The BAHAMAS project: Evaluating the accuracy of the halo model in predicting the non-linear matter power spectrum

The halo model formalism is widely adopted in cosmological studies for predicting the growth of large-scale structure in the Universe. However, to date there have been relatively few direct comparisons of the halo model with more accurate (but much more computationally expensive) cosmological simulations. We test the accuracy of the halo model in reproducing the non-linear matter power spectrum, P(k), when the main inputs of the halo model (specifically the matter density profiles, halo mass function, and linear bias) are taken directly from the BAHAMAS simulations and we assess how well the halo model reproduces P(k) from the same simulations. We show that the halo model generally reproduces P(k) in the deep non-linear regime (1-halo) to typically a few percent accuracy, but struggles to reproduce (approx. 15% error) P(k) at intermediate scales of 0.1 < k [h/ Mpc] < 3 at z=0, marking the transition between the 1-halo and 2-halo terms. We show that the magnitude of this error is a strong function of the halo mass definition (through its effects on radial extent of haloes) and of redshift. Furthermore, we test the accuracy of the halo model in recovering the relative impact of baryons on P(k). We show that the systematic errors in recovering the absolute P(k) largely cancel when considering the relative impact of baryons. This suggests that the halo model can make precise predictions for the baryonic suppression, offering a fast and accurate way to adjust collisionless matter power spectra for the presence of baryons and associated processes.