E3d — galaxy-pair bridge stack (small-scale WHIM design)
Setup: CMASS-N z 0.45–0.55 pairs with transverse separation 6.0–14.0 Mpc/h and line-of-sight separation < 6.0 Mpc/h (570049 pairs). Estimator: y at the pair midpoint minus the mean of the four off-axis points at identical angular distance from each galaxy (±90° rotations) — a circularly symmetric halo contributes zero by construction, so any positive mean is gas that lives preferentially ON the inter-pair axis. Errors: bootstrap over pairs (500 resamples).
| map | pairs used | bridge excess (y) | error | SNR |
|---|---|---|---|---|
| ACT | 237813 | 8.211e-09 | 9.448e-09 | 0.87 |
| PLANCK | 570049 | 3.389e-08 | 2.265e-09 | 14.96 |
Verdict and caveat
- Planck 15σ is a bridge + leakage upper bound, not a pure detection. At a 10′ beam, the second halo’s smeared profile contributes more at the midpoint than at the off-axis control (which sits farther from it), so the estimator retains a positive halo term. The measured 3.4×10⁻⁸ bounds the true bridge from above.
- ACT is clean (leakage negligible at 1.6′) but underpowered: ±9.4×10⁻⁹ per-pair-set error cannot resolve a literature-level bridge of ~1×10⁻⁸ (would be ~1σ — exactly what we see: 0.87σ).
- Both maps are mutually consistent with Model B at the ~10⁻⁸ level. Next (E3d-v2): full CMASS z-range, disc-averaged sampling, multi-angle ring controls — projected ACT error ~2–3×10⁻⁹, turning 10⁻⁸ into a 3–5σ test.