An analytic redshift-independent formulation of baryonic effects on the matter power spectrum

Baryonic effects created by feedback processes associated with galaxy formation are an important, poorly constrained systematic effect for models of large-scale structure as probed by weak gravitational lensing. Upcoming surveys require fast methods to predict and marginalize over the potential impact of baryons on the total matter power spectrum. Here we use the FLAMINGO cosmological hydrodynamical simulations to test a recent proposal to approximate the matter power spectrum as the sum of the linear matter power spectrum and a constant multiple, $A_{\rm mod}$, of the difference between the linear and non-linear gravity-only power spectra. We show that replacing this constant multiple with a one-parameter family of sigmoid functions of the wavenumber $k$ allows to us match the predictions of simulations with different feedback strengths for $z \leq 1, k < 3~h\cdot{\rm Mpc}^{-1}$, and the different cosmological models in the FLAMINGO suite. The baryonic response predicted by FLAMINGO models that use jet-like AGN feedback instead of the fiducial thermally-driven AGN feedback can also be reproduced, but at the cost of increasing the number of parameters in the sigmoid function from one to three. The assumption that $A_{\rm mod}$ depends only on $k$ breaks down for decaying dark matter models, highlighting the need for more advanced baryon response models when studying cosmological models that deviate strongly from $\Lambda$CDM.