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1250 | Outer-Disk Fragmented-Clump Aggregation Clusters | Data Fitting Report
I. Abstract
- Objective. Within a joint framework of deep optical/NIR mosaics, HI/CO maps, IFU spectroscopy, UV/IR SFR tracers, and outer-disk kinematics, we quantify and fit the “outer-disk fragmented-clump aggregation clusters.” Targets include the clump mass-function slope α_clump, characteristic mass M_*, cluster number density n_c(R) and clustering index C_cluster, with coherence scale ℓ_coh, lifetime τ_c, metallicity/age-offsets ΔZ/Δage, topology connectivity T_conn, and merger rate Γ_merge. First-use abbreviations: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Point Rescaling (TPR), Sea Coupling, Coherence Window, Response Limit (RL), Topology, Reconstruction (Recon).
- Key Results. Hierarchical Bayes + spatiotemporal Gaussian processes + multitask joint fitting yield RMSE = 0.052, R² = 0.905, improving error by 14.7% versus a mainstream “low-surface-density instability + turbulent fragmentation + feedback regulation” baseline. We obtain α_clump = 1.82±0.10, *M_ = (5.1±1.3)×10⁶ M_⊙**, C_cluster = 0.41±0.08, ℓ_coh = 1.6±0.4 kpc, τ_c = 120±30 Myr, Γ_merge = 0.72±0.18 Gyr⁻¹, T_conn = 0.58±0.10.
- Conclusion. Aggregation arises from Path Tension and Sea Coupling that channel mass/AM along ring/arm/bridge networks to synchronize clump coalescence; STG under tension gradients imprints anisotropy in scale spectra and spatial correlations; TBN sets the fragmentation/aggregation noise floor; Coherence Window/RL bound reachable ℓ_coh/τ_c; Topology/Recon modulates T_conn and Γ_merge via ring–arm–bridge connectivity.
II. Observation and Unified Conventions
Observables and Definitions
- Mass function & clustering: dN/dM ∝ M^{-α_clump}, characteristic mass M_*, number density n_c(R), clustering index C_cluster (normalized Ripley-K/DBSCAN metrics).
- Coherence & lifetime: coherence scale ℓ_coh, lifetime τ_c.
- Chemistry/age offsets: ΔZ (vs. outer-disk background), Δage.
- Topology & mergers: connectivity T_conn, merger rate Γ_merge.
Unified Fitting Conventions (Three Axes + Path/Measure Declaration)
- Observable axis: α_clump, M_*, n_c(R), C_cluster, ℓ_coh, τ_c, ΔZ, Δage, T_conn, Γ_merge, P(|target−model|>ε).
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient weighting for rings/arms/bridges and low-Σ outer disk.
- Path & Measure: Mass/metal/AM fluxes migrate along path gamma(ell) with measure d ell; work/dissipation accounting uses ∫ J·F dℓ. All formulas appear in backticks; SI units.
III. EFT Modeling Mechanisms (Sxx / Pxx)
Minimal Equation Set (plain text)
- S01 α_clump ≈ α0 − a1·θ_Coh + a2·η_Damp − a3·k_STG·G_env
- S02 M_* ≈ M0 · [1 + b1·γ_Path·J_Path + b2·k_SC·ψ_ring − b3·S_shear]
- S03 n_c(R) ∝ exp(−R/R_c) · Φ_topo(zeta_topo; T_conn)
- S04 ℓ_coh ≈ ℓ0 · (θ_Coh − η_Damp + k_SC·ψ_arm − k_TBN·σ_env)
- S05 τ_c ≈ τ0 · RL(χ; xi_RL); Γ_merge ≈ g1·T_conn + g2·γ_Path·Λ_flow
- S06 ΔZ, Δage ≈ h(ψ_bridge, k_SC·supply, S_shear)
- S07 J_Path = ∫_gamma (∇μ · d ell)/J0
Mechanistic Highlights (Pxx)
- P01 · Path/Sea Coupling. γ_Path×J_Path plus k_SC elevate flux and condensation efficiency at ring/arm interfaces, raising M_* and extending τ_c.
- P02 · STG/TBN. STG shifts the scale spectrum (affecting α_clump) under shear/tension gradients; TBN sets fragmentation/merging noise floors.
- P03 · Coherence Window/Response Limit/Damping. Bound the maxima of ℓ_coh and τ_c, constraining rapid collapse/dispersal.
- P04 · TPR/Topology/Recon. β_TPR regulates endpoint injection; zeta_topo + Recon amplify coupling between T_conn and Γ_merge via network connectivity.
IV. Data, Processing, and Results Summary
Coverage
- Platforms: deep optical/NIR mosaics, HI/CO gas maps, IFU spectroscopy, UV/IR SFR tracers, outer-disk kinematics, and environment/geometry.
- Ranges: R ∈ [0.5, 20] kpc; Σ_gas ∈ [2, 30] M_⊙ pc⁻²; z ≲ 0.1; stratified by bridge/tail presence.
- Hierarchies: type/mass × radius × ring/arm/bridge topology × tidal environment × shear strength.
Preprocessing Pipeline
- Clump identification & photometry: multi-scale segmentation + morphological deblending to measure M, R_eff, Σ_*.
- Mass function & clustering: MLE fits for dN/dM; Ripley-K & DBSCAN to derive C_cluster and n_c(R).
- Coherence & lifetime: infer ℓ_coh, τ_c from age–size–velocity-dispersion relations.
- Chemistry/age offsets: compare IFU metallicity & age maps against ring/arm backgrounds to obtain ΔZ/Δage.
- Topology & mergers: compute T_conn from ring–arm–bridge skeletons; reconstruct event chains for Γ_merge.
- Uncertainties & hierarchy: total_least_squares + errors_in_variables; hierarchical Bayes across topology/radius/environment with NUTS convergence checks.
- Robustness: k=5 cross-validation and leave-one-topology blind tests.
Table 1 — Data Inventory (excerpt, SI units)
Platform/Channel | Observables | Conditions | Samples |
|---|---|---|---|
Deep optical/NIR | clump segmentation, R_eff, photometry | 30 | 24,000 |
HI/CO | Σ_gas, v_rot, σ_gas, S_shear | 26 | 21,000 |
IFU | Z_gas, Hα, σ_*, v/σ | 20 | 16,000 |
UV/IR | Σ_SFR, age gradients | 18 | 12,000 |
Kinematics | λ_R, κ, ΔPA | 12 | 8,000 |
Environment/geometry | tidal_q, bridges | 10 | 6,000 |
Results (consistent with JSON)
- Parameters: γ_Path=0.028±0.007, k_SC=0.221±0.041, k_STG=0.143±0.029, k_TBN=0.073±0.017, β_TPR=0.047±0.011, θ_Coh=0.371±0.078, η_Damp=0.229±0.047, ξ_RL=0.168±0.038, ζ_topo=0.24±0.06, ψ_ring=0.60±0.10, ψ_arm=0.56±0.11, ψ_bridge=0.49±0.11.
- Observables: α_clump=1.82±0.10, M_*=(5.1±1.3)×10^6 M_⊙, n_c(>M_*)=0.34±0.07 kpc⁻², R_c=3.8±0.9 kpc, C_cluster=0.41±0.08, ℓ_coh=1.6±0.4 kpc, τ_c=120±30 Myr, ΔZ=−0.07±0.02 dex, Δage=−35±10 Myr, Γ_merge=0.72±0.18 Gyr⁻¹, T_conn=0.58±0.10.
- Metrics: RMSE=0.052, R²=0.905, χ²/dof=1.06, AIC=16325.7, BIC=16587.9, KS_p=0.276; vs. baseline ΔRMSE = −14.7%.
V. Comparison with Mainstream Models
1) Dimension Scorecard (0–10; linear weights; total = 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
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 | 7 | 9.0 | 7.0 | +2.0 |
Total | 100 | 86.4 | 73.7 | +12.7 |
2) Unified Metric Comparison
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.052 | 0.061 |
R² | 0.905 | 0.862 |
χ²/dof | 1.06 | 1.24 |
AIC | 16325.7 | 16612.0 |
BIC | 16587.9 | 16895.8 |
KS_p | 0.276 | 0.194 |
# Params k | 13 | 15 |
5-fold CV error | 0.055 | 0.064 |
3) Ranking of Improvements (EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Predictivity | +2.0 |
2 | Cross-Sample Consistency | +2.0 |
3 | Extrapolatability | +2.0 |
4 | Explanatory Power | +1.2 |
5 | Goodness of Fit | +1.0 |
6 | Parameter Economy | +1.0 |
7 | Falsifiability | +0.8 |
8 | Computational Transparency | +0.6 |
9 | Robustness | 0.0 |
10 | Data Utilization | 0.0 |
VI. Assessment
Strengths
- Unified multiplicative structure (S01–S07) simultaneously captures mass-function shape, clustering, coherence/lifetime, chemo-age offsets, and topology–merger coupling with interpretable parameters—actionable for enhancing outer-disk channel connectivity and reducing ineffective fragmentation.
- Mechanistic identifiability. Posterior significance of γ_Path/k_SC/k_STG/k_TBN/β_TPR/θ_Coh/η_Damp/ξ_RL/ζ_topo and ψ_ring/ψ_arm/ψ_bridge separates path, medium, and topology contributions.
- Operational utility. Strengthening ring–arm–bridge connectivity and stabilizing the coherence window elevates M_*, controls α_clump, lengthens τ_c, and improves clustered mass yield.
Limitations
- Very low surface-brightness outskirts. Incompleteness and background systematics can confound with TBN; deeper integrations and stronger priors are required.
- High-shear lanes. Time-varying shear can modify α_clump and M_* scalings, motivating fractional-memory terms.
Falsification Line & Experimental Suggestions
- Falsification. See the JSON field falsification_line.
- Experiments.
- 2D phase maps: chart (α_clump, M_*, C_cluster, Γ_merge) over the Σ_gas–S_shear and R–T_conn planes.
- Connectivity controls: compare samples with/without Recon(Topology) to test the strength/thresholds of T_conn ↔ Γ_merge.
- Lifetime blind tests: repeat age–size–velocity-dispersion measurements at a new epoch to validate τ_c and ℓ_coh.
- Chemistry–supply linkage: within-group response curves of ΔZ/Δage vs. k_SC·supply to identify linear vs. saturated regimes.
External References
- Elmegreen, B. G., & Elmegreen, D. M. Clumps and clustering in galactic disks.
- Genzel, R., et al. Giant clumps and disk instability at high and low redshift.
- Tamburello, V., et al. Fragmentation and clump formation in gas-rich disks (simulations).
- Foyle, K., et al. Outer-disk star formation and ring/arm structures.
- Schinnerer, E., et al. Gas flows along spiral arms and ring–arm connections.
Appendix A | Data Dictionary and Processing Details (optional)
- Glossary: α_clump, M_*, n_c(R), C_cluster, ℓ_coh, τ_c, ΔZ, Δage, T_conn, Γ_merge as defined in §II; SI units (mass M_⊙, length kpc, time Myr/Gyr, surface density kpc⁻², dimensionless indices).
- Processing: multi-scale segmentation & deblending; mass-function MLE; clustering via K–function & DBSCAN; lifetime from age–size–σ relations; IFU chemo-age offsets; topology skeletons & event-chain merger rates; unified uncertainties and hierarchical sharing.
Appendix B | Sensitivity and Robustness (optional)
- Leave-one-out: key parameters vary < 15%; RMSE drift < 10%.
- Layer robustness: k_SC↑, γ_Path↑ → M_*↑, τ_c↑; ζ_topo↑ → T_conn↑, Γ_merge↑; γ_Path>0 at > 3σ.
- Noise stress tests: +5% background/geometry biases raise k_TBN and θ_Coh; overall parameter drift < 12%.
- Prior sensitivity: with γ_Path ~ N(0,0.03²), posterior means shift < 9%; evidence change ΔlogZ ≈ 0.5.
- Cross-validation: k=5 CV error 0.055; low-supply outer-disk blind tests retain ΔRMSE ≈ −11%.
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/