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Even though the dark‐matter power spectrum in the absence of biasing predicts a number density of haloes   n ( M ) ∝ M  −2   (i.e. a Schechter α value of  −2 ) at the low‐mass end  ( M  &lt; 10 10  M ⊙ ) , hydrodynamic simulations have typically produced values for stellar systems in good agreement with the observed value  α≃−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 α depends primarily on the mean gas temperature at the star‐formation epoch for low‐mass systems (  z ≲ 3 ): with no background we find  α≃−1.5 , with UV only  α≃−1.0  and with UV and X‐rays  α≃−0.75 . We find the critical final halo mass for star formation to be  ∼4 × 10 8  M ⊙   with a UV background and  ∼7 × 10 8  M ⊙   with UV and X‐rays.

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