Baryonification: An alternative to hydrodynamical simulations for cosmological studies

We present an improved baryonification (BFC) model that modifies dark-matter-only $N$-body simulations to generate particle-level outputs for gas, dark matter, and stars. Unlike previous implementations, our approach first splits each simulation particle into separate dark matter and baryonic components, which are then displaced individually using the BFC technique. By applying the hydrostatic and ideal gas equations, we assign pressure and temperature values to individual gas particles. The model is validated against hydrodynamical simulations from the FLAMINGO and TNG suites (which feature varied feedback prescriptions) showing good agreement at the level of density and pressure profiles across a wide range of halo masses. As a further step, we calibrate the BFC model parameters to gas and stellar mass ratio profiles from the hydrodynamical simulations. Based on these calibrations, we baryonify $N$-body simulations and compare the resulting total matter power spectrum suppressions to the ones from the same hydrodynamical simulation. Carrying out this test of the BFC method at each redshift individually, we obtain a 2 percent agreement up to $k=5\,h$/Mpc across all tested feedback scenarios. We also define a reduced, 2+1 parameter BFC model that simultaneously accounts for feedback variations (2 parameters) and redshift evolution (1 parameter). The 2+1 parameter model agrees with the hydrodynamical simulations to better than 2.5 percent over the scales and redshifts relevant for cosmological surveys. Finally, we present a map-level comparison between a baryonified $N$-body simulation and a full hydrodynamical run from the TNG simulation suite. Visual inspection of dark matter, gas, and stellar density fields, along with the integrated pressure map, shows promising agreement. Further work is needed to quantify the accuracy at the level of observables.