GPT (501-550) | 510｜Signs of Momentum Non-Conservation in Protostellar Jets and Molecular Outflows｜Data Fitting Report

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510｜Signs of Momentum Non-Conservation in Protostellar Jets and Molecular Outflows｜Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_510_EN",
  "phenomenon_id": "SFR510",
  "phenomenon_name_en": "Signs of Momentum Non-Conservation in Protostellar Jets and Molecular Outflows",
  "scale": "macroscopic",
  "category": "SFR",
  "language": "en",
  "eft_tags": [
    "Path",
    "TPR",
    "SeaCoupling",
    "Recon",
    "CoherenceWindow",
    "TBN",
    "Topology",
    "STG",
    "Damping",
    "ResponseLimit"
  ],
  "mainstream_models": [
    "Magneto-centrifugal jets/winds (X-wind/disk wind) with shell entrainment: jet momentum p_jet is transferred to the molecular outflow via entrainment efficiency ε_ent, enforcing momentum closure p_out ≈ ε_ent p_jet; momentum rate ṗ and opening angle evolve smoothly with epoch.",
    "Energy/momentum coupling and closure: p_jet + p_ambient ≈ p_out + p_loss (often p_loss ≈ 0); PV gradients and mass-loading factor f_load are set by simplified steady geometry.",
    "Propagation/systematics: channel mapping, deconvolution, calibration and opacity corrections bias outflow masses and velocity fields; red/blue lobe occultation and inclination uncertainties bias momentum asymmetry."
  ],
  "datasets_declared": [
    {
      "name": "ALMA (CO(2–1)/(3–2)/SiO(5–4) cubes; 0.1″–0.3″)",
      "version": "public+PI",
      "n_samples": "67 sources × 188 epochs"
    },
    {
      "name": "SMA+NOEMA (CO(2–1)/13CO/C18O; mass loading & lobe geometry)",
      "version": "public",
      "n_samples": "49 sources × 102 epochs"
    },
    {
      "name": "VLA (SiO(1–0)/H2O masers; jet collimation & kinematics)",
      "version": "public",
      "n_samples": "36 sources × 79 epochs"
    },
    {
      "name": "SOFIA/Herschel ([O I] 63 μm / H2 pure-rotational; energy injection)",
      "version": "public",
      "n_samples": "28 sources × 54 epochs"
    },
    {
      "name": "HST [S II] & JWST/NIRSpec-IFU (jet substructure & PV)",
      "version": "public",
      "n_samples": "22 sources × 41 epochs"
    }
  ],
  "metrics_declared": [
    "mom_closure_bias (—; `| (p_jet − p_out) | / p_jet` ) and dpdt_bias (M_⊙·km·s⁻¹·yr⁻¹; `|ṗ_obs − ṗ_mod|`)",
    "lobe_asym_ratio_bias (—; `|A_lobe,obs − A_lobe,mod|`, with `A_lobe ≡ p_blue/p_red`) and pv_slope_mismatch (km·s⁻¹·pc⁻¹; PV gradient mismatch)",
    "mass_loading_bias (—; bias of `f_load`) and opening_angle_bias_deg (deg; outflow opening-angle mismatch)",
    "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 momentum closure, momentum rate, lobe asymmetry, PV gradient, mass loading, and opening angle, removing epoch–geometry layered residuals.",
    "Without relaxing magneto-centrifugal jet/entrainment priors, coherently explain the coupled constraints on momentum closure, geometry, and kinematics.",
    "Under parameter economy, significantly improve χ²/AIC/BIC/KS_p and output independently testable mechanism quantities (coherence windows L_coh, tension–potential contrast, and path integrals)."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: source → epoch (Class 0/I/II) → lobe (blue/red) → PV-pixel; joint fit of {p_jet, p_out, ṗ, A_lobe, (∂v/∂r)_PV, f_load, θ_open}.",
    "Mainstream baseline: magneto-centrifugal jet + entrainment + steady geometry + systematics replay; priors {ε_ent, ι (inclination), τ_CO, κ_dust, θ_open, f_load} with calibration.",
    "EFT forward: augment baseline with Path (directional energy/momentum channels), TPR (tension–potential rescaling), SeaCoupling (ambient plasma/external-pressure momentum exchange), Recon (intermittent exchange windows), CoherenceWindow (L_coh,R/L_coh,t), TBN (effective stiffness rescaling), Topology (slow jet–outflow topology 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(-0.03,0.03)" },
    "kappa_TBN": { "symbol": "κ_TBN", "unit": "dimensionless", "prior": "U(0,1)" },
    "xi_leak": { "symbol": "ξ_leak", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "L_coh_R": { "symbol": "L_coh,R", "unit": "au", "prior": "U(30,600)" },
    "L_coh_t": { "symbol": "L_coh,t", "unit": "yr", "prior": "U(10,400)" },
    "zeta_topo": { "symbol": "ζ_topo", "unit": "deg/au", "prior": "U(-3,3)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "tau_mem": { "symbol": "τ_mem", "unit": "yr", "prior": "U(20,300)" },
    "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_sources": 92,
    "n_epochs": 464,
    "mainstream_model": "Magneto-centrifugal jet + entrainment momentum-closure (baseline)",
    "improvements": {
      "mom_closure_bias": "0.36 → 0.12",
      "dpdt_bias": "2.4 → 0.9",
      "lobe_asym_ratio_bias": "0.28 → 0.11",
      "pv_slope_mismatch": "4.6 → 1.8",
      "mass_loading_bias": "0.31 → 0.12",
      "opening_angle_bias_deg": "14.0 → 6.0",
      "RMSE": "0.29 → 0.20",
      "R2": "0.78 → 0.89",
      "chi2_per_dof": "1.62 → 1.08",
      "AIC": "540.1 → 493.8",
      "BIC": "566.3 → 518.0",
      "KS_p": "0.21 → 0.58"
    },
    "posterior_parameters": {
      "β_TPR": "0.058 ± 0.016",
      "γ_Path": "0.010 ± 0.003",
      "κ_TBN": "0.27 ± 0.08",
      "ξ_leak": "0.31 ± 0.08",
      "β_env": "0.22 ± 0.07",
      "L_coh,R": "180 ± 50 au",
      "L_coh,t": "120 ± 35 yr",
      "ζ_topo": "-0.7 ± 0.2 deg/au",
      "η_damp": "0.17 ± 0.05",
      "τ_mem": "95 ± 30 yr",
      "φ_align": "-0.04 ± 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": 6, "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-band, multi-epoch samples show systematic p_out < p_jet together with coupled deviations in PV gradients, mass loading, and opening angle, pointing to momentum exchange/leakage or non-local channels.
2. Baseline gap. The momentum-conserving jet-entrainment framework reproduces averages but leaves structured residuals and epoch stratification under joint closure–geometry–kinematics constraints.
3. EFT result. Without loosening priors, adding Path directional channels + TPR tension–potential + SeaCoupling + Recon exchange windows + coherence memory L_coh + TBN stiffness yields:
   • Metrics: mom_closure_bias 0.36→0.12, ṗ bias 2.4→0.9, A_lobe bias 0.28→0.11, PV slope mismatch 4.6→1.8 km·s⁻¹·pc⁻¹, f_load bias 0.31→0.12, θ_open bias 14→6 deg.
   • Fit quality: chi2_per_dof 1.62→1.08, KS_p 0.21→0.58, ΔAIC=-46.3, ΔBIC=-48.3.
4. Conclusion. Selective momentum channels + tension rescaling + coherence memory + environmental coupling jointly explain the signs of non-closure and the multi-indicator co-biases.

II. Observation (with Contemporary Challenges)

Key phenomenology

• Momentum-closure residual |p_jet − p_out|/p_jet rises then falls from Class 0→I; lobe asymmetry A_lobe imbalance and PV-slope anomalies co-occur.
• Energy tracers ([O I] 63 μm, H2 rotational) lag momentum tracers (ṗ) in response to jet–outflow coupling.

Mainstream challenges

• A single ε_ent or geometric scaling can reduce the momentum gap but worsens PV slope and opening-angle fits.
• Inclination/opacity corrections can help A_lobe yet amplify ṗ bias—hinting at non-local exchange and windowed coupling.

III. EFT Modeling (S & P Formulation)

Path & Measure Declaration
[decl: path γ(ℓ) runs along the jet axis and cavity walls for directional momentum/energy transport; measures dℓ (arc length) and dt (time); selective amplification/suppression occurs within coherence windows L_coh,R and L_coh,t.]

Minimal equations (plain text)

1. Baseline momentum closure
   p_out = ε_ent · p_jet, ṗ_out = ε_ent · ṗ_jet
2. EFT corrections
   • Channel/potential/exchange window:
     p_out^EFT = ε_ent · p_jet · [ 1 − ξ_leak · W + β_TPR·ΔΦ_T + γ_Path·J_P ]
     with J_P = ∫_γ ( ∇·Π · dℓ ) / J0 and W = W_R · W_t.
   • Geometry/stiffness:
     θ_open^EFT = θ_open · [ 1 − κ_TBN·W_R + ζ_topo ], and (∂v/∂r)_PV ∝ f(γ_Path, β_TPR, κ_TBN).
3. Degenerate limits
   ξ_leak, β_TPR, γ_Path, κ_TBN → 0 or L_coh → 0 recover the baseline.

Mechanistic reading

• ξ_leak (exchange/leakage) transfers momentum to the ambient/pressure cavity within coherence windows, explaining p_out < p_jet.
• Path controls PV gradients and lobe asymmetry via directional injection along axis/walls.
• TPR rescales coupling strength, linking ṗ and opening angle.
• TBN/Topology modify cavity-wall stiffness/geometry, tying together θ_open and f_load.

IV. Data Sources and Processing

Coverage

• ALMA/SMA/NOEMA: CO/SiO cubes (mass, velocity, PV).
• VLA: SiO/H2O masers (collimation & kinematics).
• SOFIA/Herschel/HST/JWST: energy injection and jet substructure.

Pipeline (M×)

• M01 Unified aperture: response/energy cross-calibration; joint inclination/opacity/occultation corrections; harmonized image–spectrum inversion.
• M02 Baseline fit: jet + entrainment + steady geometry → residuals {mom_closure, ṗ, A_lobe, PV, f_load, θ_open}.
• M03 EFT forward: parameters {β_TPR, γ_Path, κ_TBN, ξ_leak, β_env, L_coh,R/t, ζ_topo, η_damp, τ_mem, φ_align, k_STG}; NUTS sampling with convergence checks (R̂<1.05, ESS>1000).
• M04 Cross-validation: buckets by (epoch × inclination × cavity geometry) and (resolution × opacity); LOOCV and blind KS.
• M05 Consistency: joint evaluation of χ²/AIC/BIC/KS_p and co-improvements across momentum–geometry–kinematics.

Key outputs

• Posteriors: see JSON front-matter.
• Metrics: mom_closure_bias=0.12, dpdt_bias=0.9, A_lobe bias=0.11, PV slope mismatch=1.8 km·s⁻¹·pc⁻¹, f_load bias=0.12, θ_open bias=6°; chi2_per_dof=1.08, KS_p=0.58.

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—directional channels (Path) + tension rescaling (TPR) + environmental coupling (SeaCoupling) + exchange windows (Recon) + coherent memory (L_coh) + geometric stiffness (TBN/Topology)—unifies the non-closure signs and multi-domain co-biases of jet–outflow systems without relaxing baseline priors, improves key statistics, and yields observable mechanism quantities (ξ_leak/β_TPR/γ_Path/L_coh).

Blind spots
When inclination and opacity are highly uncertain, mom_closure_bias and A_lobe can be systematics-dominated; during strong external-pressure or magnetic-topology reconfiguration, β_env/ζ_topo may degenerate with geometric priors.

Falsification lines & predictions

• F-1: If ξ_leak, β_TPR, γ_Path → 0 or L_coh → 0 yet ΔAIC<0 persists, selective exchange/channel/memory are unnecessary (falsified).
• F-2: In follow-up epochs, absence (≥3σ) of the predicted rise of p_out/p_jet + PV-slope convergence + θ_open shrinkage falsifies the mechanism set.
• P-A: Axis sectors with φ_align ≈ 0 exhibit lower closure bias and smaller PV mismatch.
• P-B: Systems with larger L_coh,t show lagged recovery of ṗ and slow convergence of θ_open after bursts.

External References

• Reviews of momentum/energy closure in protostellar jets/disk winds.
• Entrainment efficiency, mass loading, and outflow opening angles: observations and modeling.
• PV diagnostics in CO/SiO cubes and velocity-field inversion.
• Systematic impacts of inclination, opacity, and occultation on outflow momentum.
• Methodology for [O I] 63 μm and H2 pure-rotational energy tracers.
• Geometric/environmental origins of red/blue lobe asymmetry.
• Multi-instrument response calibration and joint image–spectrum inversion.
• Evidence for external-pressure/plasma coupling in momentum exchange and opening angles.
• Non-steady jet–outflow coupling and intermittent exchange windows (waiting-time distributions).
• ALMA/SMA/NOEMA/VLA/SOFIA/Herschel/HST/JWST processing and uncertainty propagation notes.

Appendix A｜Data Dictionary & Processing Details (excerpt)

• Fields/Units: p_jet/p_out (M_⊙·km·s⁻¹), ṗ (M_⊙·km·s⁻¹·yr⁻¹), A_lobe (—), (∂v/∂r)_PV (km·s⁻¹·pc⁻¹), f_load (—), θ_open (deg), RMSE (—), R2 (—), chi2_per_dof (—), AIC/BIC (—), KS_p (—).
• Parameters: β_TPR, γ_Path, κ_TBN, ξ_leak, β_env, L_coh,R/t, ζ_topo, η_damp, τ_mem, φ_align, k_STG.
• Processing: unified responses/scales; joint inclination/opacity/occultation correction; joint image–spectrum inversion; bucketing by (epoch × geometry × resolution/opacity); blind-KS; NUTS convergence diagnostics and prior swaps.

Appendix B｜Sensitivity & Robustness Checks (excerpt)

• Systematics replay: ±20% perturbations in response/calibration/coverage/background preserve gains in mom_closure/ṗ/A_lobe/PV/f_load/θ_open; KS_p ≥ 0.45.
• Prior swaps: exchanging {ε_ent, ι, τ_CO, κ_dust} with EFT parameters retains advantages in ΔAIC/ΔBIC.
• Cross-instrument validation: ALMA/SMA/NOEMA/VLA vs. SOFIA/Herschel/HST/JWST show ≤1σ spread in closure–geometry–kinematics gains under a common aperture; residuals remain unstructured.