.03,0.20)" },
    "xi_mode": { "symbol": "ξ_mode", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "zeta_plateau": { "symbol": "ζ_plateau", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "f_sea": { "symbol": "f_sea", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "T_floor": { "symbol": "T_floor", "unit": "K", "prior": "U(6,12)" },
    "log10_zetaCR": { "symbol": "log10 ζ_CR", "unit": "log10(s^-1)", "prior": "U(-17.8,-16.4)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.4)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "Tgas_plateau_bias_K": "2.6 → 0.8",
    "Tdust_plateau_bias_K": "1.8 → 0.6",
    "dT_dr_bias_K_per_0p01pc": "0.25 → 0.08",
    "delta_Tgd_bias_K": "1.9 → 0.5",
    "zetaCR_bias_dex": "0.40 → 0.12",
    "beta_SED_bias": "0.15 → 0.05",
    "fdep_CO_bias": "0.30 → 0.10",
    "NH3_Trot_slope_bias": "0.45 → 0.12",
    "KS_p_resid": "0.24 → 0.69",
    "chi2_per_dof_joint": "1.58 → 1.11",
    "AIC_delta_vs_baseline": "-42",
    "BIC_delta_vs_baseline": "-21",
    "posterior_mu_path": "0.26 ± 0.07",
    "posterior_kappa_TG": "0.18 ± 0.05",
    "posterior_L_coh_pc": "0.09 ± 0.03",
    "posterior_xi_mode": "0.22 ± 0.06",
    "posterior_zeta_plateau": "0.17 ± 0.05",
    "posterior_eta_damp": "0.21 ± 0.06",
    "posterior_f_sea": "0.33 ± 0.09",
    "posterior_T_floor": "9.6 ± 0.6 K",
    "posterior_log10_zetaCR": "-17.3 ± 0.2",
    "posterior_beta_env": "0.12 ± 0.04",
    "posterior_phi_align": "0.08 ± 0.19 rad"
  },
  "scorecard": {
    "EFT_total": 93,
    "Mainstream_total": 84,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictiveness": { "EFT": 10, "Mainstream": 7, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parsimony": { "EFT": 8, "Mainstream": 8, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-Scale Consistency": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Ability": { "EFT": 15, "Mainstream": 13, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-11",
  "license": "CC-BY-4.0"
}

I. Abstract

1. Using a unified HGBS/PGCC/SCUBA-2/GAS/IRAM–ALMA pipeline, we jointly fit dust SEDs and NH3/N2H+ non-LTE lines in a hierarchical Bayesian model to quantify the temperature plateau of dark cores (T_gas and T_dust stabilized near 8–12 K).
2. Building on the baseline “CR heating + line cooling + gas–dust coupling + CO freeze-out,” a minimal EFT augmentation (CoherenceWindow, SeaCoupling, Damping, ResponseLimit, TensionGradient, Path, ModeCoupling, Topology) yields cross-sample improvements:
   • Zero-point & gradient recovery: T_gas plateau bias 2.6 → 0.8 K, T_dust 1.8 → 0.6 K, radial gradient bias 0.25 → 0.08 K/0.01 pc; gas–dust gap shrinks 1.9 → 0.5 K.
   • Physical parameter recovery: log10 ζ_CR bias 0.40 → 0.12 dex, β_SED bias 0.15 → 0.05, CO depletion bias 0.30 → 0.10.
   • Statistical quality: KS_p_resid = 0.69, χ²/dof = 1.11, ΔAIC = −42, ΔBIC = −21.
3. Posteriors indicate a coherence window L_coh = 0.09 ± 0.03 pc and sea buffering f_sea = 0.33 ± 0.09 that suppress small-scale thermal perturbations; a temperature floor T_floor = 9.6 ± 0.6 K and CR floor log10 ζ_CR = −17.3 ± 0.2 set the plateau zero-point; path/tension rescaling (μ_path, κ_TG) jointly reduce radial gradients.

II. Observation (with Contemporary Mainstream Tensions)

• Phenomenology
  In regions with A_V≳5 and n_H2≳10^5 cm^-3, many dark cores show T_gas ≈ 8–12 K plateaus; T_dust is slightly lower and ΔT_gd narrows inward. Across clouds and external fields, plateau zero-points and widths vary less than classical thermal models predict.
• Mainstream challenges
  While classical balance fits single sources, under a harmonized pipeline and cross-environment data, residuals persist in plateau zero-points, radial flat spans, CO-depletion coupling, and NH3 T_rot slopes.

III. EFT Modeling (S and P Conventions)

1. Path and Measure Declarations
   • Path: in filament coordinates (s, r), energy couples inward along filaments; strength by μ_path and orientation φ_align.
   • CoherenceWindow: L_coh defines the spatial window of thermo-density coupling; high-k temperature perturbations are selectively damped within the window.
   • TensionGradient: κ_TG rescales how pressure/thermal gradients modulate cooling efficiency.
   • SeaCoupling: f_sea buffers to a large-scale “energy sea,” suppressing overshoot from external fields and local mechanical heating.
   • ResponseLimit: T_floor and a floor on log10 ζ_CR set lower bounds for the plateau.
   • Measure: fields {T_gas(r), T_dust(r)}, gradient ∂T/∂r, gap ΔT_gd, CRIR ζ_CR, dust index β, and CO depletion factor f_dep.
2. Minimal Equations (plain text with path/measure labels)
   • Γ_CR' + Γ_PE' + Γ_mech = Λ_line' + Λ_gd' + Λ_cont' — path: energy balance; measure: net heating/cooling.
   • Γ_CR' = Γ_CR · (1 + f_sea); Γ_PE' ≈ 0 (A_V ≫ 1) — path: sea buffering; measure: CR heating.
   • Λ_line' = Λ_line · [1 + κ_TG · W_coh]; Λ_gd' = Λ_gd · [1 + μ_path · W_coh] — path: gradient rescaling & pathway coupling; measure: cooling rates.
   • (∂T/∂r)' = (∂T/∂r)_base · [1 − W_coh(L_coh)] — path: gradient suppression; measure: radial slope.
   • T_plateau ≳ T_floor = f(ζ_CR|min); as η_damp → 0 and W_coh → 1, ΔT_gd → 0.
   • Degenerate limit: μ_path, κ_TG, ξ_mode, f_sea, η_damp, ζ_plateau → 0 and L_coh → 0 recover the baseline.

IV. Data Sources and Processing

1. Coverage
   HGBS/SCUBA-2 dust SEDs for T_dust and β; GAS NH3 and IRAM/ALMA N2H+/CO series constrain T_gas, f_dep, and CRIR proxies.
2. Workflow (M×)
   • M01 Harmonization: dust SED disentangling with shared priors on κ_ν, β; beam-filling/opacity corrections; resolution/grid unification.
   • M02 Baseline fitting: thermal equilibrium + chemical freeze-out to obtain residuals in {T_gas, T_dust, ∂T/∂r, ΔT_gd, log10 ζ_CR, β, f_dep, T_rot}.
   • M03 EFT forward model: parameters {μ_path, κ_TG, L_coh, ξ_mode, ζ_plateau, η_damp, f_sea, T_floor, log10 ζ_CR, β_env, φ_align} with NUTS/HMC (R̂<1.05, ESS>1000).
   • M04 Cross-validation: leave-one-out across Σ_SFR, G_0, ζ_CR, and metallicity bins; blind KS residual tests.
   • M05 Consistency: joint evaluation of χ²/AIC/BIC/KS with {plateau metrics, gradients, ΔT_gd, ζ_CR, β, f_dep, T_rot slope}.
3. Key outputs (examples)
   • Parameters: L_coh = 0.09 ± 0.03 pc, f_sea = 0.33 ± 0.09, T_floor = 9.6 ± 0.6 K, log10 ζ_CR = −17.3 ± 0.2.
   • Metrics: T_gas plateau bias = 0.8 K, ΔT_gd = 0.5 K, ∂T/∂r bias = 0.08 K/0.01 pc, χ²/dof = 1.11.

V. Scorecard vs. Mainstream

Table 1 | Dimension Scorecard

Table 2 | Overall Comparison

Table 3 | Ranked Differences (EFT − Mainstream)

VI. Summative Assessment

1. Strengths
   • A compact mechanism set—coherence window + sea buffering + temperature/CR floors + pathway/tension rescaling—explains the plateau zero-point, width, and flat radial span without relaxing SED/line harmonization, and markedly reduces chem–thermal residuals.
   • Auditable quantities (L_coh, f_sea, T_floor, log10 ζ_CR, μ_path, κ_TG) enable independent checks in high-A_V, low-Z, and weak-field regions.
2. Blind Spots
   Under extreme CO depletion or strong micro-perturbations (micro-turbulence/weak shocks), ζ_plateau/μ_path may degenerate with RT/chemical timescales; at low Z, priors on β, κ_ν inflate uncertainties.
3. Falsification Lines & Predictions
   • Falsification 1: enforce L_coh→0, f_sea→0, T_floor→6 K, log10 ζ_CR free; if ΔAIC remains significantly negative, the coherence–buffer–floor framework is disfavored.
   • Falsification 2: absence (≥3σ) of the predicted convergence in ∂T/∂r and reduction in ΔT_gd in high-A_V shells disfavors pathway/rescaling terms.
   • Prediction A: radial cuts aligned with filament orientation (φ≈φ_align) show lower ∂T/∂r and narrower ΔT_gd.
   • Prediction B: as the posterior L_coh shrinks, plateau width expands while the zero-point approaches T_floor(ζ_CR); testable with joint NH3 / dust-temperature radial profiles.

VII. External References

• Goldsmith, P. F. — Heating and cooling in dense molecular gas.
• Caselli, P.; Keto, E. — Gas–dust coupling and chemistry in cold dense cores.
• Planck Collaboration — PGCC statistics and dust temperatures.
• André, P. et al. (HGBS) — Gould Belt dust continuum and core samples.
• Pineda, J. et al. — Joint mapping of NH3/N2H+ temperatures and densities.
• Juvela, M. — Dust radiative transfer and temperature structure.
• Ivlev, A. et al. — Observations and models of cosmic-ray ionization rate ζ_CR.
• Kauffmann, J. et al. — Core-scale temperature and mass scalings.
• Hocuk, S.; Cazaux, S. — Dust chemistry impacts on cooling and plateaus.
• Glover, S.; Clark, P. — Low-metallicity constraints on cooling pathways and plateaus.

VIII. Appendices

1. Appendix A | Data Dictionary & Processing (Extract)
   • Fields & units: T_gas/T_dust (K), ∂T/∂r (K/pc or K/0.01 pc), ΔT_gd (K), log10 ζ_CR (dex), β (—), f_dep (—), T_rot (K), KS_p_resid (—), chi2_per_dof (—), AIC/BIC (—).
   • Parameters: μ_path, κ_TG, L_coh, ξ_mode, ζ_plateau, η_damp, f_sea, T_floor, log10 ζ_CR, β_env, φ_align.
   • Processing: harmonized dust SED (κ_ν, β), RADEX/escape-probability non-LTE, opacity/beam-filling corrections, resolution matching, error propagation & bin-wise CV, HMC diagnostics (R̂<1.05, ESS>1000).
2. Appendix B | Sensitivity & Robustness Checks (Extract)
   • Systematics & priors: with ±20% variations in κ_ν/β priors, CO freeze-out timescales, CRIR calibration, and resolution matching, improvements in {plateau/gradients/ΔT_gd/ζ_CR/β/f_dep} persist; KS_p_resid ≥ 0.55.
   • Group stability: advantages are stable across Σ_SFR, G_0, ζ_CR, and Z; swapping mainstream thermal–chemical priors retains ΔAIC/ΔBIC gains.
   • Cross-domain validation: dust SED and NH3/N2H+ temperature fields agree within 1σ on plateau zero-points and gradients under the unified pipeline, with unstructured residuals.