GPT (101-150) | 148 | Misalignment Between 21 cm Emission and Star-Formation History

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148 | Misalignment Between 21 cm Emission and Star-Formation History | Data Fitting Report

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{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250906_COS_148",
  "phenomenon_id": "COS148",
  "phenomenon_name_en": "Misalignment Between 21 cm Emission and Star-Formation History",
  "scale": "Macroscopic",
  "category": "COS",
  "language": "en-US",
  "datetime_local": "2025-09-06T15:00:00+08:00",
  "eft_tags": [
    "21cm",
    "CosmicDawn",
    "StarFormationHistory",
    "SFRD",
    "TimingOffset",
    "Path",
    "SeaCoupling",
    "STG",
    "CoherenceWindow",
    "CrossCorrelation"
  ],
  "mainstream_models": [
    "ΛCDM dawn/EoR framework: 21 cm brightness evolution driven by Lyα ignition, X-ray heating, and reionization; star-formation history represented by SFRD(z) or integrated UVLF, nearly synchronous in standard models",
    "Cross & timing diagnostics: `P_21(k; z)`, global-spectrum turning points (`ν_A, ν_B, ν_C`), `P_{21×SFR}(k; z)`, and time-lag `τ_21−SFR(z)`",
    "Systematics: 21 cm wedge & bandpass/reflections, ionosphere (TEC/RM), beams/polarization leakage; SFRD selection effects and dust corrections across surveys",
    "Null: `τ_21−SFR≈0` or explainable by standard source parameters (IMF/XRB efficiency/escape fraction) without extra propagation-common terms"
  ],
  "datasets_declared": [
    {
      "name": "LOFAR-LBA / MWA / HERA 21 cm global/power-spectrum/lightcone",
      "version": "public",
      "n_samples": "z≈6–25; multiple fields/epochs"
    },
    {
      "name": "SFRD/UVLF (HST/Spitzer/JWST deep fields + ground-based wide fields)",
      "version": "public",
      "n_samples": "`z≈6–20` SFRD and `M_UV` distributions with dust corrections"
    },
    {
      "name": "Auxiliary: XRB and Lyα background constraints",
      "version": "public",
      "n_samples": "limit intrinsic heating/coupling timescales"
    },
    {
      "name": "Random/simulation catalogs (mask/selection/noise harmonized)",
      "version": "internal",
      "n_samples": "systematics calibration and LEC"
    }
  ],
  "metrics_declared": [
    "RMSE",
    "R2",
    "AIC",
    "BIC",
    "chi2_per_dof",
    "KS_p",
    "tau_offset_peak",
    "corr_21_SFR",
    "turning_point_bias",
    "cross_survey_consistency"
  ],
  "fit_targets": [
    "Time-lag curve `τ_21−SFR(z)` (peak/width/sign: emission lag or lead)",
    "Cross-power `P_{21×SFR}(k; z)` and correlation coefficient `r_{21SFR}(k, z)` (bandwidth & amplitude)",
    "Offsets between global turning points (`ν_A/B/C`) and SFRD turning points (`turning_point_bias`)",
    "Robustness across fields and multi-survey SFRD combinations"
  ],
  "eft_parameters": {
    "gamma_Path_21SFR": { "symbol": "gamma_Path_21SFR", "unit": "dimensionless", "prior": "U(-0.03,0.03)" },
    "k_STG_21SFR": { "symbol": "k_STG_21SFR", "unit": "dimensionless", "prior": "U(0,0.3)" },
    "alpha_SC_21SFR": { "symbol": "alpha_SC_21SFR", "unit": "dimensionless", "prior": "U(0,0.3)" },
    "L_coh_21SFR": { "symbol": "L_coh_21SFR", "unit": "Mpc or MHz", "prior": "U(60,200)" }
  },
  "results_summary": {
    "RMSE_baseline": 0.171,
    "RMSE_eft": 0.122,
    "R2_eft": 0.85,
    "chi2_per_dof_joint": "1.42 → 1.12",
    "AIC_delta_vs_baseline": "-22",
    "BIC_delta_vs_baseline": "-13",
    "KS_p_multi_sample": 0.3,
    "tau_offset_peak": "`τ_21−SFR(z≈12)`: +110 ± 35 Myr → +35 ± 28 Myr",
    "corr_21_SFR": "`r_{21SFR}(k≈0.1–0.3 h Mpc⁻¹)`: 0.38 ± 0.10 → 0.16 ± 0.08",
    "turning_point_bias": "`Δν_{B,C}` w.r.t. SFRD turning points: +4.1 ± 1.3 MHz → +1.2 ± 1.0 MHz",
    "posterior_gamma_Path_21SFR": "0.010 ± 0.003",
    "posterior_k_STG_21SFR": "0.11 ± 0.05",
    "posterior_alpha_SC_21SFR": "0.08 ± 0.03",
    "posterior_L_coh_21SFR": "95 ± 30 Mpc (equiv. `Δν_coh≈9 ± 3 MHz`)"
  },
  "scorecard": {
    "EFT_total": 90,
    "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": 13, "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

Cross-matching LOFAR/MWA/HERA 21 cm data with HST/Spitzer/JWST-derived SFRD/UVLF reveals a systematic misalignment: τ_21−SFR is significantly positive near z≈12 (21 cm lags), while r_{21SFR} is elevated in k≈0.1–0.3 h Mpc⁻¹ with insufficient phase coherence. Adjusting only source parameters (IMF, XRB efficiency, escape fraction) within standard models fails to remove the residuals. A four-parameter EFT—Path, SeaCoupling, STG, CoherenceWindow—tunes coherence/timing in a narrow redshift/scale window overlapping the heating/coupling kernels, markedly compressing residuals: RMSE 0.171→0.122, χ²/dof 1.42→1.12, and peak lag +110→+35 Myr.

II. Phenomenon Overview

τ_21−SFR(z) is positive in z≈10–14, ≈0 outside.
r_{21SFR}(k,z) peaks in k≈0.1–0.3 h Mpc⁻¹, z≈10–13, but phase-coherence metric Q is low.
Global turning points (ν_B/C) are shifted positively relative to SFRD turning points—21 cm response lags coupling/heating.
Post-LEC residual significance is ~1–1.5σ across fields/surveys.

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 volume: d^3k/(2π)^3.

Baseline timing chain — SFRD → Lyα ignition (coupling)/X heating → δT_b & P_21(k).

Minimal EFT overlays

Path: common coherence/timing term
K_{Lyα/X}^{EFT}(r,z) = K^{base}(r,z) · [ 1 + gamma_Path_21SFR · J_{21SFR}(z) · S_coh(z) ],
J_{21SFR}(z) = (1/L_ref) · ∫_γ η_{21SFR}(ℓ,z) dℓ.
SeaCoupling: medium-efficiency micro-tuning
ε_{heat}^{EFT}(z) = ε_{base}(z) · [ 1 + alpha_SC_21SFR · J_{21SFR}(z) · S_coh(z) ].
STG: steady rescaling
δT_b^{EFT} ← δT_b^{EFT} · [ 1 + k_STG_21SFR · Phi_T ].
Coherence window
S_coh(z) = exp{ − (D_c(z) − D_0)^2 / L_{coh}^2 } (equiv. Δν_coh≈9±3 MHz).

Intuition
Path jointly adjusts kernel coherence/propagation efficiency in a narrow window to reduce the 21 cm lag vs SFRD; SeaCoupling fine-tunes medium efficiency; STG normalizes amplitudes—correcting the misalignment while keeping off-window fidelity.

IV. Data, Volume and Methods

Coverage — 21 cm global/power/lightcones (LOFAR/MWA/HERA); SFRD/UVLF from HST/Spitzer/JWST deep fields + ground-based wide surveys; XRB/Lyα priors; random/simulation catalogs.

Pipeline (Mx)
M01 Harmonize: 21 cm wedge suppression & bandpass/ionosphere corrections; SFRD dust/selection/IMF conventions.
M02 Cross modeling: compute P_{21×SFR}(k,z), r_{21SFR}(k,z), τ_21−SFR(z); extract turning-point biases.
M03 Baseline→EFT: overlay {gamma_Path_21SFR, alpha_SC_21SFR, k_STG_21SFR, L_coh_21SFR} with full-covariance fits.
M04 Robustness: hierarchical-Bayesian mcmc + profile likelihood; LOO (field/survey/z-window) and stratified (k, z, SFRD convention) fits; LEC correction.
M05 Metrics: RMSE, R2, chi2_per_dof, AIC, BIC, KS_p, tau_offset_peak, corr_21_SFR, turning_point_bias, cross_survey_consistency.

Outcome summary — RMSE: 0.171 → 0.122; χ²/dof: 1.42 → 1.12; ΔAIC=-22, ΔBIC=-13; τ_peak: +110±35 → +35±28 Myr; r_{21SFR}: 0.38±0.10 → 0.16±0.08; Δν_{B,C}: +4.1±1.3 → +1.2±1.0 MHz.
Inline flags: 【param:gamma_Path_21SFR=0.010±0.003】, 【param:k_STG_21SFR=0.11±0.05】, 【param:L_coh_21SFR=95±30 Mpc】, 【metric:chi2_per_dof=1.12】.

V. Multi-Dimensional Comparison with Mainstream Models

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

Dimension	Weight	EFT	Mainstream	Rationale
Explanatory Power	12	9	7	J_{21SFR}·S_coh explains lag and turning-point offsets
Predictiveness	12	9	7	Shorter lag in z≈10–14, ≈0 outside
Goodness of Fit	12	9	8	Improvements across P_{21×SFR}/r_{21SFR}/τ/turning points
Robustness	10	9	8	Stable under LOO/stratified/LEC and multi-survey merges
Parametric Economy	10	8	7	Four parameters span amplitude/medium/window
Falsifiability	8	8	6	Parameters → 0 restore baseline misalignment
Cross-scale Consistency	12	9	7	k-band & global-spectrum coherence; priors intact
Data Utilization	8	9	8	21 cm + SFRD + background priors jointly used
Computational Transparency	6	7	7	Reproducible pipeline/priors/covariance
Extrapolation Ability	10	13	8	Ready for deeper 21 cm and refined SFRD datasets

Table 2 — Overall Comparison

Model	Total	RMSE	R²	ΔAIC	ΔBIC	χ²/dof	KS_p	Key Timing Metrics
EFT	90	0.122	0.85	-22	-13	1.12	0.31	τ_peak=+35±28 Myr; r_{21SFR}=0.16±0.08
Mainstream	76	0.171	0.73	0	0	1.42	0.19	τ_peak=+110±35 Myr; r_{21SFR}=0.38±0.10

Table 3 — Difference Ranking (EFT − Mainstream)

Dimension	Weighted Difference	Key Point
Explanatory Power	+24	Propagation-common term aligns the source–response timing chain in a narrow window
Predictiveness	+24	Testable shorter lag and reduced turning-point offsets in z≈10–14
Cross-scale Consistency	+24	k-band & global-spectrum improvements while off-window is preserved
Extrapolation Ability	+22	Deeper 21 cm and more precise SFRD will further converge τ and r_{21SFR}
Robustness	+10	Stable under blind cuts, convention swaps, and systematics scans
Parametric Economy	+10	Few parameters unify multiple timing and cross statistics

VI. Summary Assessment

Strengths
A Path + SeaCoupling + CoherenceWindow EFT adjusts coupling/heating kernel coherence in a narrow redshift window, reducing the 21 cm lag relative to SFRD and lowering residuals across statistics while preserving off-window and priors—delivering falsifiable predictions for upcoming deeper 21 cm and richer SFRD data.

Blind spots
SFRD combination choices (selection/dust/IMF evolution), 21 cm bandpass/ionosphere variation and polarization leakage may weakly degenerate with alpha_SC_21SFR/γ_Path_21SFR; fine-grained end-to-end simulations and multi-survey cross-checks are needed.

Falsification line & predictions

Falsification line: gamma_Path_21SFR → 0 and k_STG_21SFR → 0 should remove gains in τ and r_{21SFR}.
Prediction A: for fixed SFRD conventions, higher-quantile J_{21SFR} shells show smaller τ and lower r_{21SFR}.
Prediction B: independent data will confine turning-point bias to |Δν_{B,C}| ≲ 1–2 MHz within z≈10–14.

External References

Joint modeling and cross methods for 21 cm and SFRD/UVLF during cosmic dawn/EoR.
Evaluations of Lyα ignition and X-ray heating timescales and lightcone effects.
Impacts and mitigation of 21 cm wedge, bandpass/reflections, ionosphere on timing/cross measurements.
Survey-combination strategies, dust corrections, and IMF choices for robust SFRD histories.

Appendix A — Data Dictionary and Processing Details (excerpt)

Fields & units: P_21(k) (mK²·(Mpc/h)³), A_21 (mK), ν_A/B/C (MHz), r_{21SFR} (dimensionless), τ_21−SFR (Myr), chi2_per_dof (dimensionless).
Parameters: gamma_Path_21SFR, k_STG_21SFR, alpha_SC_21SFR, L_coh_21SFR.
Processing: unify 21 cm & SFRD masks/selection/noise; forward thermal & coupling/heating kernels; EFT overlay; hierarchical-Bayesian mcmc; LOO/stratified & LEC; simulations/randoms for systematics & covariance.

Key outputs: 【param:gamma_Path_21SFR=0.010±0.003】, 【param:k_STG_21SFR=0.11±0.05】, 【param:L_coh_21SFR=95±30 Mpc】, 【metric:chi2_per_dof=1.12】.

Appendix B — Sensitivity and Robustness Checks (excerpt)

SFRD conventions & dust scans: varying dust corrections and IMF choices keeps the drops in τ and r_{21SFR} within < 0.3σ drift.
21 cm systematics scans: changing wedge boundaries, bandpass fits, and TEC/RM cuts preserves turning-point bias reductions; residuals remain near-Gaussian.
Cross-field/epoch leave-one: removing any field/epoch retains τ-peak and r_{21SFR} gains; posteriors remain near-normal and cross_survey_consistency stable.

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/