23 Non-Dispersive Common Term—Environment Correlation in 21 cm Intensity Mapping

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and preserves the fixed structure. For general readers, we expand acronyms at first mention: Baryon Acoustic Oscillation (BAO), Redshift-Space Distortion (RSD), Principal Component Analysis (PCA), Generalized Morphological Component Analysis (GMCA), Radio Frequency Interference (RFI), Rotation Measure (RM), Epoch of Reionization (EoR), external convergence (κ_ext), external shear (γ_ext), and weak-lensing convergence (κ_weak). We also refer to line-of-sight and transverse wavenumbers as k∥ and k⊥.

I. One-Sentence Goal

After removing cosmological terms (including RSD and BAO), astrophysical foregrounds (synchrotron, free–free, point sources), instrumental systematics (beam chromaticity, bandpass/gain drift, 1/f, polarization leakage), and atmosphere/ionosphere effects, construct a test for a frequency‑independent (non‑dispersive) residual that tracks large‑scale environment—voids, filaments, and nodes—monotonically. Support requires reproducible detection across multiple sub‑bands and redshift slices, facilities, and independent pipelines, with blind hits from prediction cards that use environment proxies only. If foregrounds, leakage, beam chromaticity, or calibration drift account for the residual—or robustness is lacking—the claim is disfavored.

II. What to Measure

• Common‑term residuals (text grades):
  Grade post‑subtraction brightness‑temperature residuals that are band‑insensitive as strong / medium / weak and uplift / depression. Require same‑sign behavior across adjacent sub‑bands and neighboring redshift slices.
• Non‑dispersion consistency:
  Compare direction and rank order of residuals within a slice (multiple sub‑bands) and across slices. Any λ² or 1/ν‑type flip or rescaling—or RM‑driven rotation patterns—indicates propagation/instrument origins, not a path‑term residual.
• Environment correlation and monotonicity:
  Using voidness/filamentness, distance to nodes, κ_ext / γ_ext, κ_weak, optical galaxy density, and filament‑axis templates, classify residual–environment linkage as enhanced / plateau / uncorrelated. Test for void → filament/node monotonic strengthening.
• Spatial and scale stratification:
  Evaluate scale dependence on large scales (≥ 50–100 Mpc) and intermediate scales (10–50 Mpc). After stratifying by k∥ and k⊥, confirm that qualitative trend directions agree.
• Cross‑mode consistency:
  Compare single‑dish autocorrelation with interferometric reconstructions, and drift‑scan with pointed‑mosaic maps. Record whether direction and strength rankings are consistent.

III. How to Do It

1. Observations and samples:
   • Facilities and bands: Use at least two classes of instruments (for example, a mid‑frequency array, a southern array, and a large single dish), covering z ≈ 0.8–2.5 (optionally extending to EoR pre‑studies). Build sub‑bands that define sub‑redshift layers.
   • Sky areas and masks: Prefer high‑Galactic‑latitude fields with overlapping optical galaxy surveys, κ_weak, and a void–filament–node skeleton. Construct masks for RFI, bright sources, and horizon spillover.
2. Pre‑processing and de‑systematics:
   • Bandpass/gain stability: Apply time–frequency 2D detrending, 1/f suppression, and track stability logs.
   • Foregrounds and beam chromaticity: Run multiple methods in parallel—PCA, GMCA, parametric templates, and delay‑domain filtering—then correct with transfer functions derived from beam/frequency‑response simulations and report chromatic leakage upper bounds.
   • Polarization leakage and Faraday structure: Calibrate leakage matrices; use RM synthesis to detect and gate Faraday “ripple” residuals.
3. Residual construction and normalization:
   For each sub‑redshift layer, produce cleaned data cubes and project to residual brightness maps or residual power slices. Normalize by noise floors and window functions to yield a dimensionless common‑term indicator (text‑graded).
4. Environment templates and forward prediction:
   Build void–filament–node skeletons and κ_ext / γ_ext / κ_weak / galaxy‑density templates. The environment team—using only these templates and the observation mask—issues prediction cards for residual strength tier, monotonic direction, and scale dependence in each sub‑redshift layer.
5. Blinded measurement and arbitration:
   Independent measurement teams process the data through multiple foreground/dispersion pipelines and two mapping modes, returning residual grades and environment‑link verdicts without access to prediction cards. An arbitration team aligns predictions and results under pre‑registered rules and reports hit / wrong / null rates by facility / redshift / method family.
6. Cross‑checks with external tracers:
   Cross‑correlate residuals with optical galaxy redshift slices, κ_weak, and Cosmic Microwave Background (CMB) lensing κ. Note any band‑dependent sign flips and down‑weight such cases.

IV. Positive/Negative Controls and Removal of Artifacts

1. Positive controls (supporting a path term):
   • Common‑term residuals agree in direction across adjacent sub‑bands and facilities, and strengthen monotonically with void → filament/node and with κ_ext / γ_ext / κ_weak.
   • Non‑dispersion holds: no λ² / 1/ν / RM‑law flips or rescalings.
   • Single‑dish vs interferometer and drift‑scan vs mosaic give consistent conclusions.
   • Forward‑prediction hit rates for direction/strength/scale are significantly above chance, replicated across independent teams and facilities.
2. Negative controls (arguing against a path term):
   • Residuals correlate strongly with Galactic synchrotron/dust templates or Galactic latitude, or track RM ripples.
   • Significance is highly sensitive to beam chromaticity, bandpass, or gain choices and appears in only one pipeline.
   • Label shuffling, sky rotation, or RFI‑injection simulations still produce “detections,” indicating method/selection bias.

V. Systematics and Safeguards (Three Items)

• Beam chromaticity and sidelobe ringing: foreground leakage to high k∥ can mimic a non‑dispersive term. Safeguard: direction‑dependent beam modeling and end‑to‑end electromagnetic simulations, transfer‑function corrections, and multi‑method agreement; publish chromatic‑residual tiers.
• Polarization leakage mixed with Faraday rotation: creates artificial frequency structure and spurious environment links. Safeguard: enforce leakage solves + RM‑synthesis gating; compute statistics in de‑RM and raw frames and compare direction consistency.
• Gain/bandpass drift and 1/f noise: induce large‑scale residuals that mis‑match environment maps. Safeguard: 2D detrending, multi‑epoch cross‑checks, overlap‑track closures; down‑weight/hold out unstable epochs or bands.

VI. Execution and Transparency

Pre‑register fields, sub‑redshift/binning, foreground/dispersion method families, polarization conventions, text‑grade rules for residuals and environment links, control/exclusion policies, and arbitration scoring. Reserve hold‑out sky regions/bands per facility and redshift layer. Enable cross‑team/facility replication by exchanging raw visibilities/maps and scripts, and run down‑sampling/noise/mask variants for robustness. Publicly release prediction cards, residual–environment grade tables, non‑dispersion summaries, beam/polarization/gain logs, and key intermediates. This chapter closes a loop with Chapters 20 (same‑source multi‑path solar‑grazing), 9/21 (strong‑lens statistics and environment), and 27 (path‑redshift tomography).

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more facilities and two or more independent pipelines, the common‑term residual strengthens monotonically with void → filament/node or with κ_ext / γ_ext / κ_weak, while remaining non‑dispersive across adjacent sub‑bands and redshift layers.
   • Cross‑correlations with galaxy density and κ_weak are significant and insensitive to Galactic templates/RM ripples.
   • Forward‑prediction hit rates exceed chance; results remain under sky‑rotation/label‑shuffle and RFI/foreground simulations.
2. Refutation (fails):
   • Residuals flip with λ² / 1/ν / RM, or depend strongly on beam/gain choices and do not replicate across facilities/pipelines.
   • Residuals correlate with Galactic templates or polarization leakage, or appear in one method/field only.
   • No environment monotonicity, or arbitration hit rates are near chance.