The effects of X-ray and UV background radiation on the low-mass slope of the galaxy mass function

Even though the dark-matter power spectrum in the absence of biasing predicts a number density of haloes n(M) proportional to M-2 (i.e. a Schechter alpha value of -2) at the low-mass end (M < 1010 M-circle dot), hydrodynamic simulations have typically produced values for stellar systems in good agreement with the observed value alpha similar or equal to -1. We explain this with a simple physical argument and show that an efficient external gas-heating mechanism (such as the UV background included in all hydro codes) will produce a critical halo mass below which haloes cannot retain their gas and form stars. We test this conclusion with gadget-2-based simulations using various UV backgrounds, and for the first time we also investigate the effect of an X-ray background. We show that at the present epoch alpha depends primarily on the mean gas temperature at the star-formation epoch for low-mass systems (z less than or similar to 3): with no background we find alpha similar or equal to -1.5, with UV only alpha similar or equal to -1.0 and with UV and X-rays alpha similar or equal to -0.75. We find the critical final halo mass for star formation to be similar to 4 x 108 M-circle dot with a UV background and similar to 7 x 108 M-circle dot with UV and X-rays.