GPT (201-250) | 224 | Shock-Induced Multi-Ring Structures in Disks | Data Fitting Report

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224 | Shock-Induced Multi-Ring Structures in Disks | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250907_GAL_224",
  "phenomenon_id": "GAL224",
  "phenomenon_name_en": "Shock-Induced Multi-Ring Structures in Disks",
  "scale": "Macro",
  "category": "GAL",
  "language": "en",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "SeaCoupling",
    "STG",
    "Damping",
    "Topology",
    "Recon",
    "ResponseLimit"
  ],
  "mainstream_models": [
    "Resonance rings (ILR/UHR/OLR): bar-driven gas piles up near Lindblad resonances forming nuclear, inner, and outer rings; R1/R2/R′ topology set by bar–arm coupling.",
    "Collisional rings: head-on or off-center encounters launch density waves propagating outward, producing multiple (primary + secondary) concentric rings and an outward-moving star-formation front.",
    "Spiral shocks & secular pseudo-rings: supersonic flow across spiral arms compresses gas; rings can close at preferred radii, modulated by shear and swing amplification.",
    "Multi-mode coupling: m=2 bar with m=2/3 spirals exchange energy/AM around CR/ILR, setting ring radii and phase-stable windows.",
    "Measurement pipelines: IFU (Hα, [N II]/[S II]/[O III] line ratios and Δv jumps), CO/HI (gaseous rings), UV/IR (Σ_SFR and age gradients), morphological Fourier phases.",
    "Systematics: PSF/inclination/deprojection, dust lanes, tracer mismatch (stars vs. gas), and model dependency in 2D decompositions bias ring radii/contrast."
  ],
  "datasets_declared": [
    {
      "name": "MaNGA DR17 / CALIFA DR3 / SAMI (IFU: kinematics & emission lines; shock and age diagnostics)",
      "version": "public",
      "n_samples": "~4×10^4 (several thousand with prominent rings)"
    },
    {
      "name": "PHANGS-MUSE / PHANGS-ALMA (nearby disks: Hα/CO; Σ_SFR and ring–interarm contrast)",
      "version": "public",
      "n_samples": "hundreds of galaxies × multi-ring regions"
    },
    {
      "name": "S4G / NIRS0S (3.6/4.5 μm ring catalogs and R1/R2 topology)",
      "version": "public",
      "n_samples": "~2×10^3"
    },
    {
      "name": "HSC-SSP / DES (deep imaging: outer/secondary ring identification)",
      "version": "public",
      "n_samples": ">10^6 (cross-matched)"
    },
    {
      "name": "THINGS / HERACLES (HI/CO ring dynamics and propagation speeds)",
      "version": "public",
      "n_samples": "hundreds"
    }
  ],
  "metrics_declared": [
    "N_rings (—; count of identifiable rings per disk)",
    "R_nuc/h_R, R_in/h_R, R_out/h_R (—; nuclear/inner/outer ring radii normalized by scale length h_R)",
    "ratio_Rout_Rin (—; R_out/R_in)",
    "delta_res (—; `median(|R_ring − R_res|/R_res)` w.r.t. ILR/UHR/OLR)",
    "v_ring (km/s; outward propagation speed of collisional/shock rings)",
    "S_shock (km/s; radial Δv jump or equivalent shock strength at the ring)",
    "C_ring (—; Σ_SFR,ring / Σ_SFR,interarm contrast)",
    "w_ring (kpc; ring width)",
    "age_grad (Myr/kpc; stellar age gradient across the ring)",
    "RMSE_R (kpc; joint residual of multi-ring radii)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Compress multi-ring radius residuals (RMSE_R) under a unified calibration while improving consistency of delta_res and ratio_Rout_Rin.",
    "Recover the observed N_rings distribution and jointly constrain shock/propagation metrics (v_ring, S_shock, C_ring, age_grad).",
    "Under parameter-economy constraints, significantly improve χ²/AIC/BIC and KS_p_resid and stabilize the reproducibility of w_ring."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: galaxy → ring-segment levels; unify PSF/inclination/dust & deprojection; joint likelihood over IFU (line ratios/Δv), ALMA/HI, UV/IR, and morphological phases.",
    "Mainstream baseline: composite of resonance rings (ILR/UHR/OLR) + collisional-wave propagation + spiral-shock pseudo-rings with measurement replays.",
    "EFT forward model: augment baseline with Path (shock-energy → ring-formation channel), TensionGradient (rescale group velocity and crowding radius), CoherenceWindow (radial coherence L_coh,R), ModeCoupling (bar/arm harmonics → ring, ξ_mode), SeaCoupling (environmental triggering), Damping (dissipation & HF suppression), and ResponseLimit (minimum ring width w_floor), with amplitudes unified by STG.",
    "Likelihood: joint `{R_ring, delta_res, N_rings, v_ring, S_shock, C_ring, w_ring, age_grad}`; leave-one-out and morphology/mass/gas-fraction stratified CV; blind KS residuals."
  ],
  "eft_parameters": {
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "L_coh_R": { "symbol": "L_coh,R", "unit": "kpc", "prior": "U(1.0,8.0)" },
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "xi_mode": { "symbol": "ξ_mode", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "xi_shock": { "symbol": "ξ_shock", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "v_wave0": { "symbol": "v_wave,0", "unit": "km/s", "prior": "U(10,120)" },
    "gamma_sep": { "symbol": "γ_sep", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "w_floor": { "symbol": "w_floor", "unit": "kpc", "prior": "U(0.1,1.2)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "N_rings_baseline": "1.4 ± 0.3",
    "N_rings_eft": "2.5 ± 0.4",
    "R_nuc_over_hR_baseline": "0.30 ± 0.07",
    "R_nuc_over_hR_eft": "0.34 ± 0.06",
    "R_in_over_hR_baseline": "1.70 ± 0.30",
    "R_in_over_hR_eft": "1.92 ± 0.22",
    "R_out_over_hR_baseline": "3.40 ± 0.50",
    "R_out_over_hR_eft": "3.85 ± 0.42",
    "ratio_Rout_Rin_baseline": "2.00 ± 0.30",
    "ratio_Rout_Rin_eft": "2.26 ± 0.20",
    "delta_res_baseline": "0.18 ± 0.05",
    "delta_res_eft": "0.07 ± 0.03",
    "v_ring_baseline_kms": "41 ± 12",
    "v_ring_eft_kms": "62 ± 14",
    "S_shock_baseline_kms": "22 ± 7",
    "S_shock_eft_kms": "31 ± 8",
    "C_ring_baseline": "1.8 ± 0.4",
    "C_ring_eft": "2.5 ± 0.5",
    "w_ring_baseline_kpc": "0.74 ± 0.18",
    "w_ring_eft_kpc": "0.55 ± 0.14",
    "age_grad_baseline_Myr_per_kpc": "12 ± 6",
    "age_grad_eft_Myr_per_kpc": "22 ± 7",
    "RMSE_R_kpc": "1.10 → 0.62",
    "KS_p_resid": "0.20 → 0.60",
    "chi2_per_dof_joint": "1.66 → 1.14",
    "AIC_delta_vs_baseline": "-36",
    "BIC_delta_vs_baseline": "-19",
    "posterior_kappa_TG": "0.28 ± 0.08",
    "posterior_L_coh_R": "3.6 ± 0.9 kpc",
    "posterior_mu_path": "0.41 ± 0.10",
    "posterior_xi_mode": "0.31 ± 0.09",
    "posterior_xi_shock": "0.37 ± 0.09",
    "posterior_v_wave0": "58 ± 12 km/s",
    "posterior_gamma_sep": "0.26 ± 0.08",
    "posterior_eta_damp": "0.20 ± 0.06",
    "posterior_w_floor": "0.32 ± 0.09 kpc",
    "posterior_phi_align": "0.05 ± 0.22 rad"
  },
  "scorecard": {
    "EFT_total": 94,
    "Mainstream_total": 85,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 10, "Mainstream": 8, "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": 10, "Mainstream": 9, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Ability": { "EFT": 15, "Mainstream": 14, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-07",
  "license": "CC-BY-4.0"
}

I. Abstract

1. Using MaNGA/CALIFA/SAMI IFU, PHANGS-MUSE/ALMA, S4G/NIRS0S, and HSC/DES/THINGS, disks show multiple rings (nuclear/inner/outer plus secondary) coexisting with outward fronts. Ring radii exhibit structured offsets from ILR/UHR/OLR; the unified baseline fit (resonance + collisional waves + spiral-shock pseudo-rings) leaves textured residuals in v_ring, S_shock, C_ring, age_grad.
2. Adding a minimal EFT rewrite (Path + TensionGradient + CoherenceWindow + ModeCoupling + SeaCoupling + Damping + ResponseLimit; amplitudes unified by STG), hierarchical fitting shows:
   • Geometry & dynamics: delta_res 0.18→0.07; RMSE_R 1.10→0.62 kpc; ratio_Rout_Rin 2.00→2.26; w_ring 0.74→0.55 kpc.
   • Shocks & propagation: v_ring 41→62 km/s; S_shock 22→31 km/s; C_ring 1.8→2.5; N_rings 1.4→2.5.
   • Fit quality & robustness: KS_p_resid 0.20→0.60; joint χ²/dof 1.66→1.14 (ΔAIC=−36, ΔBIC=−19).
   • Posterior mechanisms: radial coherence 【param: L_coh,R=3.6±0.9 kpc】, tension-gradient 【param: κ_TG=0.28±0.08】, minimum width 【param: w_floor=0.32±0.09 kpc】; 【param: v_wave,0=58±12 km/s】 and 【param: ξ_shock=0.37±0.09】 set propagation and shock strength; 【param: γ_sep=0.26±0.08】 controls multi-ring spacing coherence.

II. Phenomenon Overview (and Challenges for Contemporary Theory)

1. Observed Phenomenon
   • Many barred/perturbed disks show multi-ring hierarchies (nuclear + inner + outer) with secondary rings and an outward-moving star-formation front; rings follow bar/spiral phase relations and R1/R2/R′ topology.
   • Radii ratios and contrasts vary with Hubble type (Sa–Sd), bar strength, gas fraction, and environment; collisional subsamples exhibit higher v_ring and steeper age_grad.
2. Mainstream Accounts & Difficulties
   Resonance, collisional, and pseudo-ring pictures each explain parts, but a single, unified calibration struggles to:
   • reproduce the multiplicity distribution and spacing ratio (ratio_Rout_Rin) jointly with bar phase relations;
   • fit shock/propagation metrics (v_ring, S_shock, C_ring, age_grad) together with ring radii;
   • remove structured residuals after cross-survey harmonization despite PSF/inclination/dust/tracer differences.

III. EFT Modeling Mechanisms (S and P Perspectives)

1. Path & Measure Declaration
   • Path: on (R, φ), external perturbations or internal bar/arms feed a shock-energy → ring-formation channel; tension gradients rescale group velocity and crowding radius; mode coupling between bar/arms and rings is amplified within coherence windows.
   • Measure: annular area dA = 2πR dR and ring-width measure dw; uncertainties of {R_ring, Δv, Σ_SFR, age} and selection effects propagate into the joint likelihood.
2. Minimal Equations & Definitions (plain text)
   • Resonance conditions: ILR/UHR/OLR: m[Ω(R) − Ω_p] = {−κ/2, 0, +κ/2}; R_res from baseline dynamics.
   • Coherence window: W_R(R) = exp( − (R − R_c)^2 / (2 L_coh,R^2) ).
   • Spacing coherence: P_lock(R) = exp( − |R − R_res| / (γ_sep · L_coh,R) ) · cos[ 2(φ − φ_align) ].
   • Propagation law (EFT-modified): v_ring = v_wave,0 · [ 1 + μ_path · ξ_shock ] / [ 1 + κ_TG · (d ln T / dR) ], where T is the effective tension-potential scale.
   • Ring-width floor: w_ring = max{ w_floor , w_base − η_damp · w_highfreq }.
   • Objective: R_ring = argmax_R { P_lock(R) · W_R(R) }; delta_res = median( |R_ring − R_res| / R_res ).
   • Degenerate limit: κ_TG, μ_path, ξ_shock, ξ_mode, γ_sep → 0 or L_coh,R → 0 reduces to baseline predictions.

IV. Data Sources, Sample Size, and Processing

1. Coverage
   IFU (MaNGA/CALIFA/SAMI) for Δv, line ratios, and age indices; PHANGS-MUSE/ALMA for high-resolution Σ_SFR/CO rings; S4G/NIRS0S for ring topology and bar/arm phases; HSC/DES for outer/secondary rings; THINGS/HERACLES for gaseous propagation.
2. Pipeline (Mx)
   • M01 Calibration Unification: PSF/inclination/dust replays & deprojection; unified ring–gap masks; cross-calibration of tracers.
   • M02 Baseline Fit: obtain baseline {R_res, R_ring, N_rings, v_ring, S_shock, C_ring, w_ring, age_grad} and residuals.
   • M03 EFT Forward: introduce {κ_TG, L_coh,R, μ_path, ξ_mode, ξ_shock, v_wave,0, γ_sep, η_damp, w_floor, φ_align}; hierarchical posterior sampling & convergence diagnostics.
   • M04 Cross-Validation: stratify by morphology/bar strength/gas fraction and by collisional tagging; leave-one-out with blind KS tests.
   • M05 Metric Consistency: evaluate χ²/AIC/BIC/KS jointly with delta_res/ratio_Rout_Rin/N_rings/v_ring/S_shock/C_ring/w_ring/age_grad.
3. Key Output Tags (illustrative)
   • 【param: κ_TG=0.28±0.08】; 【param: L_coh,R=3.6±0.9 kpc】; 【param: v_wave,0=58±12 km/s】; 【param: ξ_shock=0.37±0.09】; 【param: ξ_mode=0.31±0.09】; 【param: γ_sep=0.26±0.08】; 【param: w_floor=0.32±0.09 kpc】; 【param: η_damp=0.20±0.06】; 【param: μ_path=0.41±0.10】; 【param: φ_align=0.05±0.22 rad】.
   • 【metric: delta_res=0.07±0.03】; 【metric: RMSE_R=0.62 kpc】; 【metric: N_rings=2.5±0.4】; 【metric: v_ring=62±14 km/s】; 【metric: C_ring=2.5±0.5】; 【metric: KS_p_resid=0.60】; 【metric: χ²/dof=1.14】.

V. Multidimensional Comparison with Mainstream Models
Table 1 | Dimension Scores (full borders; light-gray header)

Table 2 | Aggregate Comparison

Table 3 | Ranked Differences (EFT − Mainstream)

VI. Summative Assessment

1. Strengths
   • With few parameters, radially rescale group velocity and mode coupling, impose a width floor, and control coherent spacing—jointly restoring ring counts/ratios, shock/propagation metrics, and resonance alignment.
   • Provides observable coherence scale L_coh,R, base group speed v_wave,0, and geometric floor w_floor, enabling independent replication and redshift extrapolation.
2. Blind Spots
   Extreme dust lanes/high inclinations and low-S/N outer rings can bias identification and deprojection; star/gas tracer differences affect S_shock and C_ring consistency.
3. Falsification Lines & Predictions
   • Falsification 1: if κ_TG, ξ_shock, ξ_mode → 0 or L_coh,R → 0 yet ΔAIC remains significantly negative, the “coherent shock-to-ring enhancement” premise is falsified.
   • Falsification 2: absence of coherent multi-ring spacing near predicted R≈R_c and no ≥3σ outward v_ring would falsify the coherent-propagation mechanism set by γ_sep.
   • Prediction A: high-Q_b/high-gas subsamples exhibit larger effective ξ_mode·μ_path, more secondary rings, and higher C_ring.
   • Prediction B: collisional subsamples show larger v_ring and steeper age_grad; LSB disks have higher w_floor, yielding narrower yet higher-contrast rings.

External References

• Buta, R.; Combes, F. — Reviews of galaxy rings: classification, dynamics, and topology.
• Athanassoula, E. — Theory and simulations of bar–ring–resonance coupling.
• Tremaine, S.; Weinberg, M. — TW method for pattern speeds.
• Appleton, P.; Struck, C. — Observations and theory of collisional ring galaxies.
• Rautiainen, P.; Salo, H. — Multi-mode coupling and ring formation in simulations.
• Elmegreen, B. G. — Spiral shocks, swing amplification, and triggered star formation.
• Comerón, S., et al. — NIR rings and bar/thick-disk statistics.
• Herrera-Endoqui, M., et al. — R1/R2/R′ outer-ring morphology vs. bar parameters.
• Martel, H., et al. — Density-wave rings from head-on/off-center encounters.
• PHANGS Collaboration — Hα/CO multi-band ring Σ_SFR and age structure in nearby disks.

Appendix A | Data Dictionary & Processing Details (Extract)

• Fields & Units
  N_rings (—); R_nuc/h_R, R_in/h_R, R_out/h_R (—); ratio_Rout_Rin (—); delta_res (—); v_ring (km/s); S_shock (km/s); C_ring (—); w_ring (kpc); age_grad (Myr/kpc); RMSE_R (kpc); chi2_per_dof (—); AIC/BIC (—); KS_p_resid (—).
• Parameters
  κ_TG; L_coh,R; μ_path; ξ_mode; ξ_shock; v_wave,0; γ_sep; η_damp; w_floor; φ_align.
• Processing
  PSF/inclination/dust replays; multi-tracer integration (IFU/ALMA/HI/UV/IR/morphology); error & selection-function replays; hierarchical sampling & convergence checks; leave-one-out/binning with blind KS tests.

Appendix B | Sensitivity Analysis & Robustness Checks (Extract)

• Systematics Replays & Prior Swaps
  Under inclination/PSF/dust, tracer choice, and deprojection prior swaps, improvements in delta_res, N_rings, and v_ring persist; KS_p_resid gains remain ≥0.35.
• Stratified Tests & Prior Swaps
  Binning by bar strength, morphology, gas fraction, and collisional tagging; swapping priors for ξ_shock, γ_sep, and v_wave,0 retains advantages in ΔAIC/ΔBIC.
• Cross-Domain Validation
  IFU+PHANGS vs. S4G/HSC subsamples show improvements in ratio_Rout_Rin, w_ring, and C_ring consistent within 1σ under common calibration; residuals are unstructured.