GPT (451-500) | 500 | Overdense Branch Points in Fibrous Clouds | Data Fitting Report

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500 | Overdense Branch Points in Fibrous Clouds | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250911_SFR_500",
  "phenomenon_id": "SFR500",
  "phenomenon_name_en": "Overdense Branch Points in Fibrous Clouds",
  "scale": "macroscopic",
  "category": "SFR",
  "language": "en-US",
  "eft_tags": [
    "TensionGradient",
    "CoherenceWindow",
    "Path",
    "ModeCoupling",
    "Topology",
    "SeaCoupling",
    "Damping",
    "ResponseLimit",
    "STG",
    "Recon"
  ],
  "mainstream_models": [
    "Hierarchical fractal of filaments–fibers–cores: isothermal supersonic turbulence plus gravity explains filament skeletons and node statistics; branch density set by driving mix b and Mach statistics. It under-fits simultaneous excess in branch density and the joint biases in angle–thickness–spacing.",
    "Magnetization and anisotropic shear: B-field and shear tensor modulate fiber orientation and hub degree, producing hub–filament networks. Fits to heavy-tailed degree and branch-angle distributions remain unstable.",
    "Converging flows and shock topology: inflow and shock trains locally amplify node density but lack a unified cross-scale account of length, thickness, spacing and velocity convergence.",
    "Observational systematics: skeleton-extractor parameter dependence (Hessian/FilFinder/DisPerSE), LOS stacking, optical-depth/chemical layering, resolution and beam averaging bias branch density; cross-tracer harmonization is incomplete."
  ],
  "datasets_declared": [
    {
      "name": "Herschel Gould Belt / ATLASGAL (dust T / column; skeletons)",
      "version": "public",
      "n_samples": "~1.5×10^6 pixels"
    },
    {
      "name": "JCMT SCUBA-2 + BISTRO (850 μm + polarization; fiber orientation / B-field)",
      "version": "public",
      "n_samples": "~6.0×10^5 pixels"
    },
    {
      "name": "IRAM 30m / ALMA (N2H+/NH3/C18O; velocity convergence and thickness)",
      "version": "public",
      "n_samples": "~250 regions; ~1.8×10^6 pixels"
    },
    {
      "name": "GAS (GBT–NH3; T_kin / non-thermal)",
      "version": "public",
      "n_samples": "~1.0×10^5 sightlines"
    },
    {
      "name": "Planck 353 GHz polarization (large-scale coherence window)",
      "version": "public",
      "n_samples": "all-sky; coherence statistics"
    },
    {
      "name": "Gaia YSO density & ages (SFE contrast at nodes)",
      "version": "public",
      "n_samples": "~1.2×10^5 sources"
    }
  ],
  "metrics_declared": [
    "branch_density_bias_pc2 (pc^-2; bias of branch-point surface density)",
    "branch_angle_bias_deg (deg; bias of branch-angle distribution)",
    "hub_degree_bias (—; bias in node-degree distribution)",
    "branch_length_bias_pc (pc; bias of segment length)",
    "segment_thickness_bias_pc (pc; bias of cross-sectional thickness)",
    "spacing_bias_pc (pc; bias of node–node spacing)",
    "curvature_bias (—; bias in curvature statistics)",
    "vconv_bias_kmspc (km s^-1 pc^-1; axial velocity-convergence bias)",
    "psi_B_fiber_bias_deg (deg; bias of fiber–B-field misalignment)",
    "SFE_node_contrast_bias (—; SFE contrast at nodes vs. field)",
    "fractal_dim_bias (—; bias in spatial fractal dimension)",
    "KS_p_resid",
    "chi2_per_dof_joint",
    "AIC_delta_vs_baseline",
    "BIC_delta_vs_baseline",
    "R2_joint"
  ],
  "fit_targets": [
    "Under a unified aperture, quantify geometric–dynamical–star-formation signatures of ‘overdense branch points’ (density, angles, degree, length/thickness/spacing, curvature, velocity convergence, B-field orientation, SFE contrast, fractal D) and separate contributions from driving, shear–tension, and topology.",
    "Jointly compress `branch_density_bias_pc2/branch_angle_bias_deg/hub_degree_bias/branch_length_bias_pc/segment_thickness_bias_pc/spacing_bias_pc/curvature_bias/vconv_bias_kmspc/psi_B_fiber_bias_deg/SFE_node_contrast_bias/fractal_dim_bias`; increase `KS_p_resid/R2_joint` and decrease `chi2_per_dof_joint/AIC/BIC`.",
    "With parameter parsimony, deliver posteriors for `L_coh` (coherence window), `κ_TG` (tension-gradient rescaling), `μ_path` (path coupling), shear/orientation/inflow couplings, and branch-topology weight `ζ_branch`."
  ],
  "fit_methods": [
    "Hierarchical Bayes: cloud complex → subregion → skeleton segment → pixel/LOS; joint likelihood over dust/column skeletons, polarization orientations, line-velocity fields, and YSO density; unify beam averaging, projection and selection replay, and replay priors for skeleton parameters (threshold/min-length/smoothing).",
    "Mainstream baseline: isothermal turbulence + gravitational convergence + B-constrained orientation + shock trains; fit {branch density/angle/degree, length/thickness/spacing, curvature, velocity convergence, B–fiber angle, SFE contrast, fractal D}.",
    "EFT forward model: add TensionGradient (κ_TG), CoherenceWindow (L_coh), Path (μ_path), ModeCoupling (ξ_shear/ξ_align/ξ_flow), Topology (ζ_branch; branch-topology weight), SeaCoupling (f_sea), Damping (η_damp), ResponseLimit (P_cap, S_cap)."
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.7)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "L_coh_pc": { "symbol": "L_coh", "unit": "pc", "prior": "U(0.05,1.20)" },
    "xi_shear": { "symbol": "ξ_shear", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "xi_align": { "symbol": "ξ_align", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "xi_flow": { "symbol": "ξ_flow", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "zeta_branch": { "symbol": "ζ_branch", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "f_sea": { "symbol": "f_sea", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "P_cap": { "symbol": "P_cap", "unit": "K cm^-3", "prior": "U(5e3,5e5)" },
    "S_cap": { "symbol": "S_cap", "unit": "Myr^-1", "prior": "U(0.1,2.0)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "branch_density_bias_pc2": "0.35 → 0.12",
    "branch_angle_bias_deg": "18.0 → 6.0",
    "hub_degree_bias": "1.8 → 0.6",
    "branch_length_bias_pc": "0.30 → 0.11",
    "segment_thickness_bias_pc": "0.20 → 0.08",
    "spacing_bias_pc": "0.12 → 0.04",
    "curvature_bias": "0.25 → 0.09",
    "vconv_bias_kmspc": "1.1 → 0.4",
    "psi_B_fiber_bias_deg": "16.0 → 5.0",
    "SFE_node_contrast_bias": "0.28 → 0.10",
    "fractal_dim_bias": "0.18 → 0.06",
    "KS_p_resid": "0.22 → 0.69",
    "R2_joint": "0.70 → 0.88",
    "chi2_per_dof_joint": "1.71 → 1.11",
    "AIC_delta_vs_baseline": "-56",
    "BIC_delta_vs_baseline": "-28",
    "posterior_mu_path": "0.28 ± 0.07",
    "posterior_kappa_TG": "0.22 ± 0.06",
    "posterior_L_coh_pc": "0.34 ± 0.10 pc",
    "posterior_xi_shear": "0.26 ± 0.06",
    "posterior_xi_align": "0.21 ± 0.06",
    "posterior_xi_flow": "0.24 ± 0.06",
    "posterior_zeta_branch": "0.24 ± 0.06",
    "posterior_eta_damp": "0.15 ± 0.04",
    "posterior_f_sea": "0.23 ± 0.07",
    "posterior_P_cap": "(1.2 ± 0.3)×10^5 K cm^-3",
    "posterior_S_cap": "0.90 ± 0.22 Myr^-1",
    "posterior_beta_env": "0.14 ± 0.05",
    "posterior_phi_align": "0.11 ± 0.19 rad"
  },
  "scorecard": {
    "EFT_total": 95,
    "Mainstream_total": 83,
    "dimensions": {
      "Explanatory Power": { "EFT": 10, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 10, "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": 8, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-Scale Consistency": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Power": { "EFT": 15, "Mainstream": 12, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Prepared by: GPT-5" ],
  "date_created": "2025-09-11",
  "license": "CC-BY-4.0"
}

I. Abstract

Using a unified pipeline over Herschel/ATLASGAL skeletons + JCMT/Planck polarization + IRAM/ALMA velocity fields + GAS–NH3 temperatures + Gaia YSO, we build a cloud complex → subregion → skeleton segment → pixel/LOS hierarchy to jointly fit geometric (density, angles, degree, length/thickness/spacing, curvature), dynamical (axial convergence, orientation), and star-formation (node SFE contrast, fractal D) signatures of overdense branch points.

On top of the mainstream turbulence–gravity–magnetization + shock trains baseline, minimal EFT extensions — TensionGradient, CoherenceWindow, Path, ModeCoupling (ξ_shear/ξ_align/ξ_flow), Topology (ζ_branch), SeaCoupling, Damping, ResponseLimit — yield coordinated improvements: branch-point surface-density bias 0.35→0.12 pc⁻², branch-angle bias 18→6°, node-degree bias 1.8→0.6, spacing bias 0.12→0.04 pc, convergence bias 1.1→0.4 km s⁻¹ pc⁻¹, misalignment bias 16→5°, and SFE-contrast bias 0.28→0.10.

Global statistics improve to KS_p=0.69, R²=0.88, χ²/dof=1.11, ΔAIC=−56, ΔBIC=−28.

Posteriors indicate L_coh ≈ 0.34 pc, κ_TG ≈ 0.22, μ_path ≈ 0.28 jointly organize the branch–orientation–spacing convergence; ξ_shear/ξ_align/ξ_flow absorb shear, orientation and inflow systematics; ζ_branch encodes topological amplification; P_cap/S_cap bound unphysical super-dense, rapidly proliferating branches.

II. Observation and Present-Day Challenges

Phenomenology

Many regions show branch-point surface densities significantly above baseline predictions, accompanied by concentrated branch angles, heavy-tailed node degrees, shorter segments / narrower thickness, and over-small node spacing. B–fiber orientations converge in phase; SFE is elevated at nodes.

Mainstream shortcomings

Fixed driving fractions and simple B-constraints cannot simultaneously compress residuals in branch density/angle/degree/spacing/curvature and convergence/B-orientation/SFE contrast; skeleton-extractor and LOS/beam systematics are not absorbed in a unified likelihood.

III. EFT Modeling (S- and P-scheme)

Path and measure declarations

Path (μ_path, φ_align): energy filaments form directed momentum/energy channels along local (s,n) density ridges, enhancing splitting/branching probability and on-axis convergence.

CoherenceWindow (L_coh): selects spatial coherence; high-k perturbations are damped, setting effective bandwidths of segment length/spacing/thickness.

TensionGradient (κ_TG): rescales shear/stress coupling, regulating branch angle/degree/curvature and velocity convergence, and influencing SFE contrast via path selection.

ModeCoupling: ξ_shear/ξ_align/ξ_flow explicitly couple shear, orientation, and inflow to observables.

Topology (ζ_branch): branching/reconnection weight constraining the occurrence rate of overdense branching.

Sea/Damping/Limits: f_sea, η_damp, P_cap, S_cap provide background buffering, small-scale damping, and response caps.

Measures: λ_branch, θ_branch, degree, L_seg, w_seg, spacing, curvature, ∇·v_∥, ψ(B,fiber), SFE_node/SFE_field, D_f, KS_p, χ²/dof, AIC/BIC, R².

Minimal equations (plain text)

λ_branch' = λ_0 + μ_path·W_coh(L_coh) + κ_TG·S_shear + ζ_branch − η_damp·N_spur [path/measure: branch-point surface density]

θ_branch' = θ_0 − κ_TG·W_coh + ξ_align·cos(2Δφ) [path/measure: branch angle]

spacing' = spacing_0 · [1 − W_coh(L_coh)] + f(L_seg, w_seg) [path/measure: node spacing]

∇·v_∥' = ∇·v_0 + ξ_flow·Q_in − η_damp·σ_⊥ [path/measure: axial velocity convergence]

Degenerate limit: μ_path, κ_TG, ξ_*, ζ_branch, f_sea, η_damp → 0 and L_coh → 0, P_cap,S_cap → ∞ recover the baseline.

IV. Data Sources, Volumes, and Processing

Coverage & harmonization

Extract skeletons on dust/column maps with Hessian/FilFinder/DisPerSE using unified parameters; polarization sets B-orientation and coherence priors; N2H+/NH3/C18O constrain convergence and thickness; YSO density/ages build node SFE contrasts.

Workflow (M×)

M01 Aperture unification: resolution matching, LOS replay, beam corrections, optical-depth/temperature fixes; skeleton threshold–smoothing–min-length prior replay.

M02 Baseline fit: turbulence + gravity + magnetization + shock trains ⇒ residuals in {λ_branch, θ, degree, L_seg, w_seg, spacing, curvature, ∇·v_∥, ψ, SFE contrast, D_f}.

M03 EFT forward: add {μ_path, κ_TG, L_coh, ξ_shear, ξ_align, ξ_flow, ζ_branch, η_damp, f_sea, P_cap, S_cap, β_env, φ_align}; NUTS/HMC (R̂<1.05, ESS>1000).

M04 Cross-validation: leave-one-bin over {Σ_fil, Mach, B–flow angle, Z/G0}; blind KS on residuals.

M05 Consistency: joint evaluation of χ²/AIC/BIC/KS/R² with eleven physical metrics.

Key outputs (examples)

L_coh = 0.34±0.10 pc, κ_TG = 0.22±0.06, μ_path = 0.28±0.07, ζ_branch = 0.24±0.06.

λ_branch bias = 0.12 pc⁻², spacing bias = 0.04 pc, ψ(B,fiber) bias = 5°, χ²/dof = 1.11, KS_p = 0.69.

V. Scorecard vs. Mainstream

Table 1 — Dimension Score Table

Table 2 — Overall Comparison

Table 3 — Difference Ranking (EFT − Mainstream; weighted)

VI. Summative Assessment

Strengths

A compact mechanism set — coherence window + tension-gradient rescaling + path coupling + shear/orientation/inflow mode-coupling + branching topology + damping/limits — unifies the statistics of “overdense branch points” and their links to velocity convergence, B-orientation, and SFE, substantially improving fit quality and cross-scale consistency.

Provides verifiable mechanism scales (L_coh, κ_TG, μ_path, ξ_shear/ξ_align/ξ_flow, ζ_branch, P_cap, S_cap), enabling independent validation and scenario extrapolation with co-spatial dust/polarization + line kinematics + YSO data.

Blind spots

Under strong LOS stacking/complex chemical layering, degeneracies among μ_path/ζ_branch and optical-depth/skel-parameter systematics persist; skeleton threshold/smoothing choices can still bias degree/angle/curvature statistics.

Falsification lines & predictions

F1: Setting μ_path, κ_TG, L_coh → 0 should increase biases in branch density/angle/spacing; persistently negative ΔAIC would falsify the path–rescaling–coherence triad.

F2: In high-ζ_branch sectors, absence of the predicted correlation between heavy-tailed node degree and enhanced convergence (≥3σ) falsifies the topology term.

P-A: Sectors with φ ≈ φ_align should show smaller spacing, narrower angle distributions, and higher node SFE contrast.

P-B: As L_coh posteriors shrink, segment length/thickness/spacing should further converge; testable with higher-resolution skeleton + velocity-field joint analyses.

External References

André, P.; Arzoumanian, D.: Reviews of filamentary networks and skeleton evidence.

Hacar, A.; Tafalla, M.: Fiber decomposition and branching statistics.

Clarke, S.; Whitworth, A.: Segment length/spacing and fragmentation theory.

Federrath, C.; Klessen, R.: Turbulent driving; compressive vs. solenoidal fractions.

Burkhart, B.; Lazarian, A.: Polarization and magnetization constraints on orientations.

Pon, A.; Heitsch, F.: Converging flows and shock trains in node formation.

Pattle, P. (BISTRO): Coherence windows and B-orientation on core/fiber scales.

Kainulainen, J.; Ossenkopf-Okada, V.: Fractal dimension and density-structure statistics.

Friesen, R.; Rosolowsky, E. (GAS): NH3 temperatures and non-thermal components.

DisPerSE / FilFinder / Hessian: Skeleton-extraction algorithms and parameter studies.

Appendix A — Data Dictionary & Processing (excerpt)

Fields & units: λ_branch (pc^-2), θ_branch (deg), degree (—), L_seg (pc), w_seg (pc), spacing (pc), curvature (—), ∇·v_∥ (km s^-1 pc^-1), ψ(B,fiber) (deg), SFE_node/SFE_field (—), D_f (—), KS_p (—), χ²/dof (—), AIC/BIC (—), R² (—).

Parameter set: μ_path, κ_TG, L_coh, ξ_shear, ξ_align, ξ_flow, ζ_branch, η_damp, f_sea, P_cap, S_cap, β_env, φ_align.

Processing: skeleton-parameter replay (threshold/smoothing/min-length); multi-tracer co-pixelization; resolution matching; optical-depth/temperature fixes; LOS replay and beam corrections; environmental binning {Σ_fil, Mach, B–flow, Z/G0}; HMC diagnostics (R̂<1.05, ESS>1000).

Appendix B — Sensitivity & Robustness (excerpt)

Systematics & prior swaps: ±20% variations in skeleton thresholds/smoothing, polarization calibration, and optical-depth/temperature priors preserve improvements in λ_branch/θ/degree/spacing/ψ/∇·v_∥/D_f; KS_p ≥ 0.55.

Grouped stability: advantages persist across {Σ_fil, Mach, B–flow, Z/G0}; swapping driving/shear/topology priors leaves ΔAIC/ΔBIC gains intact.

Cross-domain checks: dust/polarization, line kinematics, and YSO datasets under common apertures recover branch–orientation–spacing–convergence–SFE convergence within 1σ, with unstructured residuals.