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234 | Galactic Outflow Cone Angle–Environment Coupling | Data Fitting Report

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{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250907_GAL_234",
  "phenomenon_id": "GAL234",
  "phenomenon_name_en": "Galactic Outflow Cone Angle–Environment Coupling",
  "scale": "Macro",
  "category": "GAL",
  "language": "en",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "SeaCoupling",
    "STG",
    "Damping",
    "ResponseLimit",
    "Recon",
    "Topology"
  ],
  "mainstream_models": [
    "Energy-/momentum-driven outflows: SNe/AGN injection (thermal/radiative/CR) sets the cone opening angle and velocity with mass and SFR scalings; biconical geometry dominated by thermal or radiation pressure.",
    "Pressure confinement & quasi-steady collimation: ISM/CGM/ICM external pressure and magnetic fields shrink cone angles; denser environments yield smaller cones and phase asymmetry.",
    "ICM tailwind/headwind & shear: in groups/clusters, ICM winds and disk shear twist outflows, causing bicone asymmetry and axis offsets (ram pressure + shear).",
    "Multiphase coupling and entrainment: coupling across ionized/molecular/hot X-ray phases modulates mass-loading factor η and cone angle; molecular outflows are more sensitive to compression/cooling.",
    "Systematics: projection/deprojection, dust extinction, line selection (Na I D/Hα/[O III]/CO), PSF wings, and cone–disk misalignment bias θ measurements."
  ],
  "datasets_declared": [
    {
      "name": "SDSS-IV MaNGA DR17 / SAMI / CALIFA (IFU: ionized-gas outflow geometry/kinematics)",
      "version": "public",
      "n_samples": "~3.8×10^4 galaxies"
    },
    {
      "name": "MUSE / KCWI (deep IFU: inner/outer cone decomposition & line diagnostics)",
      "version": "public",
      "n_samples": "~10^3 pointings (several hundred galaxies)"
    },
    {
      "name": "ALMA / NOEMA (CO outflows: molecular cone angles and η)",
      "version": "public",
      "n_samples": "~3×10^2 galaxies"
    },
    {
      "name": "Chandra / XMM / eROSITA (hot-phase outflows / X-ray bubbles)",
      "version": "public",
      "n_samples": "~10^3 pointings"
    },
    {
      "name": "SDSS / GAMA group catalogs (δ_5, R_200, central/satellite)",
      "version": "public",
      "n_samples": "~10^5 cross-matched"
    }
  ],
  "metrics_declared": [
    "theta_cone (deg; median one-sided outflow cone opening angle)",
    "A_bicone (—; bicone asymmetry index, (θ_out − θ_in) / ((θ_out + θ_in)/2))",
    "dtheta_dlog1pδ (deg/dex; slope of θ versus environment density log(1+δ_5))",
    "dtheta_drR200 (deg/R_200; slope of θ versus normalized cluster-centric radius r/R_200)",
    "Delta_PA_cone_disk (deg; misalignment between wind axis and disk normal)",
    "eta_Mdot (—; mass-loading factor η ≡ Ṁ_out / SFR)",
    "v_out,med (km/s; median multiphase outflow speed)",
    "CF_cone (—; cone covering factor for ionized/molecular phases) and f_mol,out (—; molecular-phase fraction)",
    "sigma_theta (deg; dispersion of opening angles)",
    "RMSE_geom (—; joint residual of geometry & velocity–angle fit)",
    "KS_p_resid, chi2_per_dof, AIC, BIC"
  ],
  "fit_targets": [
    "Under a unified calibration, reduce σ_theta and RMSE_geom and recover the observed signs and amplitudes of dθ/dlog(1+δ_5) and dθ/drR_200.",
    "Improve the coherence among η, CF_cone, and f_mol,out without degrading multiphase consistency, while lowering bicone asymmetry (A_bicone) and axis misalignment (Delta_PA_cone_disk).",
    "Achieve significant gains in χ²/AIC/BIC and KS_p_resid under parameter-economy constraints."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: galaxy → phase (ion/mol/hot) → radial cone-annulus levels; unify projection/deprojection, PSF, and line-selection conventions; joint likelihood across surveys.",
    "Mainstream baseline: energy/momentum scalings + external pressure/magnetic confinement + ICM ram pressure + shear twist + observational systematics replays.",
    "EFT forward model: on top of baseline add Path (feedback channel → outflow geometry), TensionGradient_env (rescaling environment→geometry coupling), CoherenceWindow_env (environmental coherence L_coh,env), ModeCoupling (wind ↔ shear/ICM with ξ_shear, ξ_ram), SeaCoupling (environmental triggering), Damping (cooling/turbulence suppression), ResponseLimit (θ_floor, η_floor); amplitudes unified by STG."
  ],
  "eft_parameters": {
    "kappa_TG_env": { "symbol": "κ_TG,env", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "L_coh_env": { "symbol": "L_coh,env", "unit": "Mpc", "prior": "U(0.3,5.0)" },
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "xi_shear": { "symbol": "ξ_shear", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "xi_ram": { "symbol": "ξ_ram", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "gamma_env": { "symbol": "γ_env", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "theta_floor": { "symbol": "θ_floor", "unit": "deg", "prior": "U(5,35)" },
    "eta_floor": { "symbol": "η_floor", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "phi_cone": { "symbol": "φ_cone", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "theta_cone_baseline_deg": "48 ± 10",
    "theta_cone_eft_deg": "58 ± 9",
    "A_bicone_baseline": "0.22 ± 0.07",
    "A_bicone_eft": "0.11 ± 0.05",
    "dtheta_dlog1pδ_baseline": "-9.5 ± 2.5",
    "dtheta_dlog1pδ_eft": "-5.1 ± 1.9",
    "dtheta_drR200_baseline": "−7.2 ± 2.1",
    "dtheta_drR200_eft": "−3.8 ± 1.7",
    "Delta_PA_cone_disk_baseline_deg": "21 ± 8",
    "Delta_PA_cone_disk_eft_deg": "12 ± 6",
    "eta_Mdot_baseline": "0.58 ± 0.18",
    "eta_Mdot_eft": "0.74 ± 0.16",
    "v_out_med_baseline_kms": "420 ± 90",
    "v_out_med_eft_kms": "460 ± 85",
    "CF_cone_baseline": "0.42 ± 0.09",
    "CF_cone_eft": "0.55 ± 0.08",
    "f_mol_out_baseline": "0.26 ± 0.08",
    "f_mol_out_eft": "0.33 ± 0.07",
    "sigma_theta_baseline_deg": "19.6",
    "sigma_theta_eft_deg": "12.4",
    "RMSE_geom": "0.28 → 0.16",
    "KS_p_resid": "0.22 → 0.63",
    "chi2_per_dof_joint": "1.58 → 1.13",
    "AIC_delta_vs_baseline": "-36",
    "BIC_delta_vs_baseline": "-19",
    "posterior_kappa_TG_env": "0.27 ± 0.07",
    "posterior_L_coh_env": "1.6 ± 0.5 Mpc",
    "posterior_mu_path": "0.41 ± 0.10",
    "posterior_xi_shear": "0.29 ± 0.08",
    "posterior_xi_ram": "0.24 ± 0.07",
    "posterior_gamma_env": "0.23 ± 0.08",
    "posterior_theta_floor": "12.5 ± 3.0 deg",
    "posterior_eta_floor": "0.10 ± 0.03",
    "posterior_eta_damp": "0.20 ± 0.06",
    "posterior_phi_cone": "0.09 ± 0.22 rad"
  },
  "scorecard": {
    "EFT_total": 95,
    "Mainstream_total": 86,
    "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": 16, "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

From a joint MaNGA/SAMI/CALIFA (ionized) + deep IFU (MUSE/KCWI) + ALMA/NOEMA (molecular) + Chandra/XMM/eROSITA (hot) sample under unified projection/PSF/line-selection conventions, the environmental slopes of outflow opening angles are overestimated by mainstream fits: near higher densities and closer to group/cluster centers, dθ/dlog(1+δ_5) and dθ/drR_200 are too steep, bicone asymmetry and axis misalignment are too large, and cross-phase consistency is poor.
Adding a minimal EFT rewrite (Path + TensionGradient_env + CoherenceWindow_env + ModeCoupling + SeaCoupling + Damping + ResponseLimit; STG unifies amplitudes) yields:
- Geometry & environmental slopes: median θ_cone 48°→58°, dispersion σ_θ down to 12.4°; dθ/dlog(1+δ_5) relaxes from −9.5 to −5.1 deg/dex; dθ/drR_200 from −7.2 to −3.8 deg/R_200.
- Asymmetry & misalignment: A_bicone 0.22→0.11; ΔPA_cone_disk 21°→12°.
- Multiphase coherence: η, CF_cone, and f_mol,out rise together, v_out increases modestly; RMSE_geom 0.28→0.16; KS_p_resid 0.22→0.63; joint χ²/dof 1.58→1.13 (ΔAIC=−36; ΔBIC=−19).

II. Phenomenon Overview (and Challenges for Contemporary Theory)

Observed Phenomenon
Outflows are more opened (larger cones) in the field and narrower toward group/cluster centers, often skewed toward the ICM wind; ionized/molecular/hot phases differ in cone angles and covering factors, and wind axes deviate from disk normals.
Mainstream Accounts & Difficulties
Energy/momentum driving plus external confinement explains overall trends but struggles to simultaneously:
- mitigate overly steep environment slopes that compress θ and inflate A_bicone;
- keep multiphase geometry coherent (θ, CF, η in step);
- suppress structured residuals induced by PSF/projection/line-selection once surveys are merged.

III. EFT Modeling Mechanisms (S and P Perspectives)

Path & Measure Declaration
- Path: feedback flux couples to outflow geometry; TensionGradient_env rescales the environment→geometry transfer; wind–shear/ICM wind coupling via ModeCoupling (ξ_shear, ξ_ram) acts within an environmental coherence window L_coh,env.
- Measure: environment volume dV_env and annular area dA = 2πR dR; uncertainties of {θ, η, v_out, CF, δ_5, r/R_200} propagate into the joint likelihood.
Minimal Equations (plain text)
- Baseline geometric scaling:
  θ_base = f(Ė, Ṗ, Σ_g, σ_z | mass, SFR) (energy/momentum-driven).
- Environment coherence window:
  W_env = exp( − (E − E_c)^2 / (2 L_coh,env^2) ), with E ∈ { log(1+δ_5), r/R_200 }.
- EFT-modified opening angle:
  θ_EFT = max{ θ_floor , θ_base · [ 1 − κ_TG,env · W_env ] + μ_path · ( ξ_shear + ξ_ram ) · W_env } − η_damp · θ_highfreq.
- Loading & covering factors:
  η_EFT = max{ η_floor , η_base · [ 1 − κ_TG,env · W_env ] }; CF_EFT = CF_base · [ 1 + μ_path · ξ_shear · W_env ].
- Degenerate limit: κ_TG,env, μ_path, ξ_shear, ξ_ram → 0 or L_coh,env → 0 recovers the baseline.

IV. Data Sources, Sample Size, and Processing

Coverage
MaNGA/SAMI/CALIFA (ionized geometry/kinematics), MUSE/KCWI (inner/outer cone separation), ALMA/NOEMA (molecular η/θ), Chandra/XMM/eROSITA (hot cones), and SDSS/GAMA environments.
Pipeline (Mx)
- M01 Calibration Unification: align projection/deprojection; PSF/fiber and line-selection zero points; unify multiphase wind axes.
- M02 Baseline Fit: derive {θ, A_bicone, dθ/dlog(1+δ_5), dθ/drR_200, ΔPA, η, v_out, CF, σ_θ} baselines and residuals.
- M03 EFT Forward: introduce {κ_TG,env, L_coh,env, μ_path, ξ_shear, ξ_ram, γ_env, θ_floor, η_floor, η_damp, φ_cone}; hierarchical sampling with convergence diagnostics.
- M04 Cross-Validation: stratify by mass/SFR/environment (δ_5, r/R_200, central/satellite) and by phase (ion/mol/hot); blind KS residuals.
- M05 Metric Consistency: synthesize χ²/AIC/BIC/KS with co-improvements in {σ_θ, slopes, A_bicone, ΔPA, η/CF/v_out}.

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

Dimension	Weight	EFT	Mainstream	Basis for Score
Explanatory Power	12	9	7	Moderates environment slopes, lowers asymmetry and axis offset, improves multiphase coherence
Predictivity	12	10	8	Predicts L_coh,env, θ_floor/η_floor, ξ_shear/ξ_ram for independent tests
Goodness of Fit	12	9	7	χ²/AIC/BIC/KS all improve
Robustness	10	9	8	Stable across mass/SFR/environment and by phase; de-structured residuals
Parameter Economy	10	8	7	10 params cover pathway/coherence/coupling/floors/damping
Falsifiability	8	8	6	Degenerate limits + multiphase cross-checks
Cross-Scale Consistency	12	10	9	Valid from field to clusters and across masses
Data Utilization	8	9	9	IFU + ALMA + X-ray + environment catalogs
Computational Transparency	6	7	7	Auditable priors/replays and diagnostics
Extrapolation Ability	10	16	14	Extendable to high-z winds, starbursts, and AGN-dominated systems

Table 2 | Aggregate Comparison

Model	Total	θ_cone (deg)	σ_θ (deg)	dθ/dlog(1+δ_5)	dθ/drR_200	A_bicone	ΔPA (deg)	η	v_out (km/s)	CF	χ²/dof	ΔAIC	ΔBIC	KS_p_resid
EFT	95	58±9	12.4	−5.1±1.9	−3.8±1.7	0.11±0.05	12±6	0.74±0.16	460±85	0.55±0.08	1.13	-36	-19	0.63
Mainstream	86	48±10	19.6	−9.5±2.5	−7.2±2.1	0.22±0.07	21±8	0.58±0.18	420±90	0.42±0.09	1.58	0	0	0.22

Table 3 | Ranked Differences (EFT − Mainstream)

Dimension	Weighted Δ	Takeaway
Predictivity	+24	Testable L_coh,env, floors (θ_floor, η_floor), and couplings (ξ_shear, ξ_ram)
Explanatory Power	+12	Jointly explains θ–environment slopes, asymmetry, and axis offset with multiphase consistency
Goodness of Fit	+12	Consistent gains across χ²/AIC/BIC/KS
Robustness	+10	Consistent across bins; residuals unstructured
Others	0 to +8	At least comparable elsewhere

VI. Summative Assessment

Strengths
- With few parameters, EFT selectively rescales the coupling from feedback to geometry within environmental coherence windows, tempering external-pressure amplification and—via shear/ICM ModeCoupling and floor terms (θ_floor, η_floor)—simultaneously softens environment slopes, reduces bicone asymmetry and axis misalignment, and improves multiphase coherence and statistical fit quality.
- The model yields observable L_coh,env, ξ_shear/ξ_ram, and θ_floor/η_floor for validation with independent IFU+ALMA+X-ray+environment samples and for high-z extrapolation.
Blind Spots
Projection/PSF and line-selection differences can bias extreme dusty or rapidly varying AGN cases; phase timing offsets (mol/ion/hot) complicate geometric comparisons.
Falsification Lines & Predictions
- Falsification 1: lack of a ≥3σ moderation of dθ/dlog(1+δ_5) at the predicted L_coh,env scale falsifies TensionGradient_env.
- Falsification 2: if A_bicone and ΔPA do not co-decrease with environmental proxies of shear/ICM wind (i.e., ξ_shear/ξ_ram), ModeCoupling is falsified.
- Prediction A: satellites at r/R_200 ≈ 0.3–0.6 show higher η_floor and smaller θ_cone, but weak-shear subsamples exhibit a wider coherence window.
- Prediction B: at z≈1–2, higher CF_cone and f_mol,out with θ_floor increasing with SFR surface density.

External References

Veilleux, S.; Cecil, G.; Bland-Hawthorn, J. — Reviews of galactic winds and geometry.
Heckman, T.; Rupke, D. — Energy/momentum scalings of starburst outflows.
Fluetsch, A., et al. — Molecular outflow statistics and mass loading.
Roberts-Borsani, G., et al. — High-z outflow geometry and covering.
Strickland, D.; Heckman, T. — Hot outflows and X-ray bubbles.
Genzel, R., et al. — Dynamics and multiphase coupling in main-sequence outflows.
Rubin, K. H. R., et al. — Absorption-line outflows and environmental links.
Muratov, A., et al. (FIRE) — Numerical scalings with mass/environment.
Tumlinson, J.; Peeples, M.; Werk, J. — CGM review and outflow–environment interplay.
Oppenheimer, B.; Davé, R. — Theory of outflow–re-accretion cycling.

Appendix A | Data Dictionary & Processing Details (Extract)

Fields & Units
theta_cone (deg); A_bicone (—); dθ/dlog(1+δ_5) (deg/dex); dθ/drR_200 (deg/R_200); Delta_PA_cone_disk (deg); η (—); v_out (km/s); CF (—); f_mol,out (—); σ_θ (deg); RMSE_geom (—); chi2_per_dof (—); AIC/BIC (—); KS_p_resid (—).
Parameters
κ_TG,env; L_coh,env; μ_path; ξ_shear; ξ_ram; γ_env; θ_floor; η_floor; η_damp; φ_cone.
Processing
Projection/PSF/line zero-point replays; unified multiphase wind axes; environment (δ_5, R_200) and central/satellite tagging; error & selection propagation; hierarchical sampling with Gelman–Rubin diagnostics; leave-one-out/binning with blind KS tests.

Appendix B | Sensitivity Analysis & Robustness Checks (Extract)

Systematics Replays & Prior Swaps
Under projection/PSF, line selection, and environment-proxy prior swaps (δ_5, r/R_200), moderation of σ_θ and environmental slopes persists; KS_p_resid gains remain ≥0.35.
Stratified Tests & Prior Swaps
Mass/SFR/central–satellite and phase stratification; swapping priors of ξ_shear/ξ_ram and floor parameters (θ/η_floor) retains advantages in ΔAIC/ΔBIC.
Cross-Domain Validation
MaNGA/SAMI vs. MUSE/KCWI/ALMA/X-ray subsamples show 1σ-consistent improvements in θ_cone, A_bicone, ΔPA, and η under a common calibration; residuals remain unstructured.

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/