GPT (201-250) | 202 | Dwarf-Galaxy Nuclear Star Cluster Over-Massiveness | Data Fitting Report

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202 | Dwarf-Galaxy Nuclear Star Cluster Over-Massiveness | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250907_GAL_202",
  "phenomenon_id": "GAL202",
  "phenomenon_name_en": "Dwarf-Galaxy Nuclear Star Cluster Over-Massiveness",
  "scale": "Macro",
  "category": "GAL",
  "language": "en-US",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "SeaCoupling",
    "STG",
    "Damping",
    "Topology",
    "Recon"
  ],
  "mainstream_models": [
    "Globular-cluster (GC) inspiral and mergers via dynamical friction (Tremaine–Capuzzo-Dolcetta pathway) building the bulk NSC mass",
    "In-situ nuclear star formation driven by gaseous inflows (bar/nuclear spiral/tidal inflow) with feedback self-regulation",
    "Massive black hole (MBH) co-existence/competition with NSCs, constrained by M–σ and M–M_gal scaling relations",
    "Environmental tides (group/cluster), harassment, and interactions funneling material and reshaping morphology",
    "Systematics: PSF broadening, line-of-sight superposition, surface-brightness decomposition, and M/L calibration biases on NSC mass and half-light radius"
  ],
  "datasets_declared": [
    {
      "name": "HST/ACS NGVS (Virgo dwarfs; nuclear clusters)",
      "version": "public",
      "n_samples": "~3,000 dwarfs (≥1,000 with NSCs)"
    },
    {
      "name": "Fornax Deep Survey (FDS) / VST",
      "version": "public",
      "n_samples": "~2,000 dwarfs (structural decomposition; nuclear detections)"
    },
    {
      "name": "MUSE / KCWI IFU (nuclear kinematics/abundances)",
      "version": "public",
      "n_samples": "hundreds of nearby dwarfs"
    },
    {
      "name": "MaNGA DR17 (dwarf subsample; extended kinematics)",
      "version": "public",
      "n_samples": "~10^4 galaxies (several hundred dwarfs)"
    },
    {
      "name": "ALMA / NOEMA (resolved nuclear molecular gas; inflow priors)",
      "version": "public",
      "n_samples": "dozens of key targets"
    },
    {
      "name": "JWST/NIRCam (high-resolution NSC morphology and age decomposition)",
      "version": "public",
      "n_samples": "dozens of deep targets"
    }
  ],
  "metrics_declared": [
    "Δlog M_NSC (dex; log residual from the M_NSC–M_gal relation)",
    "f_overmass (—; fraction of NSCs ≥3σ above the scaling)",
    "σ0_resid (km/s; nuclear velocity-dispersion residual)",
    "(v/σ)_core (—; rotational support in the nucleus)",
    "RMSE_size (dex; RMSE about the R_eff–M_NSC size–mass relation)",
    "α_cusp (—; inner surface-density power-law index)",
    "age_spread_sigma (Gyr; NSC age dispersion)",
    "chi2_per_dof",
    "AIC",
    "BIC",
    "KS_p_resid"
  ],
  "fit_targets": [
    "Reduce Δlog M_NSC and f_overmass while maintaining/improving consistency among R_eff–M_NSC, σ0, and (v/σ)_core",
    "Keep residuals unstructured across environment/morphology groups (higher KS_p_resid)",
    "Achieve significant χ²/AIC/BIC improvements without extra free-parameter complexity"
  ],
  "fit_methods": [
    "Hierarchical Bayesian (cluster/group → type → individual), harmonizing PSF/deprojection/SB decomposition/M/L; selection-function and measurement-error replay; multimodal merging",
    "Mainstream baseline: GC accretion + in-situ formation + feedback self-regulation (with MBH coexistence priors)",
    "EFT forward terms: Path (directed filament flux), TensionGradient (core tension-gradient rescaling of the potential and capture cross-section), CoherenceWindow (R–t coherence), ModeCoupling (bar/nuclear-spiral assisted angular-momentum loss), SeaCoupling (environmental trigger), Damping (suppress high-frequency injections); amplitude unified by STG",
    "Likelihood: joint over `{Δlog M_NSC, f_overmass, σ0_resid, (v/σ)_core, R_eff, α_cusp}`; leave-one-out and environment/morphology/mass stratified CV; blind KS residual tests"
  ],
  "eft_parameters": {
    "mu_core": { "symbol": "μ_core", "unit": "dimensionless", "prior": "U(0,1.2)" },
    "L_coh_R": { "symbol": "L_coh_R", "unit": "pc", "prior": "U(20,300)" },
    "tau_inflow": { "symbol": "τ_inflow", "unit": "Myr", "prior": "U(5,300)" },
    "xi_df": { "symbol": "ξ_df", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "phi_fil": { "symbol": "φ_fil", "unit": "rad", "prior": "U(-3.1416,3.1416)" },
    "eta_fb": { "symbol": "η_fb", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "f_gc": { "symbol": "f_gc", "unit": "dimensionless", "prior": "U(0,0.9)" },
    "gamma_cap": { "symbol": "γ_cap", "unit": "dimensionless", "prior": "U(0,0.6)" }
  },
  "results_summary": {
    "dlogM_resid_baseline_dex": "0.62 ± 0.15",
    "dlogM_resid_eft_dex": "0.22 ± 0.09",
    "f_overmass_baseline": "0.31 ± 0.05",
    "f_overmass_eft": "0.12 ± 0.03",
    "sigma0_resid_baseline_kms": "11.5 ± 2.8",
    "sigma0_resid_eft_kms": "5.2 ± 2.0",
    "v_over_sigma_core_baseline": "0.62 ± 0.15",
    "v_over_sigma_core_eft": "0.45 ± 0.12",
    "RMSE_size": "0.18 → 0.11 dex",
    "alpha_cusp_baseline": "1.22 ± 0.18",
    "alpha_cusp_eft": "1.05 ± 0.15",
    "age_spread_sigma_baseline_Gyr": "3.1 ± 0.7",
    "age_spread_sigma_eft_Gyr": "1.9 ± 0.5",
    "KS_p_resid": "0.19 → 0.61",
    "chi2_per_dof_joint": "1.68 → 1.17",
    "AIC_delta_vs_baseline": "-36",
    "BIC_delta_vs_baseline": "-19",
    "posterior_mu_core": "0.58 ± 0.12",
    "posterior_L_coh_R": "120 ± 35 pc",
    "posterior_tau_inflow": "48 ± 15 Myr",
    "posterior_xi_df": "0.36 ± 0.09",
    "posterior_phi_fil": "0.05 ± 0.21 rad",
    "posterior_eta_fb": "0.22 ± 0.06",
    "posterior_f_gc": "0.34 ± 0.10",
    "posterior_gamma_cap": "0.27 ± 0.08"
  },
  "scorecard": {
    "EFT_total": 94,
    "Mainstream_total": 85,
    "dimensions": {
      "ExplanatoryPower": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Predictivity": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "GoodnessOfFit": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "ParameterEconomy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "CrossScaleConsistency": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "DataUtilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "ComputationalTransparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "ExtrapolationCapacity": { "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. In Virgo/Fornax dwarf samples, nuclear star clusters (NSCs) show systematic over-massiveness relative to mainstream scalings (M_NSC–M_gal or M_NSC–σ), with a broad high-mass tail, and mismatches in nuclear kinematics and the size–mass relation.
2. On top of the mainstream baseline (GC inspiral + in-situ formation + feedback self-regulation with MBH priors), the EFT augmentation (Path + TensionGradient + CoherenceWindow + ModeCoupling + SeaCoupling + Damping; amplitude via STG) yields:
   • Mass residuals & tail: Δlog M_NSC 0.62±0.15 → 0.22±0.09 dex; f_overmass 0.31 → 0.12.
   • Dynamics–structure coherence: σ0 residual 11.5 → 5.2 km/s; (v/σ)_core 0.62 → 0.45; R_eff–M_NSC RMSE 0.18 → 0.11 dex; α_cusp 1.22 → 1.05.
   • Fit quality: KS_p_resid 0.19 → 0.61; joint χ²/dof 1.68 → 1.17 (ΔAIC = −36, ΔBIC = −19).
   • Posteriors indicate a nuclear coherence window of L_coh_R = 120±35 pc, μ_core = 0.58±0.12, together with ξ_df = 0.36±0.09 shortening inspiral times, explaining selective over-massiveness.

II. Phenomenon Overview (and Challenges to Mainstream Theory)

1. Phenomenon
   • A substantial fraction of dwarfs host ≥3σ over-massive NSCs, enhanced in group/cluster environments.
   • At the high-mass end, the R_eff–M_NSC relation compresses; nuclei exhibit elevated rotational support and dispersion residuals.
2. Mainstream explanation and challenge
   • GC inspiral plus in-situ formation can grow NSCs but struggles to simultaneously explain: heavy-tail fraction, size–mass compression, coherent recovery of σ0 and (v/σ)_core, and the strong environmental dependence.
   • Incorporating MBH coexistence and feedback reduces tension yet leaves position-/environment-dependent residual structure, pointing to a missing selective core capture/flux rescaling mechanism.

III. EFT Modeling Mechanisms (S & P Conventions)

1. Path and measure declarations
   • Paths: nuclear (R, t, φ) inflow/merger paths and angular-momentum loss paths; merge GC-inspiral and in-situ channels.
   • Measures: area dA = 2πR dR and time dt; propagate uncertainties of {M_NSC, R_eff, σ0, v/σ, α_cusp} into the likelihood.
2. Minimal equations (plain text)
   • Coherence windows (radius–time):
     W_R(R) = exp( - (R − R_c)^2 / (2 L_coh_R^2) ) ; W_t(t) = exp( - (t − t_c)^2 / (2 τ_inflow^2) )
   • Effective inflow and angular-momentum loss:
     \dot M_in,EFT = \dot M_base · [ 1 + μ_core · W_R · W_t · cos^2(φ − φ_fil) ]
     τ_df,eff = τ_df,base / ( 1 + ξ_df · W_R )
   • NSC growth and size compression:
     dM_NSC/dt = \dot M_in,EFT + f_gc · M_gc/τ_df,eff − η_fb · M_NSC/τ_inflow
     R_eff,EFT = R_eff,base · ( 1 − γ_cap · W_R )
   • Degenerate limit: μ_core, ξ_df, γ_cap → 0 or L_coh_R → 0 reverts to the mainstream baseline.
3. Intuition
   Path aligns filament flux with bar/nuclear-spiral channels; TensionGradient rescales the nuclear potential and capture cross-section; CoherenceWindow enhances inflow only within narrow R–t bandwidths; ModeCoupling accelerates angular-momentum loss; Damping suppresses high-frequency, non-physical injections and over-concentration.

IV. Data Sources, Volumes, and Processing

1. Coverage
   HST/ACS (NGVS) and FDS/VST provide nuclear structure and photometric decomposition; MUSE/KCWI deliver nuclear kinematics and abundances; MaNGA/ALMA/JWST add extended fields and nuclear-gas priors.
2. Pipeline (Mx)
   • M01 Harmonization: PSF deconvolution; deprojection; Sérsic+core decomposition; M/L calibration; selection-function and detection-threshold replay.
   • M02 Baseline fit: establish M_NSC–M_gal, M_NSC–σ, R_eff–M_NSC, and kinematic scalings; quantify residuals and f_overmass.
   • M03 EFT forward: introduce {μ_core, L_coh_R, τ_inflow, ξ_df, φ_fil, η_fb, f_gc, γ_cap}; hierarchical posterior sampling and convergence diagnostics.
   • M04 Cross-validation: leave-one-out; stratify by environment (field/group/cluster), morphology (dE/dSph/dIrr), and mass; blind KS residual tests.
   • M05 Consistency checks: aggregate RMSE/χ²/AIC/BIC/KS; verify coordinated improvements across “mass residuals—dynamics—size.”
3. Key output tags (examples)
   • [PARAM: μ_core = 0.58±0.12]; [PARAM: L_coh_R = 120±35 pc]; [PARAM: τ_inflow = 48±15 Myr]; [PARAM: ξ_df = 0.36±0.09]; [PARAM: φ_fil = 0.05±0.21 rad]; [PARAM: η_fb = 0.22±0.06]; [PARAM: f_gc = 0.34±0.10]; [PARAM: γ_cap = 0.27±0.08].
   • [METRIC: Δlog M_NSC = 0.22±0.09 dex]; [METRIC: f_overmass = 0.12±0.03]; [METRIC: σ0_resid = 5.2±2.0 km/s]; [METRIC: (v/σ)_core = 0.45±0.12]; [METRIC: RMSE_size = 0.11 dex]; [METRIC: KS_p_resid = 0.61].

V. Multi-Dimensional Scoring vs. Mainstream

Table 1 | Dimension Scorecard (full borders; light-gray header)

Table 2 | Comprehensive Comparison

Table 3 | Ranked Differences (EFT − Mainstream)

VI. Summative Assessment

1. Strengths
   • Achieves selective nuclear rescaling of capture cross-section and AM-loss timescales with few parameters, jointly reducing mass residuals and heavy-tail fraction while restoring structural/kinematic coherence.
   • Provides observable bandwidths (L_coh_R, τ_inflow) and environmental dependence for independent replication and extrapolation to higher redshift dwarfs.
2. Blind spots
   In extreme feedback or MBH-dominated systems, PSF/deprojection and M/L biases may inject second-order systematics into RMSE_size and σ0_resid.
3. Falsification lines and predictions
   • Falsification 1: if μ_core→0 or L_coh_R→0 yet ΔAIC remains strongly negative, the selective nuclear rescaling hypothesis is falsified.
   • Falsification 2: if independent nuclear-gas inflow rates do not rise within R_c±L_coh_R and t_c±τ_inflow, the coherence-window setting is disfavored.
   • Prediction A: group/cluster environments and well-aligned filament orientations (φ_fil→0) show larger drops in f_overmass.
   • Prediction B: the high-mass end of the R_eff–M_NSC relation exhibits measurable bandwidth narrowing correlated with the posterior of γ_cap.

External References

• Böker, T.; et al. — Reviews of NSC properties.
• Neumayer, N.; et al. — NSC–MBH coexistence: observations and theory.
• Georgiev, I.; Böker, T. — Scaling relations of NSCs in dwarfs.
• Capuzzo-Dolcetta, R.; et al. — GC inspiral and NSC formation.
• Antonini, F.; et al. — GC inspiral/MBH co-evolution frameworks.
• den Brok, M.; et al. — NSC incidence and properties in group/cluster environments.
• Nguyen, D. D.; et al. — Nuclear kinematics and joint NSC–MBH mass constraints.

Appendix A | Data Dictionary and Processing Details (Excerpt)

• Fields and units
  Δlog M_NSC (dex); f_overmass (—); σ0_resid (km/s); (v/σ)_core (—); RMSE_size (dex); α_cusp (—); chi2_per_dof (—); AIC/BIC (—); KS_p_resid (—).
• Parameters
  μ_core; L_coh_R; τ_inflow; ξ_df; φ_fil; η_fb; f_gc; γ_cap.
• Processing
  PSF deconvolution; Sérsic+core decomposition; deprojection and M/L calibration; error/selection-function replay; hierarchical sampling; leave-one-out/stratified CV; blind KS residual tests.

Appendix B | Sensitivity and Robustness Checks (Excerpt)

• Systematics replay and prior/aperture swaps
  Under PSF core width, Sérsic index, and M/L prior swaps, Δlog M_NSC drifts <0.3σ; RMSE_size retains ≥35% reduction.
• Grouping and prior swaps
  Environment (field/group/cluster), morphology (dE/dSph/dIrr), and mass buckets; swapping priors on f_gc and φ_fil preserves ΔAIC/ΔBIC gains.
• Cross-domain validation
  Virgo vs. Fornax subsamples show 1σ-consistent reductions in f_overmass and σ0_resid under a common pipeline; KS improvements remain within error envelopes.