ST-based Component Separation of tSZ in the FLAMINGO Lensed Simulations

Abstract: The Internal Linear Combination (ILC) is provably optimal among linear combinations of frequency maps that match a target power spectrum under a Gaussian model. We compare ILC against two scattering-transform (ST) based estimators for thermal Sunyaev-Zel'dovich (tSZ) recovery on the FLAMINGO lensed simulations using a new JAX-GPU ST library (jaxst): FoCUS, a six-frequency ST refinement anchored to ILC; and STsep, a single-frequency ScatCov-based separator following Regaldo-Saint Blancard, Auclair, and Tsouros, with target-mean and target-variance priors derived from a disjoint training set of truth tSZ patches (analogous to using a foreground simulation suite to fix the expected tSZ amplitude). Throughout, we are explicit that the FLAMINGO stacked\_*.npy files are noiseless sky-signal stacks; all inputs to ILC, FoCUS, and STsep are observed maps constructed as the noiseless stack plus an SO/Planck noise realisation with the documented unit conversions, evaluated on two independent noise splits so the recovered power spectrum can be reported as a noise-bias-free split-cross . Truth tSZ is beam-matched to the per-patch ILC effective beam before any pixel- or spectrum-level comparison. On 20 noisy patches (, pixels), STsep at 150 GHz alone, initialised from the same-split ILC output and refined under a ScatCov loss with target-mean and target-variance priors, beats ILC and FoCUS on every metric we tested: pixel correlation (vs for ILC), pixel RMS (64% lower than ILC's ), ScatCov distance (vs ), KS distance (vs ), and a more-than-order- of-magnitude improvement on extreme-tail cluster pixel recovery (30 at , 14 at ). In a more aggressive limited-frequency setup with only the three SO bands (\,GHz) and explicit SO noise, the SED-difference recipe that drives single-frequency STsep is noise-dominated --- the 217 GHz noise alone overwhelms the truth tSZ amplitude --- and neither the SED-init nor the multi-frequency STsep recovers the truth. This is a genuine negative result for ILC-free ScatCov separation on FLAMINGO at SO noise levels: realistic noise is a quantitative gate, and the previous noiseless intuition does not survive it. FoCUS at six frequencies provides a small but consistent per-patch improvement over ILC. A sliding-window ST anomaly diagnostic maps the regions where ILC has under-recovered cluster ScatCov even at fixed and . Two correct take-aways follow: an ST estimator initialised from ILC and constrained by simulation-estimated amplitude priors is a quantitative improvement over ILC on FLAMINGO under realistic noise, both on Gaussian per-pixel statistics and on non-Gaussian morphology / tail recovery; and ST results should be reported with the noise policy, beam convention, and noise-debiased spectrum estimator explicit, since all three change the headline numbers materially.