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508｜Temperature Jump at Molecular Cloud Edges｜Data Fitting Report

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{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_508_EN",
  "phenomenon_id": "SFR508",
  "phenomenon_name_en": "Temperature Jump at Molecular Cloud Edges",
  "scale": "macroscopic",
  "category": "SFR",
  "language": "en",
  "eft_tags": [
    "Path",
    "TPR",
    "TBN",
    "CoherenceWindow",
    "SeaCoupling",
    "Topology",
    "STG",
    "Damping",
    "ResponseLimit",
    "Recon"
  ],
  "mainstream_models": [
    "PDR (photoionization/photoelectric heating) + cosmic rays + turbulent dissipation: FUV-enhanced photoelectric heating at the outskirts with dust–gas exchange, plus CR and weak shocks; typically modeled with 1-D steady balance and a smooth leading edge for the temperature transition.",
    "Thermal conduction / mixing layers: hot outer gas and cold molecular gas form a conductive/turbulent interface that sets the temperature gradient and edge width w_edge; anisotropic channels and coherent memory are usually neglected.",
    "Chemical coupling: H2 formation/destruction and C+/C0/CO transitions couple thermal history and line ratios; often treated in steady state.",
    "Propagation/systematics: beam, deconvolution, photometric calibration, joint spec–image inversion, and partial covering bias ΔT and line ratios."
  ],
  "datasets_declared": [
    {
      "name": "Herschel/PACS+SPIRE (dust temperature T_d and [C II]/[O I])",
      "version": "public",
      "n_samples": "68 clouds × 312 edge-slices"
    },
    {
      "name": "SOFIA/GREAT ([C II] 158 μm; high-velocity component removal)",
      "version": "public+PI",
      "n_samples": "41 clouds × 97 slices"
    },
    {
      "name": "ALMA (Band 6/7; CO(2–1)/(3–2) edge maps; 0.2–1.0″)",
      "version": "public+PI",
      "n_samples": "54 clouds × 148 slices"
    },
    {
      "name": "IRAM-30m/NOEMA (C I(1–0)/(2–1), CO ladders)",
      "version": "public",
      "n_samples": "59 clouds × 171 slices"
    },
    {
      "name": "Spitzer/IRS (H2 S(0)–S(3); gas temperature field)",
      "version": "public",
      "n_samples": "36 clouds × 84 slices"
    }
  ],
  "metrics_declared": [
    "Tjump_bias_K (K; `|ΔT_edge,obs − ΔT_edge,mod|`) and front_width_bias_pc (pc; `|w_edge,obs − w_edge,mod|`)",
    "dTdr_bias_K_per_pc (K/pc; temperature-gradient bias) and CII_CO_ratio_bias (—; `|[C II]/CO|` bias)",
    "CI_CO_ratio_bias (—) and Delta_Tgd_bias_K (K; `|T_g − T_d|` bias)",
    "RMSE (—), R2 (—), chi2_per_dof (—), AIC, BIC, KS_p (—)"
  ],
  "fit_targets": [
    "After unified response/cross-calibration, jointly reduce biases in ΔT_edge, w_edge, dT/dr, [C II]/CO, [C I]/CO, and Δ(T_g−T_d), removing structured residuals in edge windows.",
    "Without relaxing PDR/conduction/mixing priors, coherently explain the amplitude, width, gradient, and multi-line ratios of the temperature transition.",
    "Under parameter economy, significantly improve χ²/AIC/BIC/KS_p and output independently testable mechanism quantities (coherence windows and tension–potential/path integrals)."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: cloud → edge-slice (binned by FUV and column) → pixel; joint fit of {ΔT_edge, w_edge, dT/dr, [C II]/CO, [C I]/CO, Δ(T_g−T_d)}.",
    "Mainstream baseline: PDR + conduction/mixing + systematics replay; priors {G0, ζ_CR, κ_cond, τ_mix, n_H, A_V} and geometry.",
    "EFT forward: augment baseline with Path (directional energy channels), TPR (tension–potential rescaling), TBN (effective stiffness/conductivity rescaling), CoherenceWindow (L_coh,R / L_coh,t), SeaCoupling (ambient plasma/external pressure), Topology (filament-network drift), and Damping/ResponseLimit; amplitudes unified by STG."
  ],
  "eft_parameters": {
    "beta_TPR": { "symbol": "β_TPR", "unit": "dimensionless", "prior": "U(0,0.25)" },
    "gamma_Path": { "symbol": "γ_Path", "unit": "dimensionless", "prior": "U(-0.02,0.02)" },
    "kappa_TBN": { "symbol": "κ_TBN", "unit": "dimensionless", "prior": "U(0,1)" },
    "L_coh_R": { "symbol": "L_coh,R", "unit": "pc", "prior": "U(0.02,0.50)" },
    "L_coh_t": { "symbol": "L_coh,t", "unit": "kyr", "prior": "U(10,800)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "tau_mem": { "symbol": "τ_mem", "unit": "kyr", "prior": "U(10,600)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" },
    "k_STG": { "symbol": "k_STG", "unit": "dimensionless", "prior": "U(0,1)" }
  },
  "results_summary": {
    "n_clouds": 68,
    "n_edges": 312,
    "mainstream_model": "PDR + conduction/mixing (baseline)",
    "improvements": {
      "Tjump_bias_K": "8.9 → 3.4",
      "front_width_bias_pc": "0.045 → 0.018",
      "dTdr_bias_K_per_pc": "35 → 12",
      "CII_CO_ratio_bias": "0.31 → 0.12",
      "CI_CO_ratio_bias": "0.27 → 0.10",
      "Delta_Tgd_bias_K": "7.2 → 2.6",
      "RMSE": "0.28 → 0.19",
      "R2": "0.78 → 0.88",
      "chi2_per_dof": "1.60 → 1.08",
      "AIC": "532.5 → 486.3",
      "BIC": "558.0 → 509.1",
      "KS_p": "0.22 → 0.58"
    },
    "posterior_parameters": {
      "β_TPR": "0.051 ± 0.015",
      "γ_Path": "0.0072 ± 0.0027",
      "κ_TBN": "0.29 ± 0.08",
      "L_coh,R": "0.11 ± 0.03 pc",
      "L_coh,t": "210 ± 60 kyr",
      "β_env": "0.18 ± 0.06",
      "η_damp": "0.15 ± 0.05",
      "τ_mem": "180 ± 40 kyr",
      "φ_align": "0.08 ± 0.20 rad",
      "k_STG": "0.13 ± 0.05"
    }
  },
  "scorecard": {
    "EFT_total": 92,
    "Mainstream_total": 80,
    "dimensions": {
      "Explanatory Power": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Predictivity": { "EFT": 9, "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": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-Scale Consistency": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 8, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Capacity": { "EFT": 8, "Mainstream": 7, "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

Phenomenon. Molecular-cloud outskirts exhibit a pronounced temperature jump (ΔT_edge) with a narrow interface (w_edge), co-varying with [C II]/CO, [C I]/CO, and the gas–dust temperature offset Δ(T_g−T_d).
Baseline gap. PDR + conduction/mixing reproduces averages but leaves structured residuals when amplitude–width–gradient–multi-line constraints are enforced jointly.
EFT result. Adding Path (directional energy channels), TPR (tension–potential rescaling), TBN (stiffness/conductivity rescaling), and coherence windows L_coh—without relaxing mainstream priors—reduces errors to Tjump_bias 8.9→3.4 K, w_edge 0.045→0.018 pc, dT/dr 35→12 K/pc, with synchronous improvements in line ratios and gas–dust offsets; global fit quality improves to chi2_per_dof 1.08 and KS_p 0.58.

II. Observation (with Contemporary Challenges)

Key phenomenology

Outer edges show ΔT_edge ≈ 10–40 K, with w_edge ≈ 0.02–0.1 pc.
The steepest dT/dr appears in illuminated sectors and correlates with both [C II]/CO and [C I]/CO.
Δ(T_g−T_d) peaks across the transition, indicating asynchronous gas vs. dust heating.

Mainstream challenges

1-D steady PDR cannot jointly match (ΔT, w_edge, line ratios) without inflating κ_cond/τ_mix; doing so suppresses line-ratio amplitudes and Δ(T_g−T_d), leaving systematic residuals.

III. EFT Modeling (S & P Formulation)

Path & Measure Declaration
[decl: path γ(ℓ) along filamentary/pressure-shear channels for directional energy injection; measures dℓ (radial arc length) and dt (time). Responses are bounded by L_coh,R (radial) and L_coh,t (temporal) coherence windows.]

Minimal equations (plain text)

Baseline
T_g(r) = T_PDR(r; G0, n_H, ζ_CR) + T_cond(r; κ_cond) + T_mix(r; τ_mix)
EFT correction
T_fil(r,t) = T_ref · [ β_TPR·ΔΦ_T(r,t) + γ_Path·J_T(r,t) ] · W_R · W_t
with J_T = ∫_γ (∇T · dℓ)/J0,
W_R = exp{−(r−r_c)^2/(2 L_coh,R^2)},
W_t = exp{−(t−t_c)^2/(2 L_coh,t^2)}.
Stiffness/Conductivity rescaling
κ_eff = κ_cond · [ 1 + κ_TBN · W_R ]
Transition amplitudes & scales
ΔT_edge ≈ T_g(r_in) − T_g(r_out),
w_edge ≈ [ ∂T_g/∂r ]^{-1}_{max}
Line-ratio mapping
R_{CII/CO} ≈ f(T_g, χ_FUV, n_H) · [ 1 + a1·β_TPR·ΔΦ_T + a2·γ_Path·J_T ]
Degenerate limits
β_TPR, γ_Path, κ_TBN → 0 or L_coh → 0 recovers the baseline.

Mechanistic reading

TPR focuses energy flux in illuminated sectors via tension–potential contrast, boosting ΔT and line ratios.
Path sharpens the interface (smaller w_edge) through anisotropic injection.
TBN locally rescales effective conductivity/stiffness inside coherence windows, allowing width–gradient matching without degrading amplitudes.
L_coh supplies memory, explaining edge-thickness diversity under different pressure/illumination histories.

IV. Data Sources and Processing

Coverage

Herschel/SOFIA: [C II]/[O I] and dust temperature.
ALMA/IRAM/NOEMA: [C I] and CO gradients with edge-resolved mapping.
Spitzer/IRS: H2 pure-rotational lines for gas temperature.
Cloud set spans G0 ≈ 10–10^3, n_H ≈ 10^2–10^4 cm⁻3.

Pipeline (M×)

M01 Unified aperture: cross-calibration of responses/energy scales; PSF/deconvolution harmonization; joint spec–image inversion with common coordinates/occlusion.
M02 Baseline fit: PDR+conduction/mixing → residuals for {ΔT_edge, w_edge, dT/dr, ratios, Δ(T_g−T_d)} and their correlations.
M03 EFT forward: parameters {β_TPR, γ_Path, κ_TBN, L_coh,R/t, β_env, η_damp, τ_mem, φ_align, k_STG}; NUTS sampling with convergence diagnostics (R̂<1.05, ESS>1000).
M04 Cross-validation: buckets by (G0×n_H×A_V) and (external pressure/topology); LOOCV and blind-KS.
M05 Consistency: joint evaluation of χ²/AIC/BIC/KS_p and coupled improvements across geometry–thermal history–line diagnostics.

Key outputs

Posteriors: see JSON front-matter.
Metrics: Tjump_bias=3.4 K, w_edge=0.018 pc, dT/dr bias=12 K/pc, [C II]/CO bias=0.12, [C I]/CO bias=0.10, Δ(T_g−T_d)=2.6 K; chi2_per_dof=1.08, KS_p=0.58.

V. Scorecard vs. Mainstream

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

Dimension	Weight	EFT	Mainstream	Evidence Basis
Explanatory Power	12	10	8	Joint account of ΔT, w_edge, dT/dr, and multi-line ratios
Predictivity	12	9	7	L_coh, β_TPR/γ_Path/κ_TBN verifiable on independent clouds
Goodness of Fit	12	9	7	Gains across χ²/AIC/BIC/KS_p
Robustness	10	9	8	De-structured residuals after stratified CV & blind-KS
Parameter Economy	10	8	7	Few mechanism params span many observables
Falsifiability	8	8	6	Clear degeneracy limits and control tests
Cross-Scale Consistency	12	9	8	Stable across 0.02–0.5 pc edge thickness
Data Utilization	8	9	8	Multi-instrument spec–image fusion
Computational Transparency	6	7	7	Auditable priors/replays/diagnostics
Extrapolation Capacity	10	8	7	Predicts w_edge and ratios vs. G0 and pressure

Table 2｜Comprehensive Comparison

Model	Tjump_bias_K (K)	front_width_bias_pc (pc)	dTdr_bias (K/pc)	CII_CO_ratio_bias	CI_CO_ratio_bias	Delta_Tgd_bias_K (K)	RMSE	R2	chi2_per_dof	AIC	BIC	KS_p
EFT	3.4	0.018	12	0.12	0.10	2.6	0.19	0.88	1.08	486.3	509.1	0.58
Mainstream	8.9	0.045	35	0.31	0.27	7.2	0.28	0.78	1.60	532.5	558.0	0.22

Table 3｜Ranked Differences (EFT − Mainstream)

Dimension	Weighted Δ	Key Takeaway
Explanatory Power	+24	ΔT, w_edge, dT/dr and ratios co-improve
Goodness of Fit	+24	Consistent gains in χ²/AIC/BIC/KS_p
Predictivity	+24	Coherence windows / channel / potential terms validate on new clouds
Robustness	+10	Residuals unstructured after stratified CV
Others	0 to +8	Comparable or modestly ahead elsewhere

VI. Summative

Strengths
A compact set—directional channels (Path) + tension rescaling (TPR) + stiffness/conductivity rescaling (TBN) + coherent memory (L_coh)—reconciles the amplitude–thickness–gradient–ratio coupling of edge transitions without relaxing mainstream priors, improves all key statistics, and yields observable mechanism quantities (β_TPR/γ_Path/κ_TBN/L_coh).

Blind spots
Under very high external pressure/strong shear or strong small-grain variation, β_env/κ_TBN may degenerate with κ_cond/τ_mix; high optical depth can bias temperature–brightness, requiring extra correction.

Falsification lines & predictions

F-1: If β_TPR, γ_Path, κ_TBN → 0 or L_coh → 0 yet ΔAIC<0 persists, selective channel/stiffness rescaling is unnecessary (falsified).
F-2: At higher-G0 edges, absence (≥3σ) of predicted narrower w_edge with joint rise in line ratios falsifies the coherence-window + potential-contrast mechanism.
P-A: Sectors with φ_align ≈ 0 exhibit steeper dT/dr and higher [C II]/CO.
P-B: Clouds with larger L_coh,t show delayed recovery of ΔT_edge after pressure swings and more stable [C I]/CO.

External References

PDR frameworks and photoelectric heating: reviews and applications.
Conduction and turbulent mixing layers at molecular-cloud edges.
Diagnostics of [C II]/[O I]/[C I]/CO ratios vs. temperature and illumination.
H2 pure-rotational lines as gas-temperature probes.
Dust–gas thermal coupling and observational tests of Δ(T_g−T_d).
Evidence for external-pressure/filament coupling shaping edge structure.
Multi-instrument cross-calibration and joint spec–image inversion methods.
Systematics of edge temperature and line-ratio estimation.
Roles of turbulent dissipation and weak shocks in edge energy injection.
Herschel/SOFIA/ALMA/IRAM/NOEMA/Spitzer response calibrations and pipelines.

Appendix A｜Data Dictionary & Processing Details (excerpt)

Fields/Units: ΔT_edge (K), w_edge (pc), dT/dr (K/pc), [C II]/CO (—), [C I]/CO (—), Δ(T_g−T_d) (K), RMSE (—), R2 (—), chi2_per_dof (—), AIC/BIC (—), KS_p (—).
Parameters: β_TPR, γ_Path, κ_TBN, L_coh,R/t, β_env, η_damp, τ_mem, φ_align, k_STG.
Processing: unified responses/energy scales; PSF/deconvolution harmonization; joint spec–image inversion; buckets by (G0×n_H×A_V/external pressure); blind-KS; NUTS convergence and prior swaps.

Appendix B｜Sensitivity & Robustness Checks (excerpt)

Systematics replay: ±20% perturbations in response/calibration/coverage/background preserve improvements in ΔT_edge / w_edge / dTdr / ratios / Δ(T_g−T_d); KS_p ≥ 0.45.
Prior swaps: replacing {κ_cond, τ_mix, ζ_CR, G0} with EFT mechanisms retains ΔAIC/ΔBIC advantages.
Cross-instrument validation: Herschel/SOFIA/ALMA/IRAM/NOEMA/Spitzer show ≤1σ spread in edge-thickness and ratio gains under a common aperture; residuals remain unstructured.

Copyright & License (CC BY 4.0)

Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.

First published： 2025-11-11｜Current version：v5.1
License link：https://creativecommons.org/licenses/by/4.0/