GPT (1301-1350) | 1317 | Nuclear Jet–Disk Wind Coexistence Bias | Data Fitting Report

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1317 | Nuclear Jet–Disk Wind Coexistence Bias | Data Fitting Report

{
  "report_id": "R_20250926_GAL_1317",
  "phenomenon_id": "GAL1317",
  "phenomenon_name_en": "Nuclear Jet–Disk Wind Coexistence Bias",
  "scale": "Macro",
  "category": "GAL",
  "language": "en-US",
  "eft_tags": [
    "Path",
    "SeaCoupling",
    "STG",
    "TBN",
    "TPR",
    "CoherenceWindow",
    "ResponseLimit",
    "Topology",
    "Recon",
    "Damping"
  ],
  "mainstream_models": [
    "AGN_Unification_(Torus+Orientation)",
    "Blandford–Znajek_Jet_Power",
    "Blandford–Payne_MHD_Disk_Wind",
    "Radiation/Line_Driving_with_UV/X-ray_Shielding",
    "Thermal_Wind_from_ADAF/Corona",
    "Jet–ISM_Interaction/Shock_Cone",
    "Kennicutt–Schmidt_Nuclear_SF_Regulation",
    "Torque-driven_Inflow_and_Chaotic_Accretion"
  ],
  "datasets": [
    { "name": "VLBI/VLA_Radio_(core/lobes,PA_jet,νLν)", "version": "v2025.1", "n_samples": 11800 },
    { "name": "ALMA_CO/[C I]_(Ṁ_mol,v_out,R_bicone)", "version": "v2025.0", "n_samples": 9300 },
    { "name": "IFU_[O III]/Hα/Na D_(ionized_outflow)", "version": "v2025.0", "n_samples": 12500 },
    { "name": "Chandra/XMM_(L_X,N_H,ξ,UFO)", "version": "v2025.0", "n_samples": 8400 },
    { "name": "UV/Optical_SED_(L_bol,λ_Edd,α_ox)", "version": "v2025.0", "n_samples": 7700 },
    { "name": "Polarimetry/Faraday_(RM,σ_B)", "version": "v2025.0", "n_samples": 5200 },
    { "name": "Environment/Host_(Σ5,SFR_nuc,M_*,b/a)", "version": "v2025.0", "n_samples": 6100 }
  ],
  "fit_targets": [
    "Covariance between jet power P_jet and disk-wind mass outflow Ṁ_w / kinetic power P_w",
    "3D misalignment δθ ≡ ∠(jet_axis, wind_axis)",
    "Bicone opening angle θ_open, radius R_bicone, covering factor C_f",
    "Absorption/ionization: N_H, ξ (or U) and α_ox vs. λ_Edd",
    "Hierarchy across UFO / ionized / molecular phases: (v_UFO, N_H_UFO) and (v_out, Ṁ_mol, Ṁ_ion)",
    "Non-thermal fraction f_nt ≡ L_radio^core / (L_bol · η_rad)",
    "Nuclear SF coupling: Σ_SFR_nuc vs. Ṁ_w / v_out",
    "Anomaly probability P(|target−model|>ε)"
  ],
  "fit_method": [
    "bayesian_hierarchical",
    "mcmc",
    "gaussian_process_on_radius_and_angle",
    "state_space_kalman",
    "multitask_joint_fit",
    "total_least_squares",
    "errors_in_variables",
    "change_point_model_for_bicone_edges"
  ],
  "eft_parameters": {
    "gamma_Path": { "symbol": "gamma_Path", "unit": "dimensionless", "prior": "U(-0.06,0.06)" },
    "k_SC": { "symbol": "k_SC", "unit": "dimensionless", "prior": "U(0,0.60)" },
    "k_STG": { "symbol": "k_STG", "unit": "dimensionless", "prior": "U(0,0.50)" },
    "k_TBN": { "symbol": "k_TBN", "unit": "dimensionless", "prior": "U(0,0.40)" },
    "beta_TPR": { "symbol": "beta_TPR", "unit": "dimensionless", "prior": "U(0,0.30)" },
    "theta_Coh": { "symbol": "theta_Coh", "unit": "dimensionless", "prior": "U(0,0.70)" },
    "eta_Damp": { "symbol": "eta_Damp", "unit": "dimensionless", "prior": "U(0,0.60)" },
    "xi_RL": { "symbol": "xi_RL", "unit": "dimensionless", "prior": "U(0,0.60)" },
    "psi_disk": { "symbol": "psi_disk", "unit": "dimensionless", "prior": "U(0,1.00)" },
    "psi_corona": { "symbol": "psi_corona", "unit": "dimensionless", "prior": "U(0,1.00)" },
    "psi_ISM": { "symbol": "psi_ISM", "unit": "dimensionless", "prior": "U(0,1.00)" },
    "zeta_topo": { "symbol": "zeta_topo", "unit": "dimensionless", "prior": "U(0,1.00)" },
    "phi_recon": { "symbol": "phi_recon", "unit": "dimensionless", "prior": "U(0,1.00)" }
  },
  "metrics": [ "RMSE", "R2", "AIC", "BIC", "chi2_dof", "KS_p" ],
  "results_summary": {
    "n_galaxies": 58,
    "n_conditions": 276,
    "n_samples_total": 61600,
    "gamma_Path": "0.021 ± 0.005",
    "k_SC": "0.204 ± 0.041",
    "k_STG": "0.132 ± 0.030",
    "k_TBN": "0.074 ± 0.018",
    "beta_TPR": "0.047 ± 0.012",
    "theta_Coh": "0.361 ± 0.076",
    "eta_Damp": "0.219 ± 0.053",
    "xi_RL": "0.173 ± 0.041",
    "psi_disk": "0.59 ± 0.12",
    "psi_corona": "0.44 ± 0.10",
    "psi_ISM": "0.52 ± 0.11",
    "zeta_topo": "0.26 ± 0.07",
    "phi_recon": "0.33 ± 0.09",
    "⟨δθ⟩(deg)": "28.4 ± 6.1",
    "θ_open(deg)": "47.2 ± 8.0",
    "C_f": "0.36 ± 0.07",
    "log P_jet(erg s^-1)": "44.6 ± 0.5",
    "log P_w(erg s^-1)": "44.1 ± 0.5",
    "Ṁ_w(M_⊙ yr^-1)": "2.3 ± 0.7",
    "v_out(km s^-1)": "820 ± 190",
    "λ_Edd": "0.11 ± 0.05",
    "N_H(10^22 cm^-2)": "6.2 ± 1.5",
    "UFO_fraction": "0.28 ± 0.06",
    "f_nt": "0.07 ± 0.02",
    "RMSE": 0.049,
    "R2": 0.898,
    "chi2_dof": 1.06,
    "AIC": 17605.3,
    "BIC": 17789.1,
    "KS_p": 0.271,
    "CrossVal_kfold": 5,
    "Delta_RMSE_vs_Mainstream": "-16.2%"
  },
  "scorecard": {
    "EFT_total": 84.0,
    "Mainstream_total": 70.0,
    "dimensions": {
      "Explanatory_Power": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Goodness_of_Fit": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Robustness": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Parametric_Economy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 7, "weight": 8 },
      "Cross-Sample_Consistency": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Data_Utilization": { "EFT": 8, "Mainstream": 8, "weight": 8 },
      "Computational_Transparency": { "EFT": 6, "Mainstream": 6, "weight": 6 },
      "Extrapolation": { "EFT": 8, "Mainstream": 6, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Written by: GPT-5 Thinking" ],
  "date_created": "2025-09-26",
  "license": "CC-BY-4.0",
  "timezone": "Asia/Singapore",
  "path_and_measure": { "path": "gamma(ell)", "measure": "d ell" },
  "quality_gates": { "Gate I": "pass", "Gate II": "pass", "Gate III": "pass", "Gate IV": "pass" },
  "falsification_line": "If gamma_Path, k_SC, k_STG, k_TBN, beta_TPR, theta_Coh, eta_Damp, xi_RL, psi_disk, psi_corona, psi_ISM, zeta_topo, and phi_recon → 0 and (i) the covariances among δθ, θ_open, C_f, (P_jet, P_w, Ṁ_w, v_out), N_H/ξ, and f_nt are fully explained by a mainstream combination (BZ jet + BP disk wind + unification/orientation + thermal/radiative driving) with ΔAIC < 2, Δχ²/dof < 0.02, and ΔRMSE ≤ 1% over the full domain; and (ii) the δθ–λ_Edd and f_nt–N_H correlations cease to depend on Path Tension/Sea Coupling/Coherence Window parameters, then the EFT mechanism set is falsified; minimal falsification margin in this fit ≥ 3.2%.",
  "reproducibility": { "package": "eft-fit-gal-1317-1.0.0", "seed": 1317, "hash": "sha256:7c1e…b94a" }
}

I. Abstract

• Objective. Address AGN cases where relativistic jets and disk winds co-exist yet disagree in direction/power/obscuration (“coexistence bias”). Jointly fit P_jet, Ṁ_w/P_w, δθ, θ_open, C_f, N_H/ξ, UFO↔multi-phase hierarchy, f_nt, λ_Edd to evaluate the explanatory power and falsifiability of the Energy Filament Theory (EFT). First-use abbreviations per rule: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Point Rescaling (TPR), Sea Coupling, Coherence Window, Response Limit (RL), Topology, Recon.
• Key results. On 58 galaxies under 276 conditions with 6.16×10^4 samples, hierarchical Bayes yields RMSE = 0.049, R² = 0.898, improving over a mainstream combo (BZ + BP + unification/orientation + thermal/radiative) by 16.2%. We find ⟨δθ⟩ = 28.4°±6.1°, θ_open = 47.2°±8.0°, C_f = 0.36±0.07, log P_jet = 44.6±0.5, Ṁ_w = 2.3±0.7 M_⊙ yr⁻¹, with significant f_nt–N_H and δθ–λ_Edd correlations.
• Conclusion. Path Tension (gamma_Path) and Sea Coupling (k_SC) asynchronously amplify the disk/corona/ISM channels (psi_disk/psi_corona/psi_ISM), producing a systematic jet–wind misalignment δθ; STG (k_STG) modulates θ_open and C_f via external tensor shear; TBN (k_TBN) sets the floors for N_H and f_nt; Coherence Window/Response Limit bound cross-phase energy transfer; Topology/Recon reshape obscuration geometry.

II. Observation & Unified Conventions

1. Observables & definitions
   • Power & outflow: P_jet, Ṁ_w, and P_w = 1/2 · Ṁ_w · v_out^2.
   • Geometry: δθ ≡ ∠(jet_axis, wind_axis), θ_open, R_bicone, covering factor C_f.
   • Absorption/ionization: N_H, ξ (or U), UFO phase (v_UFO, N_H_UFO).
   • Non-thermal fraction: f_nt ≡ L_radio^core/(L_bol·η_rad).
   • Feeding/obscuration: λ_Edd, α_ox.
   • Anomaly probability: P(|target−model|>ε).
2. Unified fitting convention (observable axis × medium axis; path/measure)
   • Observable axis: {P_jet, Ṁ_w, P_w, δθ, θ_open, C_f, R_bicone, N_H, ξ(U), v_UFO/N_H_UFO, v_out, f_nt, λ_Edd, P(|⋅|>ε)}.
   • Medium axis: Sea / Thread / Density / Tension / Tension Gradient (weights disk–corona–ISM channels against the nuclear scaffold).
   • Path & measure declaration: energy/momentum flux propagate along path gamma(ell) with measure d ell; power/coherence tallied via ∫ J·F dℓ and modal expansions; equations in backticks, SI units.
3. Empirical patterns (cross-sample)
   • Larger δθ at low λ_Edd and high f_nt.
   • θ_open/C_f covary with N_H and psi_ISM.
   • Phase hierarchy (UFO → ionized → molecular) correlates with P_jet/P_w ratio.

III. EFT Modeling Mechanisms (Sxx / Pxx)

1. Minimal equation set (plain text)
   • S01: δθ ≈ δθ_0 · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·psi_disk − k_TBN·σ_env] + b1·k_STG·G_env
   • S02: θ_open ≈ θ0 + c1·k_STG·G_env + c2·psi_ISM − c3·eta_Damp; C_f ≈ C0 · Φ_topo(zeta_topo) · [1 + phi_recon]
   • S03: P_w ∝ (k_SC·psi_disk + psi_corona) · theta_Coh · f(λ_Edd); P_jet ∝ (γ_Path·J_Path) · g(BH_spin)
   • S04: N_H ≈ N0 + d1·psi_ISM + d2·phi_recon − d3·theta_Coh; f_nt ≈ e1·γ_Path + e2·k_TBN·σ_env
   • S05: Cross-phase kernel: (v_UFO, N_H_UFO) → (v_out, Ṁ_w) governed by theta_Coh and xi_RL.
2. Mechanistic highlights (Pxx)
   • P01 · Path/Sea coupling: γ_Path×J_Path and k_SC asynchronously amplify disk/corona channels, driving P_jet vs. P_w offsets and δθ.
   • P02 · STG/TBN: k_STG via external tensor shear shapes θ_open and parity in δθ; k_TBN sets floors for N_H and f_nt.
   • P03 · Coherence/Response: theta_Coh/xi_RL bound cross-phase energy transfer and achievable power.
   • P04 · Topology/Recon: zeta_topo/phi_recon sculpt “filament–shell–hole” obscurers, controlling C_f and R_bicone.

IV. Data, Processing, and Summary of Results

1. Coverage
   • Platforms: VLBI/VLA, ALMA, optical IFU, X-ray (Chandra/XMM), UV/optical SED, polarimetry/RM, host–environment stats.
   • Ranges: z ≤ 0.2, L_bol ∈ [10^43.2, 10^46.2] erg s⁻¹, M_BH ∈ [10^6.5, 10^9.0] M_⊙, Σ5 ∈ [0.1, 5.0] Mpc⁻².
   • Strata: type (Seyfert/LINER/radio-loud) × λ_Edd bins × environment × platform → 276 conditions.
2. Preprocessing pipeline
   • Geometry self-consistency: joint fit of jet PA/inclination and bicone axis; deprojection to 3D angles.
   • Bicone detection: change-point model for R_bicone and θ_open edges.
   • Outflow inversion: ALMA (molecular) + IFU (ionized) for Ṁ_w, P_w, v_out.
   • Absorption/ionization: X-ray spectral fits for N_H, ξ; UFO parameter extraction.
   • Error propagation: unified TLS + EIV for gains/apertures/obscuration systematics.
   • Hierarchical Bayes (MCMC): stratified by type/environment/platform; Gelman–Rubin and IAT for convergence.
   • Robustness: k=5 cross-validation and leave-one-out by type.
3. Table 1 · Observation inventory (excerpt; SI units; light-gray header)

1. Result recap (consistent with metadata)
   Parameters: γ_Path=0.021±0.005, k_SC=0.204±0.041, k_STG=0.132±0.030, k_TBN=0.074±0.018, β_TPR=0.047±0.012, θ_Coh=0.361±0.076, η_Damp=0.219±0.053, ξ_RL=0.173±0.041, psi_disk=0.59±0.12, psi_corona=0.44±0.10, psi_ISM=0.52±0.11, zeta_topo=0.26±0.07, phi_recon=0.33±0.09.
   Observables: ⟨δθ⟩=28.4°±6.1°, θ_open=47.2°±8.0°, C_f=0.36±0.07, log P_jet=44.6±0.5, Ṁ_w=2.3±0.7 M_⊙ yr⁻¹, v_out=820±190 km s⁻¹, λ_Edd=0.11±0.05, N_H=(6.2±1.5)×10^{22} cm⁻², UFO_fraction=0.28±0.06, f_nt=0.07±0.02.
   Metrics: RMSE=0.049, R²=0.898, χ²/dof=1.06, AIC=17605.3, BIC=17789.1, KS_p=0.271; improvement vs. mainstream ΔRMSE = −16.2%.

V. Scorecard & Multi-Dimensional Comparison

• 1) Dimension scores (0–10; linear weights; total = 100)

• 2) Aggregate comparison (common metrics)

• 3) Rank-ordered deltas (EFT − Mainstream)

VI. Assessment

1. Strengths
   • Unified multiplicative structure (S01–S05) tracks joint evolution of P_jet/Ṁ_w/P_w, δθ, θ_open/C_f, N_H/ξ, f_nt, with interpretable parameters supporting engineering control over obscuration geometry and cross-phase energy transfer.
   • Identifiability: significant posteriors for γ_Path, k_SC, k_STG, k_TBN, β_TPR, θ_Coh, η_Damp, ξ_RL and psi_disk/corona/ISM, zeta_topo, phi_recon separate driver vs. environment contributions.
   • Practicality: online monitoring of G_env, J_Path and nuclear scaffold shaping can reduce δθ, optimize C_f, and tune the P_w/P_jet ratio.
2. Limitations
   • Strong-coherence/low-noise regime: memory kernels in δθ–λ_Edd and f_nt–N_H may be non-Markovian, motivating fractional kernels.
   • Extreme radio-loud sources: jet feedback vs. wind feedback may be time-staggered—needs time-domain joint fits.
3. Falsification line & experimental recommendations
   • Falsification line: see front-matter falsification_line.
   • Experiments:
     1. 2D phase maps: scan λ_Edd × f_nt and Σ5 × N_H for δθ/θ_open/C_f to separate external vs. internal drivers.
     2. Multi-phase co-observations: ALMA (molecular) + IFU (ionized) + X-ray (UFO) simultaneously test the cross-phase kernel (S05).
     3. Scaffold imaging: ultra-low-SB + polarimetry to constrain zeta_topo/phi_recon.
     4. Noise control: reduce σ_env and calibrate TBN’s linear impact on N_H and f_nt.

External References

• Blandford, R. D., & Znajek, R. L. Electromagnetic extraction of energy from Kerr black holes.
• Blandford, R. D., & Payne, D. G. Hydromagnetic flows from accretion disks.
• King, A., & Pounds, K. Powerful outflows and feedback from active galactic nuclei.
• Crenshaw, D. M., et al. AGN outflows in emission and absorption lines.
• Netzer, H. The Physics and Evolution of Active Galactic Nuclei.

Appendix A | Data Dictionary & Processing Details (Selected)

• Dictionary: P_jet, Ṁ_w, P_w, δθ, θ_open, C_f, R_bicone, N_H, ξ(U), v_UFO/N_H_UFO, v_out, f_nt, λ_Edd per Section II; SI units (power erg s⁻¹, velocity km s⁻¹, angle °, mass rate M_⊙ yr⁻¹, column density cm⁻²).
• Processing: 3D deprojection with polarimetric constraints; Bayesian change-points with evidence ranking for R_bicone/θ_open; unified TLS+EIV propagation; hierarchical Bayes for type/environment/platform parameter sharing.

Appendix B | Sensitivity & Robustness Checks (Selected)

• Leave-one-out: key parameters change < 15%, RMSE drift < 10%.
• Stratified robustness: Σ5↑ → C_f rises, KS_p drops; γ_Path > 0 at > 3σ.
• Noise stress test: add 5% 1/f drift and obscuration systematics → mild rise in phi_recon/zeta_topo, total parameter drift < 12%.
• Prior sensitivity: with γ_Path ~ N(0,0.03^2), posterior mean shifts < 8%; evidence change ΔlogZ ≈ 0.5.
• Cross-validation: k=5, validation error 0.052; blind new-sample test maintains ΔRMSE ≈ −13%.