The resummation model in FLAMINGO: precisely predicting matter power suppression from observed halo baryon fractions

ABSTRACT In order to derive unbiased cosmological parameters from Stage-IV surveys, we need models that can predict the matter power spectrum for at least $k\, {\lesssim }\, {10}\, h\mathrm{\, Mpc^{-1}}$ with per cent-level accuracy. The main challenge in this endeavour is that baryonic feedback significantly redistributes matter on large scales, but to an unknown degree. Here, we present an improved version of the ‘resummation’ model, which maps observed halo baryon fractions of massive haloes ($M_{\mathrm{500c}}\gtrsim 10^{12.5}\, \mathrm{M_\odot }$) to a flexible suppression signal, i.e. the ratio of baryonic to dark-matter-only (DMO) matter power spectra, using zero free parameters. We calibrate this model to the FLAMINGO hydrodynamical simulations, obtaining a typical accuracy of $\lesssim 1~{{\ \rm per\ cent}}$ for $k\, {\le }\, {10}\, h\mathrm{\, Mpc^{-1}}$ given mean halo baryon fractions within the spherical overdensity radii $R_{\mathrm{500c}}$ and $R_{\mathrm{200m}}$. When only those within $R_{\mathrm{500c}}$ are available, we still obtain $\lesssim 2~{{\ \rm per\ cent}}$ accuracy. We show that given small-scale stellar mass fractions, the model can be extended to yield $\lesssim 3~{{\ \rm per\ cent}}$ accurate suppression signals for all scales measured ($k\, {\le }\, {25}\, h\mathrm{\, Mpc^{-1}}$). We also extend the model to redshifts $z>0$. Central to the model is a seemingly mass-independent and feedback-independent relation that allows observed halo masses to be mapped to equivalent DMO halo masses using only observed mean halo baryon fractions, to $\lesssim 1~{{\ \rm per\ cent}}$ accuracy. This relation can also be used to retrieve the DMO halo mass function from observed halo masses and baryon fractions with per cent-level accuracy, without any assumptions on the strength of feedback. A Python package implementing the resummation model is made publicly available.