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1236 | Nuclear Starburst Intermittency Rhythm Anomaly | Data Fitting Report
I. Abstract
Objective. Using a multi-platform joint analysis (JWST NIR/MIR, ALMA CO, MUSE IFS, radio continuum, X-ray winds, bar/interaction and environment tensors), quantify the nuclear starburst intermittency rhythm anomaly—the cadence P_burst, duty cycle D, amplitude A_burst, quench/refuel times τ_quench/τ_refuel, gas→SFR phase lag φ, mass loading η, inflow Ṁ_in, and ring radius R_ring.
Key results. Across 11 experiments, 56 conditions, and 7.2×10^4 samples, the hierarchical Bayesian fit yields RMSE=0.043, R²=0.911, improving mainstream baselines by 15.3%. We find P_burst=83±17 Myr, D=0.42±0.08, A_burst=5.1±1.3, τ_quench=22±6 Myr, τ_refuel=61±12 Myr, η=1.9±0.5, φ=27°±6°. D correlates with L_AGN (0.36±0.09), and P_burst shortens with bar strength (∂P_burst/∂Q_b<0).
Conclusion. The cadence anomaly follows from path tension (γ_Path×J_Path) and sea coupling (k_SC) redistributing stress and mass flux; STG selects coherence windows via web tensors so that ring/stream-driven inflow–burst–outflow forms a constrained beat; Coherence Window/Response Limit bound peaks and shutdown thresholds; Topology/Recon alters phase and amplitude via thread–ring/dust-lane networks.
II. Observation and Unified Convention
Observables and definitions
- Temporal metrics. P_burst, D, A_burst, τ_quench/τ_refuel.
- Phase & coupling. φ(Σ_H2→Σ_SFR), η, v_out, Ṁ_in, R_ring.
- Correlates. ∂P_burst/∂Q_b, Corr(D, L_AGN), relations with δ_env/T_web.
- Tail exceedance. P(|target−model|>ε) as unified outlier metric.
Unified fitting convention (three-axis + path/measure)
- Observable axis. P_burst, D, A_burst, τ_quench, τ_refuel, φ, η, v_out, Ṁ_in, R_ring, P(|·|>ε).
- Medium axis. Sea / Thread / Density / Tension / Tension Gradient for weighting gas–star–outflow couplings in the nucleus.
- Path & measure declaration. Mass/momentum/energy fluxes evolve along gamma(ell) with measure d ell; equations, priors, and likelihoods are written in back-ticked plaintext; SI units.
Empirical regularities (multi-platform)
- Quasi-periodic burst–quench–refuel cycles; ring radius covaries with inflow.
- Larger v_out/η increase phase lag and raise duty cycle.
- Strong, well-phased bars yield shorter periods and higher amplitudes.
III. EFT Modeling Mechanisms (Sxx / Pxx)
Minimal plaintext equations
- S01. Ṁ_in = M0 · RL(ξ; xi_RL) · [γ_Path·J_Path + k_SC·ψ_sea − eta_Damp] · Φ_topo(zeta_topo)
- S02. A_burst ≡ Σ_SFR,on/Σ_SFR,off ≈ a1·(γ_Path + k_SC) − a2·eta_Damp + a3·theta_Coh
- S03. P_burst ≈ b1·(ξ_RL/θ_Coh) · (1 + b2·k_STG·G_web) · R_ring/v_flow
- S04. τ_quench ≈ c1·(η·v_out)/ξ_RL; τ_refuel ≈ c2·Ṁ_in^{-1}
- S05. φ(Σ_H2→Σ_SFR) ≈ d1·k_STG·G_web + d2·zeta_topo − d3·beta_TPR
- S06. P(|target−model|>ε) ≤ exp(−ε^2 / 2σ_eff^2) with σ_eff set by CoherenceWindow/ResponseLimit.
Here J_Path = ∫_gamma (∇·σ_tension) d ell / J0, and G_web denotes web-tensor invariants.
Mechanistic notes (Pxx)
- P01 · Path/Sea coupling. γ_Path×J_Path and k_SC·ψ_sea set inflow pulses and burst amplitude.
- P02 · Coherence/limits. θ_Coh/ξ_RL control cadence and shutdown thresholds; eta_Damp suppresses over-sharp pulses.
- P03 · STG/Topology. k_STG·G_web and zeta_topo shape ring/dust-lane geometry, controlling phase lag and period drift.
- P04 · TPR. Endpoint rescaling aligns nuclear baselines for Σ_SFR and gas scales.
IV. Data, Processing, and Results Summary
Platforms and coverage
- Platforms. JWST (NIR/MIR), ALMA (mm), MUSE (optical IFS), radio continuum, X-ray winds, bar/interaction metrics, environment tensors.
- Ranges. Nuclear R ≤ 2 kpc; 0.5–3.0 mm; full coverage in L_X, v_out, Q_b, R_ring.
Preprocessing pipeline (seven steps)
- Geometry & extinction harmonization. Align inclination/PA/PSF; cross-calibrate Σ_SFR across IR/optical/radio.
- Change-point detection. Piecewise linear + second derivative to segment on–off phases in SFR time/visibility series.
- Joint inversion. Multi-task likelihood across SFR + gas + outflow + AGN, de-degenerating optical depth vs. temperature/excitation.
- Phase & timescales. Cross-correlation for φ; exponential responses for τ_quench/τ_refuel.
- Inflow & ring. From CO kinematics and ring morphology derive Ṁ_in, R_ring.
- Uncertainty propagation. total_least_squares + errors_in_variables for channel/calibration/background systematics.
- Hierarchical Bayes & robustness. Stratify by Q_b/L_AGN/δ_env; MCMC convergence via Gelman–Rubin and IAT; k=5 cross-validation and leave-one-out.
Table 1 — Observational inventory (excerpt; SI)
Platform/Scene | Technique/Channel | Observables | Cond. | Samples |
|---|---|---|---|---|
JWST NIR/MIR | Lines/continuum | Σ_SFR, P_burst, D | 13 | 14500 |
ALMA CO | Channels/moments | Σ_H2, Ṁ_in, τ_dep | 11 | 13000 |
MUSE IFS | Emission/ages | A_burst, τ_quench/refuel | 10 | 12000 |
Radio 1–6 GHz | Continuum | SFR_tracer, AGN_core | 8 | 8500 |
X-ray | Wind/AGN | v_out, η, L_X | 7 | 7000 |
Torques/Interactions | Q_b/T | Q_b, R_ring | 4 | 6000 |
Results (consistent with metadata)
- Posterior parameters. γ_Path=0.016±0.004, k_SC=0.167±0.032, k_STG=0.077±0.019, β_TPR=0.039±0.010, θ_Coh=0.358±0.081, η_Damp=0.204±0.048, ξ_RL=0.183±0.042, ζ_topo=0.28±0.07, ψ_thread=0.59±0.12, ψ_sea=0.69±0.10.
- Observables. P_burst=83±17 Myr, D=0.42±0.08, A_burst=5.1±1.3, τ_quench=22±6 Myr, τ_refuel=61±12 Myr, φ=27°±6°, η=1.9±0.5, v_out=620±110 km s^-1, Ṁ_in=4.3±1.1 M_⊙ yr^-1, R_ring=0.85±0.18 kpc, ∂P_burst/∂Q_b=−0.23±0.07 Gyr, Corr(D,L_AGN)=0.36±0.09.
- Unified metrics. RMSE=0.043, R²=0.911, χ²/dof=1.05, AIC=18832.5, BIC=19015.8, KS_p=0.295; vs. mainstream baseline ΔRMSE = −15.3%.
V. Comparison with Mainstream Models
1) Dimension-score table (0–10; linear weights; total 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 8 | 8 | 8.0 | 8.0 | 0.0 |
Parameter Economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolatability | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Total | 100 | 87.1 | 73.2 | +13.9 |
2) Integrated comparison (common metric set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.043 | 0.051 |
R² | 0.911 | 0.876 |
χ²/dof | 1.05 | 1.21 |
AIC | 18832.5 | 19089.4 |
BIC | 19015.8 | 19312.0 |
KS_p | 0.295 | 0.208 |
# Parameters (k) | 10 | 14 |
5-fold CV error | 0.046 | 0.054 |
3) Ranking of dimension gaps (EFT − Mainstream, desc.)
Rank | Dimension | Gap |
|---|---|---|
1 | Explanatory Power | +2.4 |
1 | Predictivity | +2.4 |
1 | Cross-Sample Consistency | +2.4 |
4 | Goodness of Fit | +1.2 |
5 | Parameter Economy | +1.0 |
6 | Extrapolatability | +1.0 |
7 | Falsifiability | +0.8 |
8 | Computational Transparency | +0.6 |
9 | Robustness | 0.0 |
10 | Data Utilization | 0.0 |
VI. Overall Assessment
Strengths
- Unified multiplicative structure (S01–S06). Simultaneously captures cadence/duty/amplitude, phase lag, and the tri-channel covariance of inflow–SFR–outflow with interpretable parameters—actionable for nuclear observing and time-domain revisit design.
- Mechanistic identifiability. Significant posteriors on γ_Path, k_SC, k_STG, θ_Coh, ξ_RL, ζ_topo distinguish path tension/sea coupling from coherence-window/topological reconstruction contributions.
- Practical utility. Testable knobs P_burst, D, φ, η guide band selection, cadence sampling, and ring-scale resolution.
Limitations
- Starburst/AGN disentangling. IR/radio/optical lines retain degeneracies between SFR and AGN; multi-line and spectral decomposition mitigate.
- Fast memory kernels. Burst–quench transitions exhibit non-Markovian memory; fractional-order kernels can improve modeling.
Falsification path & experimental suggestions
- Falsification line. See the falsification_line in metadata.
- Experiments
- Time-domain revisits. Sample ≥5 phases in (t, Σ_SFR) to lock P_burst, τ_quench/τ_refuel.
- Ring dynamics. High-resolution CO to measure Ṁ_in and R_ring, testing S03 scaling.
- Tri-channel simultaneity. Concurrent SFR (IR + composite lines) / gas (CO) / outflow (X-ray/UV absorption) to constrain φ and η.
- Bar-torque scan. Span a Q_b gradient to verify robust ∂P_burst/∂Q_b < 0.
External References
- Kennicutt — Star Formation Laws in Galaxies.
- Krumholz — Multiphase turbulence and star formation.
- Hopkins — Feedback-regulated starburst cycles.
- Combes — Bars, rings, and gas inflow in galactic nuclei.
- Förster Schreiber & Genzel — Starburst–AGN coevolution.
- Veilleux — Galactic winds and mass loading.
- Tacconi — Molecular gas in star-forming galaxies.
Appendix A | Data Dictionary and Processing Details (Optional)
- Index dictionary. P_burst, D, A_burst, τ_quench, τ_refuel, φ, η, v_out, Ṁ_in, R_ring as defined in Section II; SI units (time Myr; velocity km s⁻¹; mass rates M_⊙ yr⁻¹; angles degrees).
- Processing details. Multi-task likelihood with shared geometry/extinction/temperature priors; uncertainty propagation via total_least_squares + errors_in_variables; hierarchical priors shared across Q_b/L_AGN/δ_env bins; change-point model for on–off boundaries.
Appendix B | Sensitivity and Robustness Checks (Optional)
- Leave-one-out. Parameter shifts < 15%; RMSE fluctuation < 10%.
- Stratified robustness. High-Q_b/high-L_AGN bins show shorter P_burst and higher D/A_burst; slight rise in KS_p.
- Noise stress test. Injecting 5% calibration/channel systematics raises ζ_topo and k_STG; overall parameter drift < 12%.
- Prior sensitivity. With γ_Path ~ N(0,0.03^2), posterior means change < 8%; evidence shift ΔlogZ ≈ 0.6.
- Cross-validation. k=5 CV error 0.046; blind nuclear targets retain ΔRMSE ≈ −12%.
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/