37 Identifying a Smooth “Floor” in Galaxy-Cluster tSZ/kSZ Residuals

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and keeps the structure fixed. Under unified frequency/time standards and source-end calibration, we combine multi-instrument, multi-band Sunyaev–Zel’dovich (SZ) observations of clusters with environmental layers. After constraining/de-mixing thermal SZ (tSZ) and kinetic SZ (kSZ) and unifying beam/bandpass, we test whether residual maps and stacked profiles contain a cross-band smooth, time-stable, cross-instrument-reproducible floor. We then probe monotonic or plateau-like links to line-of-sight environment (lensing convergence, large-scale-structure strata, inter-cluster filament connectivity, intra-cluster dynamical state). If the floor matches dust/radio color temperatures, Cosmic Infrared Background (CIB) fluctuations, bandpass/beam mismatch, map transfer functions/scan striping, or point-source leftovers—or fails cross-band/array/team replication—the claim is disfavored.

I. One-Sentence Goal

Decide whether cluster SZ residuals host a non-dispersive, smooth baseline that co-occurs across instruments and strengthens with environment, rather than known foregrounds or mapping artifacts.

II. What to Measure

• Smooth-floor index (text grades):
  After common beam/bandpass unification, extract constant bias and slow-drift slope from residual brightness/intensity for individual clusters and stacked samples (binned by mass/redshift/environment). Grade strong / medium / weak; uplift / depression and report cross-band / cross-instrument sign stability.
• Non-dispersion across bands:
  In millimeter–submillimeter channels, test residual color: the floor’s strength and ordering should be carrier-insensitive, rejecting typical laws for dust (rises with frequency), radio (falls), and constrained tSZ. Frequency-driven flips/scalings imply dispersive/foreground origins.
• Zero-lag co-occurrence (cross-array aligned):
  Under a single external time/frequency standard, compare different instruments/seasons/scan batches and grade zero-lag peaks and side-lobe contrast. Significant cross-array zero-lag earns additional credit.
• Radial and morphological robustness:
  In core-to-outskirts annuli and morphology partitions (cool-core/merger, round/elliptical, substructure richness), verify that the floor is radially stable and shape-agnostic; confinement to isolated sub-pixels/sectors downgrades confidence.
• Environment linkage and stratification:
  Co-register with lensing κ/γ, galaxy density, filament connectivity, and supercluster membership; label floor behavior as enhance / plateau / uncorrelated, stratified by M500, redshift, dynamical state.
• Ratio robustness and template orthogonality:
  Check multi-band ratios for the “rigid shift, ratio unchanged” property: stable ratios with absolute smooth residuals support the floor; require near-orthogonality to dust/radio/CIB templates.
• Seasonal/yearly reproducibility and event response:
  Test sign/ordering across seasons/years; in merger/shock candidates or strong-lensing foreground subsets, look for same-direction or threshold-like responses.

III. How to Do It

1. Data and arrays:
   • All-sky and deep fields: combine multi-band satellite all-sky/half-sky and ground deep-survey data.
   • Samples: SZ-selected catalogs, X-ray clusters, optical-richness samples with mass/redshift/morphology metadata.
   • Environment layers: lensing κ/γ, galaxy–filament reconstructions, CIB/dust/radio templates, velocity-field proxies.
2. Unified calibration and de-systematics:
   • Beam and bandpass: publish per-channel beams/sidelobes and bandpass kernels/color corrections; map all to a common beam/bandpass, with band-edge hold-outs.
   • Map transfer functions: release scan–de-striping–filter transfer functions and noise properties; restrict to safe multipole ranges.
   • Component-separation dual path: (a) constrained ILC / template regression that nulls tSZ/kSZ, suppresses dust/radio, and preserves color-flat degrees of freedom; (b) parametric matched-filter fits of tSZ/kSZ/dust/radio per cluster—run blind to each other.
   • Point sources and CIB control: use radio/dust catalogs and CIB fluctuation models for masks and inject–recover tests; publish residual upper bounds.
3. Sequence construction and comparison:
   • Co-window/co-kernel grid: per cluster × band × instrument × time window, tabulate floor and zero-lag indices (text grades).
   • Profiles and stacks: stack in mass/redshift/environment bins; label core-to-outskirts constancy and color flatness.
   • Template orthogonality and differencing: run dust/radio/CIB/Galactic differencing and orthogonality tests; require the floor to be nearly orthogonal to these templates.
4. Forward prediction, blinding, arbitration:
   • Environment-forward team: using only environment layers/masks, issue prediction cards (floor direction/strength, non-dispersion, zero-lag, and radial-plateau expectations).
   • Measurement teams (independent pipelines): run ≥ 2 cleaning paths and two alignment strategies without sharing residuals.
   • Arbitration: align prediction cards and results; report hit / wrong / null across band/instrument/season/method strata.
5. Cross-consistency:
   • Align floor direction/strength with Chapter 29 (CMB micro-distortion time history and persistent floor).
   • Compare low-frequency–mm behavior with Chapter 5 (ARCADE-2 radio-background floor).
   • Share environment slices with Chapter 27 (4D path-redshift tomography).

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls (support a smooth floor):
   • Same-sign, stable constants across multiple bands/instruments with zero-lag co-occurrence after alignment.
   • Non-dispersion: insensitivity to carrier/band edges and inconsistency with dust/radio/CIB colors.
   • Monotonic/plateau dependence on environment, enhanced in high-connectivity/high-κ subsets.
   • Prediction-card hits significantly above chance, replicated across methods/instruments/seasons.
2. Negative controls (against a smooth floor):
   • Residual colors match dust/radio/CIB or follow known dispersive laws.
   • Significance confined to one band/instrument/season or fragile to beam/bandpass/alignment/multipole choices.
   • Label swaps/rotated stacks/random shifts still “detect” a floor—selection/method bias.
   • Deep masks/stricter color corrections/band-edge hold-outs erase the signal, or transfer/striping reproduces it.

V. Systematics and Safeguards (Three Items)

• Bandpass–color mis-match: inter-instrument bandpass differences and incomplete color corrections can forge “flat” residuals. Safeguard: common bandpass kernels, color-temperature marginalization, band-edge hold-outs, and published color-correction logs.
• Beam/transfer mismatch: sidelobes and de-striping residuals add constants in stacks. Safeguard: common beam convolution, safe multipole windows, inject–recover, and scan-subset hold-outs.
• Point sources and CIB fluctuations: compact sources and lens-boosted CIB mimic floors. Safeguard: deep masks/source inject–recover, CIB fluctuation priors, and multi-band color vetoes.

VI. Execution and Transparency

Pre-register samples/bands/instruments, common beams/bandpass kernels and transfer functions, criteria for non-dispersion/zero-lag/radial plateau, environment variables/bins, positive/negative controls, and arbitration scoring. Define held-out units (high-κ/high-connectivity vs low-κ references, strong point-source fields, merger candidates). Enable cross-team/cross-instrument replication via basebands/map cutouts/masks/logs/scripts; run down-sampling/noise/kernel-variant/alignment-perturbation tests. Publicly release prediction cards, floor-index tables, zero-lag and non-dispersion summaries, bandpass/beam/transfer/color/mask logs, and key intermediates.

VII. Pass/Fail Criteria

1. Support (passes):
   • In ≥ 2 pipelines, ≥ 2 instruments/surveys, ≥ 3 bands, recover a non-dispersive smooth floor with zero-lag co-occurrence.
   • The floor monotonically/plateaus with environment and remains robust to beam/bandpass/alignment/mask/multipole choices.
   • Prediction-card hits exceed chance and replicate in held-out units.
2. Refutation (fails):
   • Results follow dust/radio/CIB colors or are dominated by beam/bandpass/transfer artifacts; cross-band/cross-instrument replication fails.
   • Parameter fragility or disappearance in held-out units.
   • Arbitration hits near chance, indistinguishable from foreground/method artifacts.