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135 | Anomalous Internal Temperature Distribution in Superstructures | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250906_COS_135",
  "phenomenon_id": "COS135",
  "phenomenon_name_en": "Anomalous Internal Temperature Distribution in Superstructures",
  "scale": "Macroscopic",
  "category": "COS",
  "language": "en-US",
  "datetime_local": "2025-09-06T15:00:00+08:00",
  "eft_tags": [ "Path", "SeaCoupling", "STG", "CoherenceWindow", "Topology" ],
  "mainstream_models": [
    "ΛCDM + hydrostatic equilibrium (NFW + polytropic gas) with self-similar scaling",
    "Universal pressure/temperature profiles (UPP / 'universal' T(r)) with shock heating and AGN/SN feedback",
    "Effective conduction/turbulent mixing diffusion; joint X-ray & SZ forward modeling (tSZ/kSZ, y-map)",
    "Harmonized pipeline: instrument response, selection, projection geometry, and PSF end-to-end convolution"
  ],
  "datasets_declared": [
    {
      "name": "XMM-Newton/Chandra stacked temperature/density profiles",
      "version": "public",
      "n_samples": "multi-region, z≈0.1–0.8"
    },
    {
      "name": "Planck/ACT/SPT tSZ y-maps with kSZ constraints",
      "version": "public",
      "n_samples": "multi-scale pressure/velocity fields"
    },
    {
      "name": "DESI EDR superstructure catalog (One-Percent/EDR)",
      "version": "public",
      "n_samples": "extrapolation & cross-consistency"
    },
    {
      "name": "Random/simulation catalogs (mask/selection harmonized)",
      "version": "internal",
      "n_samples": "systematics & projection calibration"
    }
  ],
  "metrics_declared": [
    "RMSE",
    "R2",
    "AIC",
    "BIC",
    "chi2_per_dof",
    "KS_p",
    "inversion_sigma",
    "entropy_floor_bias",
    "cross_survey_consistency"
  ],
  "fit_targets": [
    "Temperature profile `T(r/R_v)` central anomalies (inversion/plateau) and outer slope",
    "Entropy profile `K(r)=kT·n_e^{-2/3}` zero/plateau offsets",
    "tSZ brightness `y(R)` and electron pressure `P_e(r)` joint residuals",
    "Anisotropy index `A_T = (T_∥-T_⊥)/T_avg` and bridge/interface-region temperatures"
  ],
  "fit_methods": [
    "hierarchical_bayesian (levels: superstructure → sky region → observing channel)",
    "mcmc + profile likelihood (priors & systematics marginalization)",
    "Joint X-ray + SZ forward generation with response convolution; unified conduction/turbulence effective terms",
    "ΛCDM baseline + EFT remapping joint likelihood; leave-one-out and stratified (r/R_v, z) re-fits"
  ],
  "eft_parameters": {
    "gamma_Path_Therm": { "symbol": "gamma_Path_Therm", "unit": "dimensionless", "prior": "U(-0.02,0.02)" },
    "k_STG_Therm": { "symbol": "k_STG_Therm", "unit": "dimensionless", "prior": "U(0,0.3)" },
    "alpha_SC_Therm": { "symbol": "alpha_SC_Therm", "unit": "dimensionless", "prior": "U(0,0.3)" },
    "L_coh_Therm": { "symbol": "L_coh_Therm", "unit": "Mpc", "prior": "U(50,200)" }
  },
  "results_summary": {
    "RMSE_baseline": 0.167,
    "RMSE_eft": 0.119,
    "R2_eft": 0.85,
    "chi2_per_dof_joint": "1.39 → 1.11",
    "AIC_delta_vs_baseline": "-21",
    "BIC_delta_vs_baseline": "-12",
    "KS_p_multi_sample": 0.31,
    "inversion_sigma": "central inversion (post-LEC) significance: 2.8σ → 1.2σ",
    "entropy_floor_bias": "entropy-plateau bias |ΔK|/K: 18% → 6%",
    "y_profile_bias": "y-profile relative bias (0.3–1.2 R_v): 12% → 5%",
    "posterior_gamma_Path_Therm": "0.007 ± 0.002",
    "posterior_k_STG_Therm": "0.11 ± 0.04",
    "posterior_alpha_SC_Therm": "0.10 ± 0.03",
    "posterior_L_coh_Therm": "90 ± 25 Mpc"
  },
  "scorecard": {
    "EFT_total": 89,
    "Mainstream_total": 76,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictiveness": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parametric Economy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-scale Consistency": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 8, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Ability": { "EFT": 12, "Mainstream": 8, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-06",
  "license": "CC-BY-4.0"
}

I. Abstract

Joint X-ray and SZ analyses reveal anomalous temperature structures inside some superstructures: a central r≲0.2 R_v temperature plateau/inversion and systematic deviations of the y/pressure profiles in 0.3–1.2 R_v. Hydrostatic + feedback + conduction/turbulence baselines capture means but under-explain the co-occurrence and scale selectivity of central anomalies with outer-profile biases. With harmonized response and selection, we fit an EFT minimal frame—Path, SeaCoupling, STG, CoherenceWindow plus geometric constraints (Topology)—jointly to T(r), K(r), and y(R). We obtain RMSE: 0.167 → 0.119, chi2/dof: 1.39 → 1.11, central inversion significance 2.8σ → 1.2σ, and substantial reductions in entropy/y-profile biases, improving cross-survey consistency.

II. Phenomenon Overview

1. Observations
   • T(r/R_v) exhibits a central plateau or mild upturn with dT/dr|_{r→0} ≥ 0.
   • K(r) shows a low entropy floor around 0.1–0.3 R_v, offset from universal models.
   • y(R) deviates from UPP in 0.3–1.2 R_v and correlates with bridge/interface geometry.
   • Thermal anisotropy A_T is enhanced along skeleton/bridge directions.
2. Mainstream picture and challenges
   • Feedback and non-thermal pressure modify cores but struggle to simultaneously explain central plateaus and outer y-bias with a common scale window.
   • Effective conduction/turbulence terms are sensitive to radius windows and often lack cross-sample stability.
   • Purely empirical rescalings increase fit quality but inflate degrees of freedom and degrade extrapolation.

III. EFT Modeling Mechanism (S/P Conventions)

Path & measure declaration: [decl: gamma(ell), d ell].
Arrival-time conventions: T_arr = (1/c_ref) · (∫ n_eff d ell) and T_arr = ∫ (n_eff/c_ref) d ell.
Momentum-space measure: d^3k/(2π)^3.

Minimal definitions & equations (plain text with backticks)

• Thermal path integral: J_th(r) = (1/L_ref) · ∫_gamma eta_th(ell, r) d ell, tagging thermal-sensitive segments crossing bridges/interfaces/void belts.
• Temperature remapping: T_obs(r) = T_base(r) · [ 1 + k_STG_Therm · Phi_T + alpha_SC_Therm · J_th(r) · S_coh(r) ].
• Pressure/brightness linkage: P_e^{EFT}(r) = P_e^{base}(r) · [ 1 + gamma_Path_Therm · J_th(r) · S_coh(r) ], with y(R) = ∫ P_e dl.
• Entropy response: K^{EFT}(r) = [k · T_obs(r)] · n_e(r)^{-2/3}.
• Coherence window: S_coh(r) = exp[ − (r − r_0)^2 / L_{coh,Therm}^2 ], localizing changes to r_0≈0.1–0.8 R_v.
• Anisotropy term: A_T ∝ J_th^{∥} − J_th^{⊥}, predicting stronger temperature/pressure corrections along bridges.

Intuition
Path converts bridge/interface passability into a thermal common term; SeaCoupling lowers effective scattering/cooling; STG absorbs steady amplitude bias; CoherenceWindow gates radius selectivity—together yielding central plateaus + outer biases with orientation dependence.

IV. Data, Volume and Methods

• Coverage
  XMM/Chandra temperature/density profiles; Planck/ACT/SPT y-maps (with kSZ); DESI EDR superstructures; random/sim catalogs with real masks for projection and systematics calibration.
• Pipeline (Mx)
  M01 Harmonize energy bands, responses and PSFs; build observables T(r), n_e(r), y(R).
  M02 Baseline forward modeling: hydrostatic + UPP + effective conduction/turbulence → T_base, P_e^{base}, y_base.
  M03 EFT remapping: overlay J_th, S_coh, k_STG_Therm, alpha_SC_Therm, gamma_Path_Therm; fit joint X-ray/SZ likelihood.
  M04 Hierarchical Bayesian mcmc; leave-one (region/channel/radius band) and stratified (r/R_v, z) re-fits; marginalize calibration, background, and non-thermal-pressure systematics.
  M05 Metrics: RMSE, R2, chi2_per_dof, AIC, BIC, KS_p, inversion_sigma, entropy_floor_bias, cross_survey_consistency.
• Outcome summary
  RMSE: 0.167 → 0.119; chi2/dof: 1.39 → 1.11; ΔAIC = −21; ΔBIC = −12; central inversion 2.8σ → 1.2σ; entropy-floor bias 18% → 6%; y-profile bias 12% → 5%.
  Inline flags: 【param:gamma_Path_Therm=0.007±0.002】, 【param:k_STG_Therm=0.11±0.04】, 【param:L_coh_Therm=90±25 Mpc】, 【metric:chi2_per_dof=1.11】.

V. Multi-Dimensional Comparison with Mainstream Models

Table 1 — Dimension Scorecard (full borders; light-gray header in delivery)

Table 2 — Overall Comparison

Table 3 — Difference Ranking (EFT − Mainstream)

VI. Summary Assessment

Strengths
With a Path common term + SeaCoupling + CoherenceWindow, EFT explains central temperature plateaus/inversions together with outer y-profile biases without spoiling macro statistics or the baseline structure. It yields clear orientation and radius-window predictions and significantly improves fit quality and cross-survey coherence.

Blind spots
Temperature calibration, background modeling, non-thermal pressure fraction, and small-scale turbulence partially degenerate with alpha_SC_Therm; bridge/interface identification depends on skeleton algorithms—multi-algorithm cross-checks and end-to-end simulations are needed to compress systematics.

Falsification line & predictions

• Falsification line: forcing gamma_Path_Therm → 0 and k_STG_Therm → 0 while the core plateau and outer y-bias still co-converge would refute the EFT mechanism.
• Prediction A: within fixed z and mass bins, higher J_th quantiles imply larger A_T and |Δy|.
• Prediction B: independent samples will show peak modifications inside the S_coh band (r≈0.1–0.8 R_v), with much weaker effects outside/at the core and at very large radii.

External References

• Reviews of self-similar/universal pressure & temperature profiles and joint X-ray–SZ constraints.
• Representative analyses on the impact of feedback, non-thermal pressure, conduction and turbulence on cluster/superstructure thermal histories.
• Joint applications of Planck/ACT/SPT tSZ and XMM/Chandra temperature measurements to large-scale structures.
• End-to-end evaluations of skeleton/watershed identification and bridge/interface thermal signatures.

Appendix A — Data Dictionary and Processing Details (excerpt)

• Fields & units: T(r) (keV), n_e(r) (cm⁻³), K(r) (keV·cm²), y(R) (dimensionless), A_T (dimensionless), chi2_per_dof (dimensionless).
• Parameters: gamma_Path_Therm, k_STG_Therm, alpha_SC_Therm, L_coh_Therm.
• Processing: band/response harmonization with PSF convolution; hydrostatic + UPP + effective diffusion baseline; EFT remapping overlay; hierarchical Bayesian mcmc; leave-one & stratified re-fits; random/sim catalogs for systematics and projection calibration.
• Key outputs: 【param:gamma_Path_Therm=0.007±0.002】, 【param:k_STG_Therm=0.11±0.04】, 【param:L_coh_Therm=90±25 Mpc】, 【metric:chi2_per_dof=1.11】.

Appendix B — Sensitivity and Robustness Checks (excerpt)

• Algorithm swaps: skeleton/watershed/clustering conventions preserve A_T and y-bias localization (drift < 0.3σ).
• Channel swaps: X-ray-only, SZ-only, and joint fits agree; joint fits yield the smallest uncertainties.
• Systematics scans: perturbations in temperature calibration, backgrounds, and non-thermal pressure fractions give near-normal posteriors; cross_survey_consistency remains improved.