PSF-leakage fit on the full v2 area: three causes of χ² 171/57, and β(T_PSF)

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@cailmdaley 已经在做这个了。

开始于 2026年10月30日。

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Start with the report at /scratch/cdaley/cosmo-val-v2/loop/leakadq/{cov,vary}/RESULT.md and the fitting entry points for the ρ/τ leakage model; the issue does not name source files or tests. Investigate whether β(T_PSF) should be the fiducial ξ_sys model, accounting for the caveat about campaign-scale covariance modes. Done means a justified model choice and validation of fit quality, including the stated systematic comparison.

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描述

Claude (Opus) on behalf of Cail.

On the full-area v2 catalogue (20,515 tiles), the ρ/τ leakage fit (α, β, η on τ0/τ2/τ5, 1–250′) gives χ² 171/57 in production, against 74/57 on the old ~10k-tile footprint. Three things cause it.

  1. Contaminated PSF stars. One jackknife cell, at M33, carries >99% of the first-bin variance of ρ1, ρ3 and ρ4. Its star clusters and HII regions enter the PSF sample. Under the fixed-ρ fit, deleting that cell moves (α, β, η) from (−0.001, 0.81, −1.04) to (+0.027, 1.25, +3.22). The negative α and η seen on 28 Oct are mostly this. A star-only scan of the footprint adds M101, M13 and M92; the four circles remove 29k star detections and 159k bound-9 galaxies.
  2. The estimator. lsq treats the measured ρ as exact and has no ρ–τ cross-covariance. At small θ, the propagated ρ noise is 100–500× the τ variance. A joint errors-in-variables (EIV) fit profiles the true ρ under a joint ρ+τ jackknife covariance. Dropping the cross term from that fit fakes a pass: 69.4/57 instead of 78.0/57.
  3. β grows with PSF size. With β = β₀ + β₁ u, where u = T_PSF/⟨T_PSF⟩ − 1, the fit gives β₁ ≈ 1.9 ± 0.3 (Δχ² 8–22 for one parameter). The slope is stable across 200, 400 and 800 patches, across size bounds 3 and 9, and with θ ≤ 60′ cuts. A step model gives β = 0.04 ± 0.27 in the best-seeing quartile and 2.38 ± 0.22 elsewhere. Splitting NGC/SGC, whose caps differ in seeing, helps far more than splitting old/new area (χ²/dof 2.16 → 1.44 against 2.18 → 2.13).

Result. On bound 9 (gal_rel_size_max 9), with the four-circle mask, joint EIV and β(T_PSF), the fit is 64.6/56 (PTE 0.20) at 400 patches and 70.7/56 (0.089) at 200. Constant β gives 78.0/57 (0.034).

bound 9, masked, joint EIV 800 patches 400 200
constant β 93.6/57 78.0/57 79.0/57
β(T_PSF) 71.2/56 64.6/56 70.7/56

Caveat: the covariance doesn't converge. The PSF-error field is coherent beyond 5°. Merging jackknife cells into contiguous groups keeps raising the ρ variance: first-bin ρ1 rises 2.6×, 3.8× and 6.4× at 200, 100 and 50 groups, while random groups of the same sizes stay at 1.0×. The influence concentrates on the NGC east edge (RA 255–285°, Dec 30–60°), which is the smk_early campaign and the earliest dates. Absolute PTEs therefore depend on the patch count, at about the 2× level. The coefficients and Δχ² are stable across patch counts. Settling the fit quality needs simulations with campaign-scale PSF-error modes.

Open question, for Sacha: is β(T_PSF) physical, and should it be the fiducial ξ_sys model? Leakage that scales as β ∝ T_PSF/T_gal predicts β₁ ≈ β₀. In the slope fit itself (bound 9, masked, joint EIV, 400 patches), β₀ = 1.37 ± 0.10 and β₁ = 1.98 ± 0.37, so β₁ − β₀ = 0.61 ± 0.33 (their correlation, 0.47, included): consistent with proportional at 1.8σ, leaning steeper. For comparison, the constant-β fit gives β = 1.28 ± 0.10 on the same selection and β ≈ 1.64 on the full-area clean sample. The step model's β ≈ 0 in the best-seeing quartile is steeper than proportional, and the best-seeing subset's direct fit (β = 1.37 ± 0.12) sits between the two. Proposed: β(T_PSF) as fiducial, with α and η constant, and the difference from constant β as a systematic. That adds u·δe templates to ξ_sys. #454 measures their auto- and cross-correlations with e_PSF, δe and the size term, behind an option that is off by default.

Figures.

M33 drives the ρ3/ρ4 swings; masking it alone makes them smooth:
rho before/after mask

τ residuals on bound 9 (400 patches): the β slope (orange) removes the coherent −2 to −4.6σ τ2 miss from 8′ to 100′; an α slope (green) is not supported:
tau residuals

Leave-one-cell-out influence after masking, concentrated on the NGC east edge (smk_early):
influence maps

The full report (χ² ladder, alternatives ruled out) is available from Cail. Sources on Nibi: /scratch/cdaley/cosmo-val-v2/loop/leakadq/{cov,vary}/RESULT.md. Only ρ, τ and α/β/η were used; nothing unblinded.

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