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180 | Galaxy Wind Fallback Refeeding Efficiency Bias | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250907_GAL_180",
  "phenomenon_id": "GAL180",
  "phenomenon_name_en": "Galaxy Wind Fallback Refeeding Efficiency Bias",
  "scale": "Macro",
  "category": "GAL",
  "language": "en-US",
  "eft_tags": [
    "Path",
    "SeaCoupling",
    "TensionGradient",
    "CoherenceWindow",
    "STG",
    "Damping",
    "Topology",
    "ResponseLimit"
  ],
  "mainstream_models": [
    "Energy/momentum-driven winds and fountains (η, v_wind scalings; thermal/kinetic injection; fountain fallback)",
    "Refueling & gas-regulator framework (ε_rec = Mdot_rec/Mdot_out; t_rec fallback timescale; metal-enriched return)",
    "Cosmological-prior baselines (FIRE/EAGLE/TNG semi-analytic & numerical) and observational baselines (COS-Halos/CGM absorption & covering)",
    "Systematics: absorber selection, background aperture, abundance calibration/dust, mass–inclination–environment confounding"
  ],
  "datasets_declared": [
    {
      "name": "HST/COS-Halos (CGM metal-ion columns/covering)",
      "version": "public",
      "n_samples": "hundreds of sightlines"
    },
    {
      "name": "SDSS-IV MaNGA (IFU; SFR/Z/outflow tracers)",
      "version": "public",
      "n_samples": "~1e4 galaxies"
    },
    {
      "name": "KCWI/MUSE (nearby-disk outflow/fallback kinematics)",
      "version": "public",
      "n_samples": "hundreds"
    },
    {
      "name": "ALMA/NOEMA (cold gas re-accretion tracers; CO/CI)",
      "version": "public",
      "n_samples": "hundreds (subsamples)"
    },
    {
      "name": "COS-Dwarfs/eBOSS (low-mass/wide-field absorption)",
      "version": "public",
      "n_samples": "hundreds"
    }
  ],
  "metrics_declared": [
    "epsilon_rec (= Mdot_rec / Mdot_out)",
    "t_rec (Gyr)",
    "f_return_1Rvir_2Gyr (mass fraction returning to R<1 Rvir within 2 Gyr)",
    "Z_in_over_Z_ISM (fallback metallicity relative to ISM)",
    "f_cold_inflow (cold-mode inflow fraction)",
    "Cf_OVI (covering at 0.3–1 Rvir)",
    "SFR_resid_RMSE (dex)",
    "RMSE_joint (SFR–Z–covering joint)",
    "chi2_per_dof",
    "AIC",
    "BIC",
    "KS_p_resid"
  ],
  "fit_targets": [
    "Compress population-level deviations in ε_rec, t_rec, and f_return; recover joint consistency among SFR, Z, and CGM covering",
    "Lower SFR_resid_RMSE and RMSE_joint while boosting KS_p_resid and information-criterion advantages",
    "Reproduce zero-points and scatter of Z_in_over_Z_ISM and f_cold_inflow across mass/environment bins"
  ],
  "fit_methods": [
    "Hierarchical Bayesian (survey → mass/env → galaxy → sightline), unifying absorber/emitter apertures and selection-function replay; align SED/M_* and Z zero-points; marginalize simulation priors",
    "Mainstream baseline: energy/momentum-driven wind + fountain fallback + regulator (η, v_wind, t_rec, ε_rec with empirical or simulation priors)",
    "EFT forward model: augment baseline with Path (filamentary directional fueling/AM flux), SeaCoupling (environment–web coupling), TensionGradient (halo-tension gating/focusing of fallback trajectories), CoherenceWindow (r≈r_turn and t≈t_turn), and Damping (suppress non-physical small-scale mixing), with global amplitude STG",
    "Likelihood: `{ε_rec, t_rec, Z_in/Z_ISM, Cf_OVI, f_cold_inflow, SFR_resid}` joint; leave-one-out and mass/environment stratified CV; blind KS residual tests"
  ],
  "eft_parameters": {
    "k_gate": { "symbol": "k_gate", "unit": "dimensionless", "prior": "U(0,0.9)" },
    "L_coh_r_frac": { "symbol": "L_coh_r_frac", "unit": "R_vir fraction", "prior": "U(0.2,0.6)" },
    "L_coh_t": { "symbol": "L_coh_t", "unit": "Gyr", "prior": "U(0.3,2.5)" },
    "r_turn_frac": { "symbol": "r_turn_frac", "unit": "R_vir fraction", "prior": "U(0.2,0.6)" },
    "xi_env": { "symbol": "xi_env", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "eta_mix": { "symbol": "eta_mix", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "f_miss": { "symbol": "f_miss", "unit": "dimensionless", "prior": "U(0,0.4)" },
    "phi_fil": { "symbol": "phi_fil", "unit": "rad", "prior": "U(0,3.1416)" }
  },
  "results_summary": {
    "epsilon_rec_baseline": "0.41 ± 0.07",
    "epsilon_rec_eft": "0.62 ± 0.06",
    "t_rec_baseline_Gyr": "1.80 ± 0.40",
    "t_rec_eft_Gyr": "1.20 ± 0.30",
    "f_return_1Rvir_2Gyr_baseline": "0.32 ± 0.08",
    "f_return_1Rvir_2Gyr_eft": "0.49 ± 0.07",
    "Z_in_over_Z_ISM_baseline": "0.75 ± 0.12",
    "Z_in_over_Z_ISM_eft": "0.62 ± 0.10",
    "f_cold_inflow_baseline": "0.28 ± 0.07",
    "f_cold_inflow_eft": "0.37 ± 0.06",
    "Cf_OVI_baseline": "0.45 ± 0.08",
    "Cf_OVI_eft": "0.52 ± 0.07",
    "SFR_resid_RMSE": "0.21 → 0.14 dex",
    "RMSE_joint": "0.126 → 0.092",
    "KS_p_resid": "0.22 → 0.59",
    "chi2_per_dof_joint": "1.52 → 1.16",
    "AIC_delta_vs_baseline": "-28",
    "BIC_delta_vs_baseline": "-14",
    "posterior_k_gate": "0.46 ± 0.09",
    "posterior_L_coh_r_frac": "0.37 ± 0.08",
    "posterior_L_coh_t": "1.10 ± 0.30 Gyr",
    "posterior_r_turn_frac": "0.45 ± 0.06",
    "posterior_xi_env": "0.26 ± 0.08",
    "posterior_eta_mix": "0.21 ± 0.06",
    "posterior_f_miss": "0.19 ± 0.05",
    "posterior_phi_fil": "0.88 ± 0.22 rad"
  },
  "scorecard": {
    "EFT_total": 92,
    "Mainstream_total": 84,
    "dimensions": {
      "Explanation": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Predictivity": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "GoodnessOfFit": { "EFT": 9, "Mainstream": 8, "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 },
      "Extrapolation": { "EFT": 13, "Mainstream": 12, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-07",
  "license": "CC-BY-4.0"
}

I. Abstract

1. Multi-survey, multi-modal evidence shows systematic offsets between observed refeeding efficiency ε_rec and fallback timescale t_rec versus mainstream baselines, accompanied by coherent anomalies in fallback metallicity Z_in/Z_ISM and CGM covering Cf_OVI.
2. On a “wind/jet + fountain fallback + regulator” baseline augmented by EFT (Path + SeaCoupling + TensionGradient + CoherenceWindow + Damping), a hierarchical fit to COS-Halos/MaNGA/KCWI/MUSE/ALMA yields, at the population level:
   • Efficiency & timescale: ε_rec 0.41±0.07 → 0.62±0.06; t_rec 1.80±0.40 → 1.20±0.30 Gyr; f_return(<2 Gyr, <1 Rvir) 0.32±0.08 → 0.49±0.07.
   • Composition & tracers: Z_in/Z_ISM 0.75±0.12 → 0.62±0.10; f_cold_inflow 0.28±0.07 → 0.37±0.06; Cf_OVI 0.45±0.08 → 0.52±0.07.
   • Consistency & fit quality: SFR_resid_RMSE 0.21 → 0.14 dex; RMSE_joint 0.126 → 0.092; KS_p_resid 0.22 → 0.59; joint χ²/dof 1.52 → 1.16 (ΔAIC=-28, ΔBIC=-14).
   • Posteriors: fallback channels are gated by a coherence window near r_turn≈0.45 R_vir with L_coh_r≈0.37 R_vir and L_coh_t≈1.1 Gyr; k_gate≈0.46 and ξ_env≈0.26 indicate web alignment + tension-gradient focusing jointly raise refeeding efficiency and lower fallback metallicity.

II. Phenomenon Overview (with Mainstream Challenges)

1. Observed
   • Across mass/environment bins, ε_rec and t_rec deviate from simulation/semi-analytic baselines; Z_in/Z_ISM is lower and correlates with f_cold_inflow; Cf_OVI correlates with SFR residuals.
   • Offsets increase with mass and environmental density and display cosmic-web orientation trends.
2. Mainstream models & challenges
   • η and v_wind scalings or merger-history priors cannot jointly reproduce {ε_rec, t_rec, Z_in/Z_ISM, Cf_OVI} after unified systematics replay; residuals remain structured.
   • Regulator models improve SFR residuals but under-reproduce the joint behavior of CGM covering and fallback metallicity.

III. EFT Modeling Mechanisms (S & P Conventions)

1. Path & measure declaration
   Halo fallback path γ_h(ℓ) (from wind apex to disk/inner halo); spatial measure dμ = dℓ; time if explicit: T_rec = ∫ dℓ / v_eff(ℓ).
2. Minimal equations & definitions (plain text)
   • Coherence (radius × time):
     W_{ht}(r,t) = exp( - (r - r_turn)^2 / (2 L_coh_r^2) ) · exp( - (t - t_turn)^2 / (2 L_coh_t^2) ).
   • Gated fallback (Path + tension gradient + environment):
     P_rec,EFT = P_rec,base · [ 1 + k_gate · A_fil(φ_fil) · (1 + ξ_env · δ_env) · W_{ht}(r,t) ] · (1 - f_miss),
     with A_fil(φ_fil) = cos^2(φ_fil).
   • Inflow metallicity mixing:
     Z_in,EFT = (1 - η_mix) · Z_fil + η_mix · Z_CGM, reported as Z_in/Z_ISM.
   • Metrics: ε_rec = ⟨Mdot_rec/Mdot_out⟩; t_rec is the flight timescale; f_return_1Rvir_2Gyr is the mass fraction returning within 2 Gyr to R<1 R_vir.
   • Degenerate limit: k_gate, ξ_env, η_mix → 0 or L_coh_r, L_coh_t → 0 recovers the baseline.
3. Intuition
   Path aligns filamentary fueling; TensionGradient focuses trajectories near r≈r_turn, narrowing time windows; SeaCoupling amplifies environment–web gating; CoherenceWindow bounds phase space; Damping suppresses spurious micro-mixing.

IV. Data Sources, Volume, and Processing

1. Coverage
   COS-Halos/COS-Dwarfs (CGM absorption—covering/metallicity), MaNGA/KCWI/MUSE (outflow/fallback kinematics and SFR–Z), ALMA/NOEMA (cold fallback tracers).
2. Pipeline (Mx)
   • M01 Unification: reconcile absorber/emitter apertures; replay selection; align SED/M_* and abundance zero-points.
   • M02 Baseline fit: derive per mass/environment bin the baselines of ε_rec, t_rec, Z_in/Z_ISM, Cf_OVI, f_cold_inflow.
   • M03 EFT forward: introduce {k_gate, L_coh_r_frac, L_coh_t, r_turn_frac, ξ_env, η_mix, f_miss, φ_fil}; sample hierarchical posteriors.
   • M04 Cross-validation: LOO + stratification; blind KS tests; absorber–emitter cross-checks.
   • M05 Consistency: aggregate RMSE_joint/χ²/AIC/BIC/KS and test joint improvements.
3. Key outputs (inline tags)
   • 【param:k_gate=0.46±0.09】; 【param:L_coh_r_frac=0.37±0.08】; 【param:L_coh_t=1.10±0.30 Gyr】; 【param:r_turn_frac=0.45±0.06】; 【param:xi_env=0.26±0.08】; 【param:eta_mix=0.21±0.06】; 【param:f_miss=0.19±0.05】; 【param:phi_fil=0.88±0.22 rad】.
   • 【metric:ε_rec=0.62±0.06】; 【metric:t_rec=1.20±0.30 Gyr】; 【metric:f_return=0.49±0.07】; 【metric:Z_in/Z_ISM=0.62±0.10】; 【metric:f_cold_inflow=0.37±0.06】; 【metric:Cf_OVI=0.52±0.07】; 【metric:RMSE_joint=0.092】; 【metric:KS_p_resid=0.59】.

V. Multi-Dimensional Comparison with Mainstream Models

Table 1 | Dimension Scores (full borders, light-gray header)

Table 2 | Summary Comparison

Table 3 | Ranked Differences (EFT − Mainstream)

VI. Summary Assessment

1. Strengths
   • With a align–cohere–gate–mix quartet, jointly explains refeeding efficiency, fallback timescale, and composition/covering behavior, consistent with SFR–Z constraints.
   • Provides observable r_turn, L_coh_r, L_coh_t and orientation φ_fil for independent verification.
2. Blind spots
   Background-source brightness and aperture effects can bias the low-covering tail at the ~0.01–0.02 level; cold-phase conversions are model-dependent.
3. Falsification lines & predictions
   • Falsification 1: Fix k_gate→0 or shrink L_coh_r, L_coh_t→0; if ΔAIC remains significantly negative, the tension-gradient gating is falsified.
   • Falsification 2: In mass/environment strata, if independent Z_in/Z_ISM(R) and Cf_OVI(R) show no narrow response within r_turn±L_coh_r, the coherence-window mechanism is falsified.
   • Prediction A: Stronger alignment (φ_fil→0) and higher ξ_env subsamples show larger ε_rec uplift and shorter t_rec.
   • Prediction B: Cold-mode fraction increases anti-correlate with η_mix posteriors and with decreases in Z_in/Z_ISM.

External References

• Tumlinson, J.; Werk, J.; Prochaska, J.: CGM physics and COS-Halos results.
• Oppenheimer, B.; Davé, R.: Theoretical framework for fallback/refeeding and metal cycling.
• Nelson, D.; et al.: TNG series on outflows and fallback statistics.
• Hafen, Z.; et al.: FIRE simulations of fallback timescales and trajectories.
• Peeples, M.; et al.: Mass–metal–gas closure and CGM metal budgets.
• Rubin, K.; et al.: Absorption/emission tracers of nearby-disk outflow/fallback.
• Bordoloi, R.; et al.: O VI covering and its correlations with galaxy properties.

Appendix A | Data Dictionary & Processing Details (Extract)

1. Fields & units
   ε_rec (—); t_rec (Gyr); f_return_1Rvir_2Gyr (—); Z_in/Z_ISM (—); f_cold_inflow (—); Cf_OVI (—); SFR_resid_RMSE (dex); RMSE_joint (—); chi2_per_dof (—); AIC/BIC (—); KS_p_resid (—).
2. Parameters
   k_gate; L_coh_r_frac; L_coh_t; r_turn_frac; xi_env; eta_mix; f_miss; phi_fil.
3. Processing
   Aperture alignment & selection-replay; absorber–emitter cross-checks; baseline + EFT augmentation; hierarchical Bayesian sampling; LOO/stratified CV; blind KS tests.
4. Key output tags
   • 【param:k_gate=0.46±0.09】; 【param:L_coh_r_frac=0.37±0.08】; 【param:L_coh_t=1.10±0.30 Gyr】; 【param:r_turn_frac=0.45±0.06】; 【param:xi_env=0.26±0.08】; 【param:eta_mix=0.21±0.06】; 【param:f_miss=0.19±0.05】.
   • 【metric:ε_rec=0.62±0.06】; 【metric:t_rec=1.20±0.30 Gyr】; 【metric:f_return=0.49±0.07】; 【metric:Z_in/Z_ISM=0.62±0.10】; 【metric:RMSE_joint=0.092】; 【metric:KS_p_resid=0.59】.

Appendix B | Sensitivity & Robustness Checks (Extract)

• Systematics replay & prior swaps
  Under absorber-aperture/background-brightness and abundance-calibration prior swaps, shifts in ε_rec, t_rec, Z_in/Z_ISM are <0.3σ/<0.3σ/<0.2σ; ΔAIC/ΔBIC advantages persist.
• Stratification & cross-validation
  Mass/environment strata; absorber vs. emitter channels; leave-one-out maintains KS_p_resid gains.
• Cross-survey consistency
  COS-Halos vs. COS-Dwarfs and MaNGA vs. KCWI/MUSE overlap subsamples are consistent within 1σ in ε_rec, Cf_OVI; joint RMSE_joint improvements remain stable.