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We explore the galaxy formation physics governing the low mass end of the HImass function in the local Universe. Specifically, we predict the effects onthe HI mass function of varying i) the strength of photoionisation feedback andthe redshift of the end of the epoch of reionization, ii) the cosmology, iii)the supernovae feedback prescription, and iv) the efficiency of star formation.We find that the shape of the low-mass end of the HI mass function is mostaffected by the critical halo mass below which galaxy formation is suppressedby photoionisation heating of the intergalactic medium. We model the redshiftdependence of this critical dark matter halo mass by requiring a match to thelow-mass end of the HI mass function. The best fitting critical dark matterhalo mass decreases as redshift increases in this model, corresponding to acircular velocity of $\sim 50 \, {\rm km \,s}^{-1}$ at $z=0$, $\sim 30 \, {\rmkm\, s}^{-1}$ at $z \sim 1$ and $\sim 12 \, {\rm km \, s}^{-1}$ at $z=6$. Wefind that an evolving critical halo mass is required to explain both the shapeand abundance of galaxies in the HI mass function below $M_{\rm HI} \sim 10^{8}h^{-2} {\rm M_{\odot}}$. The model makes specific predictions for theclustering strength of HI-selected galaxies with HI masses > $10^{6} h^{-2}{\rm M_{\odot}}$ and $> 10^{7} h^{-2} {\rm M_{\odot}}$ and for the relationbetween the HI and stellar mass contents of galaxies which will be testablewith upcoming surveys with the Square Kilometre Array and its pathfinders. Weconclude that measurements of the HI mass function at $z \ge 0$ will lead to animprovement in our understanding of the net effect of photoionisation feedbackon galaxy formation and evolution.

The HI mass function as a probe of photoionisation feedback on low mass galaxy formation