The effect of active galactic nuclei feedback on the halo mass function

We investigate baryon effects on the halo mass function (HMF), with emphasis on the role played by active galactic nuclei (AGN) feedback. Haloes are identified with both friends-of-friends (FoF) and spherical overdensity (SO) algorithms. We embed the standard SO algorithm into a memory-controlled frame program and present the Python spherIcAl Overdensity code - piao (Chinese character: ). For both FoF and SO haloes, the effect of AGN feedback is that of suppressing the HMFs to a level even below that of dark matter (DM) simulations. The ratio between the HMFs in the AGN and in the DM simulations is similar to 0.8 at overdensity Delta(c) = 500, a difference that increases at higher overdensity Delta(c) = 2500, with no significant redshift and mass dependence. A decrease of the halo masses ratio with respect to the DM case induces the decrease of the HMF in the AGN simulation. The shallower inner density profiles of haloes in the AGN simulation witnesses that mass reduction is induced by the sudden displacement of gas induced by thermal AGN feedback. We provide fitting functions to describe halo mass variations at different overdensities, which can recover the HMFs with a residual random scatter less than or similar to 5 per cent for halo masses larger than 10(13) h(-1) M circle dot.