Comparison of the default halo-model prediction with power spectra from the BAHAMAS AGN simulation at z = 0. Points with errors show the measured power spectra with an error-on-the-mean calculated from the finite number of modes that contribute to each k. The upper two panels show spectra for “all matter” (purple), CDM (green), gas (light blue), stars (orange) and electron pressure (dark blue). The electron pressure field has units of 100 eV cm⁻³. The effect of power aliasing can be seen as an upturn in power at the highest k (∼7 h Mpc⁻¹) shown for each spectrum (see Appendix B). Lines show the halo-model predictions using the default model discussed in Sect. 3: solid lines and points show auto-spectra while broken lines and open points show cross-spectra with the total matter field. We see that the trends in the halo model agree reasonably well with the simulations but that there are disagreements in the details. In the lower two panels we show the “response function” calculated with respect to the matter–matter power in the gravity-only model: . The simulations spectra have been divided by those from the DMONLY simulation and the halo model has been divided by a standard halo-model prediction that assumes all matter to be in NFW haloes. The horizontal-dashed-black lines in the lower left panel show the expected large scale Ω_c/Ω_m, (Ω_c/Ω_m)², Ω_b/Ω_m, and (Ω_b/Ω_m)² asymptotes for the CDM and gas cross–matter and auto-spectra. We see that the response functions are generally smoother than the raw power spectra: a consequence of cosmic variance cancellations at large scales and cancellation of aliasing effects at small scales.