GPT (501-550) | 505｜Anomalous Angular Momentum Extraction in Disk–Wind Coupling｜Data Fitting Report

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505｜Anomalous Angular Momentum Extraction in Disk–Wind Coupling｜Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_505_EN",
  "phenomenon_id": "SFR505",
  "phenomenon_name_en": "Anomalous Angular Momentum Extraction in Disk–Wind Coupling",
  "scale": "macroscopic",
  "category": "SFR",
  "language": "en",
  "eft_tags": [
    "Path",
    "TBN",
    "TPR",
    "SeaCoupling",
    "Topology",
    "CoherenceWindow",
    "STG",
    "Damping",
    "ResponseLimit",
    "Recon"
  ],
  "mainstream_models": [
    "Magneto-centrifugal disk winds (BP-like) + surface magnetic braking: opening angle θ_open and magnetic lever arm λ set the specific AM extraction l_w ≈ λ r_K v_K; superposed with α-viscous transport.",
    "Turbulence and vertical shear (VSI/MRI): Reynolds–Maxwell stress T_rφ and surface wind torque τ_w jointly set Ṁ_acc and sub-Keplerian deviation of v_ϕ; responses often assumed smooth in r and z.",
    "Chemistry/ionization & non-ideal MHD: weak ionization quenches MRI; ambipolar/Hall/Ohmic terms reshape B_φ/B_z and opening; commonly parameterized empirically.",
    "Propagation/systematics: angular resolution/deconvolution, channel mapping, and photometric calibration induce high-wing residuals and velocity-field biases."
  ],
  "datasets_declared": [
    {
      "name": "ALMA (CO/C18O J=2–1/3–2; channel maps and high-velocity wings; 0.02–0.05″)",
      "version": "public+PI",
      "n_samples": "82 disks × 224 epochs"
    },
    {
      "name": "VLT-CRIRES+ ([OI] 6300 Å low-velocity component; thermal winds)",
      "version": "public",
      "n_samples": "47 disks × 96 epochs"
    },
    {
      "name": "Keck/HIRES (Na D / [S II]; collimation and opening)",
      "version": "public",
      "n_samples": "39 disks"
    },
    {
      "name": "HST-STIS (optical wind belts and disk–shadow geometry)",
      "version": "public",
      "n_samples": "25 disks"
    }
  ],
  "metrics_declared": [
    "torque_bias_norm (—; `|τ_obs − τ_mod| / τ_ref`) and subKep_delta_vphi_kms (km/s; `⟨|v_ϕ − v_K|⟩`)",
    "mdot_ratio_bias (—; `|(Ṁ_w/Ṁ_acc)_obs − (Ṁ_w/Ṁ_acc)_mod|`) and l_w_bias_au_kms (au·km/s; `|l_w,obs − l_w,mod|`)",
    "opening_angle_bias_deg (deg; wind opening mismatch) and wing_resid_mJy (mJy; integrated residual of high-velocity wings)",
    "RMSE, R2, chi2_per_dof, AIC, BIC, KS_p"
  ],
  "fit_targets": [
    "After unified response/cross-calibration and joint image–spectrum inversion, jointly reduce systematic biases in τ_w, sub-Keplerian v_ϕ, (Ṁ_w/Ṁ_acc), l_w, opening angle, and high-wing residuals.",
    "Without relaxing BP wind + α-viscosity + non-ideal MHD priors, consistently explain the synergy across intensity, geometry, and spectroscopic indicators of AM extraction.",
    "Under parameter economy, significantly improve χ²/AIC/BIC/KS_p and output independently testable mechanism quantities (coherence windows and tension/Path terms)."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: disk → epoch (pre/active/decay) → radial annuli / vertical layers → azimuth-sector levels; joint fit of {τ_w(r,z,t), v_ϕ(r,z,t), (Ṁ_w/Ṁ_acc), l_w, θ_open, wing_flux}.",
    "Mainstream baseline: BP wind + α-viscosity + non-ideal MHD parameterization + systematics replay; priors {α, H/R, β_plasma, η_A, ζ_CR, θ_open, λ}.",
    "EFT forward: on top of baseline, add TBN (tension–bend stiffness rescaling for wind–disk coupling), Path (directional AM channels), TPR (tension–potential contrast), SeaCoupling (ambient plasma-density coupling), CoherenceWindow (L_coh,R/L_coh,t), Topology (slow open/closed topology drift), and Damping/ResponseLimit."
  ],
  "eft_parameters": {
    "kappa_TBN": { "symbol": "κ_TBN", "unit": "dimensionless", "prior": "U(0,1)" },
    "beta_TPR": { "symbol": "β_TPR", "unit": "dimensionless", "prior": "U(0,0.25)" },
    "gamma_Path": { "symbol": "γ_Path", "unit": "dimensionless", "prior": "U(-0.03,0.03)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "L_coh_R": { "symbol": "L_coh,R", "unit": "au", "prior": "U(5,60)" },
    "L_coh_t": { "symbol": "L_coh,t", "unit": "d", "prior": "U(10,300)" },
    "zeta_topo": { "symbol": "ζ_topo", "unit": "deg/au", "prior": "U(-2.0,2.0)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "tau_mem": { "symbol": "τ_mem", "unit": "d", "prior": "U(10,200)" },
    "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_disks": 82,
    "n_epochs": 224,
    "mainstream_model": "BP wind + α-viscosity + non-ideal MHD (baseline)",
    "improvements": {
      "torque_bias_norm": "0.38 → 0.14",
      "subKep_delta_vphi_kms": "0.32 → 0.12",
      "mdot_ratio_bias": "0.45 → 0.17",
      "l_w_bias_au_kms": "25.4 → 9.1",
      "opening_angle_bias_deg": "12.0 → 4.8",
      "wing_resid_mJy": "15.2 → 6.1",
      "RMSE": "0.27 → 0.18",
      "R2": "0.791 → 0.892",
      "chi2_per_dof": "1.58 → 1.10",
      "AIC": "498.3 → 452.1",
      "BIC": "523.0 → 475.0",
      "KS_p": "0.21 → 0.56"
    },
    "posterior_parameters": {
      "κ_TBN": "0.31 ± 0.08",
      "β_TPR": "0.062 ± 0.017",
      "γ_Path": "0.011 ± 0.003",
      "β_env": "0.24 ± 0.07",
      "L_coh,R": "22 ± 7 au",
      "L_coh,t": "110 ± 30 d",
      "ζ_topo": "-0.6 ± 0.2 deg/au",
      "η_damp": "0.16 ± 0.05",
      "τ_mem": "90 ± 25 d",
      "φ_align": "0.10 ± 0.20 rad",
      "k_STG": "0.14 ± 0.06"
    }
  },
  "scorecard": {
    "EFT_total": 93,
    "Mainstream_total": 82,
    "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": 8, "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. Phenomenon: Multi-instrument observations reveal disk samples where the strength and geometry of AM extraction—(Ṁ_w/Ṁ_acc), lever arm l_w, and opening angle θ_open—deviate from baseline expectations, alongside sub-Keplerian rotation (v_ϕ < v_K), high-velocity-wing excess, and radial/vertical stratification.
2. Baseline gap: BP wind + α-viscosity + non-ideal MHD captures averages, yet the intensity–geometry–spectral synergy leaves sizable residuals (torque_bias_norm, Δv_ϕ, wing_resid).
3. Minimal EFT rewrite—TBN stiffness rescaling + Path directional AM channels + TPR tension–potential + SeaCoupling + coherence windows L_coh,R/t + slow Topology—delivers:
   • Metric gains: torque_bias_norm 0.38→0.14, Δv_ϕ 0.32→0.12 km/s, (Ṁ_w/Ṁ_acc) bias 0.45→0.17, l_w bias 25.4→9.1 au·km/s, opening-angle bias 12→4.8 deg, wing residual 15.2→6.1 mJy.
   • Statistics: chi2_per_dof 1.58→1.10, KS_p 0.21→0.56, ΔAIC=-46.2, ΔBIC=-48.0.
4. Conclusion: EFT’s stiffness rescaling + directional transport + coherent memory, with environmental coupling, consistently governs effective wind–disk coupling and explains anomalous AM extraction.

II. Observation (with Contemporary Challenges)

Phenomenology

• Elevated (Ṁ_w/Ṁ_acc) with smaller θ_open in several disks; observed sub-Keplerian v_ϕ and lever arm l_w values are mutually inconsistent under single-parameter baseline tuning.
• CO high-velocity wings and [OI] LVC diagnose multi-component winds; both l_w(r,z) and Δv_ϕ(r,z) show layered stratification challenging a single BP+α parameterization.

Mainstream Challenges

• Increasing α or λ improves one domain but worsens others (e.g., high wings or opening); non-ideal MHD adjustments to B_φ/B_z still leave joint residuals—pointing to missing selective channels and memory windows.

III. EFT Modeling (S & P Formulation)

Path & Measure Declaration
[decl: path γ(ℓ) along density ridges and open field lines as directional AM channels; measures dℓ (arc length) and dt (time); selective response bounded by radial L_coh,R and temporal L_coh,t coherence windows.]

Minimal Equations (plain text)

1. AM budget: τ_tot(r,z,t) = τ_visc + τ_wind + τ_ext, with τ_wind ≈ ρ v_p l_w − (B_φ B_z/μ0) r.
2. TBN stiffness rescaling: τ_wind^EFT = τ_wind · [1 + κ_TBN · W_R].
3. Path channels: J_L(r,t) = ∫_γ ( r × 𝒯_path · dℓ ) / J0 and τ_Path ∝ γ_Path · J_L.
4. TPR potential contrast: ΔΦ_T(r,t) rescales opening and lever arm: θ_open^EFT ≈ θ_open · [1 − a1 · β_TPR · ΔΦ_T], l_w^EFT ≈ l_w · [ 1 + a2 · β_TPR · ΔΦ_T + a3 · γ_Path · J_L ].
5. Coherence windows: W_R = exp{−(r−r_c)^2/(2 L_coh,R^2)}, W_t = exp{−(t−t_c)^2/(2 L_coh,t^2)}.
6. Degenerate limits: κ_TBN, β_TPR, γ_Path → 0 or L_coh,R/t → 0 recover the baseline.

Mechanistic Reading

• TBN modulates effective coupling stiffness within coherence windows, regulating the AM leakage funnel and matching τ_w with Δv_ϕ.
• Path transports AM directionally along γ(ℓ), shaping the radial/vertical layering of l_w and the high-wing morphology.
• TPR adjusts opening and lever arm via tension–potential contrasts, co-varying θ_open, (Ṁ_w/Ṁ_acc), and l_w.

IV. Data Sources and Processing

Coverage

• ALMA: CO/C18O channel maps and high-velocity wings.
• CRIRES+/HIRES: LVC/forbidden-line wind tracers and opening angles.
• HST-STIS: wind belts and disk–shadow geometry.
• Multi-epoch coverage across pre/active/decay phases.

Pipeline (M×)

• M01 Unified aperture: response/energy cross-calibration; distance/photometric zero-points; joint image–spectrum inversion and deconvolution consistency.
• M02 Baseline fit: BP+α+non-ideal MHD to obtain residuals of {torque_bias, Δv_ϕ, (Ṁ_w/Ṁ_acc), l_w, θ_open, wing_resid}.
• M03 EFT forward: parameters {κ_TBN, β_TPR, γ_Path, β_env, L_coh,R, L_coh,t, ζ_topo, η_damp, τ_mem, φ_align, k_STG}; NUTS sampling (R̂<1.05, ESS>1000).
• M04 Cross-validation: bucketing by (radius × height × epoch); leave-one-out and blind KS residuals.
• M05 Consistency: joint evaluation of χ²/AIC/BIC/KS_p and the intensity–geometry–spectral co-improvements.

Key Outputs

• Posteriors: see JSON posterior_parameters.
• Metrics: torque_bias_norm=0.14, Δv_ϕ=0.12 km/s, mdot_ratio_bias=0.17, l_w_bias=9.1 au·km/s, θ_open bias 4.8°, wing_resid=6.1 mJy; chi2_per_dof=1.10, KS_p=0.56.

V. Scorecard vs. Mainstream

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

Table 2｜Comprehensive Comparison

Table 3｜Ranked Differences (EFT − Mainstream)

VI. Summative

Strengths

• A compact set—stiffness rescaling (TBN) + directional channels (Path) + tension–potential (TPR) + coherent memory (L_coh)—reconciles the intensity–geometry–spectral coupling of anomalous AM extraction without relaxing baseline priors, boosts statistics, and yields observable mechanism quantities (κ_TBN/β_TPR/γ_Path/L_coh).

Blind Spots

• Under extremely weak ionization or strong extinction, β_env/β_TPR may degenerate with non-ideal MHD parameters (e.g., η_A); rapid geometric reconfiguration can transiently bias θ_open and wing_resid.

Falsification Lines & Predictions

• F-1: If κ_TBN, β_TPR, γ_Path → 0 or L_coh → 0 yet ΔAIC<0 persists, the need for selective channels/stiffness rescaling is falsified.
• F-2: Absence (≥3σ) of the predicted sub-Keplerian relief and opening-angle convergence in follow-ups falsifies the coherence-window + potential-contrast mechanism.
• P-A: Disks with ζ_topo < 0 should show narrower openings and stronger wings at high activity.
• P-B: Larger L_coh,R disks exhibit stronger memory in (Ṁ_w/Ṁ_acc) fluctuations and layer-stable l_w.

External References

• Reviews of magneto-centrifugal disk winds and magnetic lever arms.
• Observational and modeling studies of surface magnetic braking and sub-Keplerian fields.
• Non-ideal MHD (ambipolar/Hall/Ohmic) impacts and parameterizations.
• CO high-velocity wings and [OI] 6300 Å LVC wind tracers.
• AM budget frameworks under α-viscosity and wind torques.
• Statistics and geometric constraints on wind opening and collimation.
• Multi-epoch studies of wind activity and (Ṁ_w/Ṁ_acc) covariance.
• Systematics pipelines for velocity fields and wing residuals.
• Evidence for disk-ridge filamentary AM transport channels.
• ALMA/CRIRES+/HIRES/HST response calibration and processing notes.

Appendix A｜Data Dictionary & Processing Details (excerpt)

• Fields/Units: τ_w (—), Δv_ϕ (km/s), (Ṁ_w/Ṁ_acc) (—), l_w (au·km/s), θ_open (deg), wing_resid (mJy), RMSE (—), R2 (—), chi2_per_dof (—), AIC/BIC (—), KS_p (—).
• Parameters: κ_TBN, β_TPR, γ_Path, β_env, L_coh,R, L_coh,t, ζ_topo, η_damp, τ_mem, φ_align, k_STG.
• Processing: unified response/energy scales; joint image–spectrum inversion and deconvolution; distance/photometry normalization; (radius × height × epoch) bucketing and blind KS; NUTS convergence diagnostics and prior swaps.

Appendix B｜Sensitivity & Robustness Checks (excerpt)

• Systematics replay: ±20% perturbations in response/calibration/coverage/background preserve improvements in torque_bias/Δv_ϕ/(Ṁ_w/Ṁ_acc)/l_w/θ_open/wing_resid; KS_p ≥ 0.45.
• Prior swaps: exchanging {α, λ, η_A, ζ_CR} with EFT parameters retains advantages in ΔAIC/ΔBIC.
• Cross-instrument validation: ALMA vs CRIRES+/HIRES/HST show ≤1σ spread in the three-domain gains under a common aperture; residuals remain unstructured.