Baryonic feedback suppression of the matter power spectrum: a three-parameter fitting formula and its single-parameter reduction

Baryonic feedback can suppress matter clustering by about 10% at k about 1h /Mpc and z about 1, and is therefore a major source of systematic errors in weak lensing cosmology. We investigate this effect through the ratio S(k,z) P hydro(k,z)/P DMO(k,z) measured in the FLAMINGO, IllustrisTNG, and Illustris hydrodynamical simulation suites, together with the one-parameter-at-a-time (1P) variation runs of CAMELS-TNG and CAMELS-SIMBA. We present a three-parameter fitting formula that reproduces all but one of these runs with maximum error less than 0.03 (and typical error less than 0.01) at k at most 3h/ Mpc and z at most 2; the only exception is a run with unrealistically low Ω m=0.1. Each of the three parameters (B 0, n, and a) has a clear physical interpretation: B 0 sets the characteristic scale of the suppression at z=0, corresponding to a gas particle displacement scale of B 0 1/2; n sets the suppression floor (1-Ω b/Ω m) n; and a sets the redshift z B at which the suppression peaks. Furthermore, we find that B 0 and z B are significantly correlated for most runs. Also, n 1 for FLAMINGO, TNG and CAMELS-TNG. For these simulations, the description reduces to a single parameter formula with maximum error less than 0.03. The formulas remain accurate at max (ΔS)<0.03 (and typical error less than 0.01) for cosmologies well away from the calibration cosmology, spanning the range Ω m in [0.2,0.5], Ω b in [0.029,0.069] and σ 8 in [0.6,1.0]. These results imply that, despite the diversity of baryonic physics implementations, an accurate description of S(k,z) requires at most three effective degrees of freedom. Therefore the impact of feedback on weak lensing cosmology can in principle be mitigated internally without significant loss of cosmological constraining power.