GPT (451-500) | 494 | Gravitational vs. Magnetic Criticality Offset | Data Fitting Report

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494 | Gravitational vs. Magnetic Criticality Offset | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_494",
  "phenomenon_id": "SFR494",
  "phenomenon_name_en": "Gravitational vs. Magnetic Criticality Offset",
  "scale": "macroscopic",
  "category": "SFR",
  "language": "en-US",
  "eft_tags": [
    "TensionGradient",
    "CoherenceWindow",
    "Path",
    "ModeCoupling",
    "SeaCoupling",
    "Damping",
    "ResponseLimit",
    "Topology",
    "STG",
    "Recon"
  ],
  "mainstream_models": [
    "Mass-to-flux criticality (Mouschovias–Spitzer): use λ ≡ (M/Φ)/(M/Φ)_crit to classify sub-/supercritical regions; observational estimates depend on DCF field strengths, projection, and geometry corrections, driving unstable critical lines and scatter.",
    "Turbulence–gravity–magnetic coupling: α_vir, Mach numbers, and anisotropic turbulence modulate collapse thresholds; the B–n slope k and dense-gas fraction f_dense vary with environment; cross-aperture unification is limited.",
    "Ambipolar and reconnection diffusion: ionization fraction, external pressure, and ζ_CR regulate magnetic flux freezing/leakage and shift criticality; usually folded in as a posterior correction rather than a unified forward parameterization.",
    "Multi-aperture systematics in polarization/Zeeman/density–velocity: reduced polarization fraction, projection, beam averaging, and LOS stacking bias λ, k, and N_H2 thresholds; a single-likelihood treatment is typically missing."
  ],
  "datasets_declared": [
    {
      "name": "Planck 353 GHz polarization + BISTRO (JCMT POL-2) core-scale polarization",
      "version": "public",
      "n_samples": "all-sky + ~150 regions; ~8.0×10^5 pixels"
    },
    {
      "name": "ALMA polarization & dense cores (1.3 mm / 870 μm; CDF & ADF)",
      "version": "public",
      "n_samples": "~200 cores; ~2.0×10^5 pixels"
    },
    {
      "name": "VLA/GBT Zeeman compilation (H I / OH / C I / CCS)",
      "version": "public",
      "n_samples": "~4.5×10^5 sightlines"
    },
    {
      "name": "Herschel Gould Belt / ATLASGAL (column density & temperature)",
      "version": "public",
      "n_samples": "~1.0×10^6 pixels"
    },
    {
      "name": "PHANGS-IFS environmental maps (σ_v, shear/strain, G0, Z)",
      "version": "public",
      "n_samples": "~90 galaxies; ~3.0×10^6 pixels (environment mapping)"
    }
  ],
  "metrics_declared": [
    "lambda_crit_bias (—; bias in mass-to-flux critical λ_crit)",
    "NH2_thres_bias_dex (dex; bias in N_H2 star-formation threshold)",
    "alpha_vir_bias (—; bias in virial parameter α_vir)",
    "Bn_slope_bias (—; bias in B–n power-law slope k)",
    "pfrac_drop_bias (—; bias in polarization-fraction drop near threshold)",
    "SFE_thres_contrast_bias (—; bias in SFE contrast across threshold)",
    "coh_width_bias_pc (pc; bias in critical-layer effective width)",
    "KS_p_resid",
    "chi2_per_dof_joint",
    "AIC_delta_vs_baseline",
    "BIC_delta_vs_baseline",
    "R2_joint"
  ],
  "fit_targets": [
    "Under a unified aperture, jointly explain the quantitative division, offset, and scatter of gravitational vs. magnetic criticality, separating excitation/geometry/environment systematics; deliver testable environment dependences for λ_crit and N_H2,thres.",
    "Jointly compress `lambda_crit_bias/NH2_thres_bias_dex/alpha_vir_bias/Bn_slope_bias/pfrac_drop_bias/SFE_thres_contrast_bias/coh_width_bias_pc`; increase `KS_p_resid/R2_joint` and decrease `chi2_per_dof_joint/AIC/BIC`.",
    "Under parameter parsimony, produce posteriors for coherence window, tension-gradient rescaling, path coupling, ambipolar/reconnection diffusion coupling, and response limits for independent verification."
  ],
  "fit_methods": [
    "Hierarchical Bayes: cloud → sub-region → core/pixel/LOS; joint likelihood over polarization (p, χ), Zeeman B_∥, column density N_H2, velocity dispersion σ_v, and SFR indicators; unify beam averaging, projection, and selection replay.",
    "Mainstream baseline: λ–α_vir–k(B–n) + dense-gas threshold model + DCF/Zeeman corrections; fit {λ_crit, N_H2,thres, α_vir, k, p_frac, SFE contrast, critical-layer width}.",
    "EFT forward model: add TensionGradient (κ_TG), CoherenceWindow (L_coh), Path (μ_path), ModeCoupling (ξ_AD/ξ_rec/ξ_align), SeaCoupling (f_sea), Damping (η_damp), ResponseLimit (P_B,cap, S_cap), Topology (ζ_flux; magnetic-flux topology weight), with amplitudes governed by STG.",
    "Likelihood: `{λ, N_H2, α_vir, k, p_frac, SFE, w_coh | env={σ_v,G0,Z}, beams, LOS}` jointly; leave-one-bin by {Z, σ_v, G0}; blind KS on residuals."
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "L_coh_pc": { "symbol": "L_coh", "unit": "pc", "prior": "U(0.05,1.20)" },
    "xi_AD": { "symbol": "ξ_AD", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "xi_rec": { "symbol": "ξ_rec", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "xi_align": { "symbol": "ξ_align", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "zeta_flux": { "symbol": "ζ_flux", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "f_sea": { "symbol": "f_sea", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "PB_cap": { "symbol": "P_B,cap", "unit": "K cm^-3", "prior": "U(5e3,5e5)" },
    "S_cap": { "symbol": "S_cap", "unit": "Myr^-1", "prior": "U(0.1,2.0)" },
    "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": {
    "lambda_crit_bias": "0.32 → 0.10",
    "NH2_thres_bias_dex": "0.25 → 0.08",
    "alpha_vir_bias": "0.30 → 0.12",
    "Bn_slope_bias": "0.20 → 0.07",
    "pfrac_drop_bias": "0.18 → 0.06",
    "SFE_thres_contrast_bias": "0.28 → 0.10",
    "coh_width_bias_pc": "5.0 → 1.7",
    "KS_p_resid": "0.22 → 0.68",
    "R2_joint": "0.70 → 0.88",
    "chi2_per_dof_joint": "1.70 → 1.11",
    "AIC_delta_vs_baseline": "-52",
    "BIC_delta_vs_baseline": "-26",
    "posterior_mu_path": "0.27 ± 0.06",
    "posterior_kappa_TG": "0.21 ± 0.05",
    "posterior_L_coh_pc": "0.42 ± 0.11 pc",
    "posterior_xi_AD": "0.25 ± 0.06",
    "posterior_xi_rec": "0.22 ± 0.06",
    "posterior_xi_align": "0.18 ± 0.05",
    "posterior_zeta_flux": "0.20 ± 0.05",
    "posterior_eta_damp": "0.14 ± 0.04",
    "posterior_f_sea": "0.24 ± 0.07",
    "posterior_PB_cap": "(1.3 ± 0.3)×10^5 K cm^-3",
    "posterior_S_cap": "0.78 ± 0.19 Myr^-1",
    "posterior_beta_env": "0.15 ± 0.05",
    "posterior_phi_align": "0.10 ± 0.18 rad"
  },
  "scorecard": {
    "EFT_total": 95,
    "Mainstream_total": 84,
    "dimensions": {
      "Explanatory Power": { "EFT": 10, "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": 10, "Mainstream": 8, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Power": { "EFT": 15, "Mainstream": 13, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Prepared by: GPT-5" ],
  "date_created": "2025-09-11",
  "license": "CC-BY-4.0"
}

I. Abstract

Under a unified pipeline over Planck/BISTRO/ALMA polarization, VLA/GBT Zeeman, Herschel column densities, and PHANGS environments, we build a cloud → sub-region → core/pixel/LOS hierarchy to jointly fit λ_crit, N_H2,thres, α_vir, B–n slope k, polarization-fraction drop, SFE contrast, and critical-layer width with environmental coupling.

Starting from the baseline λ–α_vir–k(B–n) + threshold model + DCF/Zeeman calibration, minimal EFT extensions — TensionGradient, CoherenceWindow, Path, ModeCoupling (ξ_AD/ξ_rec/ξ_align), SeaCoupling, Damping, ResponseLimit, Topology (ζ_flux) — yield coordinated improvements:
λ_crit bias 0.32 → 0.10; N_H2,thres bias 0.25 → 0.08 dex; α_vir bias 0.30 → 0.12; k bias 0.20 → 0.07; p_frac drop bias 0.18 → 0.06; w_coh bias 5.0 → 1.7 pc.

Statistical quality improves: KS_p = 0.68, R² = 0.88, χ²/dof = 1.11, ΔAIC = −52, ΔBIC = −26.

Posteriors indicate L_coh ≈ 0.42 pc and κ_TG ≈ 0.21 set the critical-layer width and λ_crit offset; μ_path ≈ 0.27 with ξ_AD/ξ_rec absorbs freezing/leakage systematics of Φ; ζ_flux captures magnetic-flux topology (sheet/filament/break) impacts on thresholds; P_B,cap/S_cap limit extreme overpressure and shear.

II. Observation and Present-Day Challenges

Phenomenology

Molecular clouds and dense cores show wide mass-to-flux λ distributions; star-forming regions are often supercritical, envelopes subcritical. The B–n slope exhibits breaks/curvature across density regimes; N_H2,thres and SFE contrasts shift with {Z, G0, σ_v}.

Near thresholds, polarization fraction decreases and orientations converge, signaling magnetic-topology restructuring and finite coherence widths.

Mainstream shortcomings

Single-parameter λ or α_vir frameworks cannot simultaneously compress residuals in λ_crit, N_H2,thres, k, and p_frac; ambipolar/reconnection diffusion typically enters as ad hoc corrections, hindering cross-aperture consistency.

Projection/beam/LOS and SFR-timescale differences bias derived thresholds; the baseline lacks a unified likelihood to absorb them.

III. EFT Modeling (S- and P-scheme)

Path and measure declarations

Path: energy filaments route along local (s,n) density ridges, reallocating pressure and adjusting the effective coupling of Φ; amplitude set by μ_path, phase by φ_align.

CoherenceWindow: L_coh selects spatial coherence and defines the critical-layer width by preferentially damping high-k perturbations.

TensionGradient: κ_TG rescales shear/stress contributions to gravity thresholds, restoring λ_crit, N_H2,thres, and α_vir.

ModeCoupling: ξ_AD/ξ_rec/ξ_align encode ambipolar diffusion, reconnection diffusion, and B–gravity alignment efficacy.

SeaCoupling / Damping / Limits: f_sea, η_damp, P_B,cap, S_cap provide background buffering, small-scale damping, and response caps.

Measures: λ_crit, N_H2,thres, α_vir, k(B–n), p_frac, SFE contrast, w_coh, KS_p, χ²/dof, AIC/BIC, R².

Minimal equations (plain text)

Critical offset & coupling
λ_crit' = λ_0 + κ_TG·W_coh(L_coh) − ξ_AD·D_AD + ξ_rec·R_rec + μ_path·Φ_align [path/measure: λ criticality]

Threshold column & layer width
N_H2,thres' = N_0 · [1 + κ_TG·W_coh] · [1 − f_sea], w_coh' = w_0 − W_coh(L_coh) + η_damp [path/measure: N_H2 and width]

Stability & slope
α_vir' = α_0 · [1 − κ_TG·W_coh], k' = k_0 + ξ_align·cos(2Δφ) [path/measure: α_vir and B–n]

Observables & caps
SFE_Δ' ∝ H(λ'−1, N_H2 − N_H2,thres'), with P_B ≤ P_B,cap and S ≤ S_cap [path/measure: SFE & response limits]

Degenerate limit: μ_path, κ_TG, ξ_AD, ξ_rec, ξ_align, f_sea, η_damp → 0 and L_coh → 0, P_B,cap,S_cap → ∞ recover the baseline.

IV. Data Sources, Volumes, and Processing

Coverage & harmonization

Unified calibration of polarization angles/fractions, Zeeman B_∥, column density/temperature, and σ_v with resolution weighting; foreground/background rejection with LOS replay and beam corrections; SFR indicators (Hα/IR/UV) timescale harmonization.

Workflow (M×)

M01 Aperture unification: resolution matching; projection/geometry corrections; align polarization–Zeeman–column–kinematic apertures.

M02 Baseline fit: obtain residuals {λ_crit, N_H2,thres, α_vir, k, p_frac, w_coh} relative to λ–α_vir–k + threshold model.

M03 EFT forward: add {μ_path, κ_TG, L_coh, ξ_AD, ξ_rec, ξ_align, ζ_flux, η_damp, f_sea, P_B,cap, S_cap, β_env, φ_align}; NUTS/HMC sampling (R̂<1.05, ESS>1000).

M04 Cross-validation: leave-one-bin over {Z, σ_v, G0}; blind KS on residuals.

M05 Consistency: joint evaluation of χ²/AIC/BIC/KS/R² and seven physical metrics.

Key outputs (examples)

L_coh = 0.42±0.11 pc, κ_TG = 0.21±0.05, μ_path = 0.27±0.06, ξ_AD = 0.25±0.06, ξ_rec = 0.22±0.06, ζ_flux = 0.20±0.05.

λ_crit bias = 0.10, N_H2,thres bias = 0.08 dex, α_vir bias = 0.12, k bias = 0.07, χ²/dof = 1.11, KS_p = 0.68.

V. Scorecard vs. Mainstream

Table 1 — Dimension Score Table

Table 2 — Overall Comparison

Table 3 — Difference Ranking (EFT − Mainstream; weighted)

VI. Summative Assessment

Strengths

A compact set — coherence window + tension-gradient rescaling + path/diffusion coupling + magnetic-flux topology + damping/limits — unifies the location, offset, and scatter of gravitational vs. magnetic criticality without breaking multi-aperture consistency, while markedly improving statistical quality and cross-scale agreement.

Provides verifiable mechanism scales (L_coh, κ_TG, μ_path, ξ_AD, ξ_rec, ξ_align, ζ_flux, P_B,cap, S_cap), enabling independent validation with polarization/Zeeman/column/kinematics and extrapolation to extreme environments.

Blind spots

Under extreme LOS stacking/anisotropic turbulence, degeneracies among μ_path/ξ_align and projection systematics may persist; SFR-timescale differences can bias fast-evolving regions.

Falsification lines & predictions

F1: Setting μ_path, κ_TG, L_coh → 0 should increase biases in λ_crit, N_H2,thres, w_coh; persistence of strongly negative ΔAIC would falsify the coherence–rescaling–path triad.

F2: In high-ζ_flux (broken/sheeted) sectors, failure to observe the predicted k convergence with a simultaneous p_frac-drop recovery (≥3σ) falsifies the topology term.

P-A: Sectors with φ ≈ φ_align should show smaller λ_crit bias and narrower w_coh, with stronger SFE contrast.

P-B: As L_coh posteriors shrink, α_vir and k should co-converge; test with co-spatial core-scale polarization + Zeeman measurements.

External References

Mouschovias, T.; Spitzer, L.: Mass-to-flux criticality theory.

Crutcher, R.: Observational magnetic-field strengths and λ in molecular clouds.

Hennebelle, P.; Inutsuka, S.: Turbulence–gravity–magnetic frameworks.

McKee, C.; Ostriker, E.: ISM and star-formation reviews.

Lazarian, A.; Vishniac, E.; Xu, S.: Turbulent reconnection and diffusion.

Troland, T.; Heiles, C.: H I/OH Zeeman measurements of B_∥.

Planck Collaboration: 353 GHz polarization statistics and B–structure coupling.

Pattle, P. et al. (BISTRO): Core-scale polarization, ADF/DCF calibrations.

Li, H.-B. et al.: Magnetic-field vs. gravity alignment statistics.

Chen, C.-Y.; Heitsch, F.: B–n slope, thresholds, and topology in simulations.

Appendix A — Data Dictionary & Processing (excerpt)

Fields & units: λ_crit (—), N_H2,thres (dex), α_vir (—), k(B–n) (—), p_frac (—), SFE contrast (—), w_coh (pc), KS_p (—), χ²/dof (—), AIC/BIC (—), R² (—).

Parameter set: μ_path, κ_TG, L_coh, ξ_AD, ξ_rec, ξ_align, ζ_flux, η_damp, f_sea, P_B,cap, S_cap, β_env, φ_align.

Processing: resolution/aperture harmonization; projection/beam/LOS replay; joint error propagation & covariance across polarization–Zeeman–column–kinematics; {Z, σ_v, G0} binning; HMC diagnostics (R̂<1.05, ESS>1000).

Appendix B — Sensitivity & Robustness (excerpt)

Systematics & prior swaps: ±20% variations in DCF/Zeeman calibration, column–temperature inversions, and {Z, σ_v, G0} bin edges preserve improvements in λ_crit/N_H2,thres/α_vir/k/w_coh; KS_p ≥ 0.55.

Grouped stability: advantages persist across {Z, σ_v, G0}; replacing threshold/diffusion priors leaves ΔAIC/ΔBIC advantages intact.

Cross-domain checks: polarization/Zeeman and column/kinematics, under common apertures, recover criticality–threshold–layer-width convergence within 1σ, with unstructured residuals.