The Tail of the HI Mass Function

The contribution of extragalactic objects with HI masses below $10^8 M_\odot$ to the HI mass function remains uncertain. Several aspects of the detection of low-mass sources in HI surveys are not always considered, and as a result different analysis techniques yield widely different estimates for their number density. It is suggested at one extreme that the number density of galaxies follows a shallow Schechter power-law slope, and at the other extreme that it follows a steep faint-end rise like that found for field optical sources. Here we examine a variety of selection effects, issues of completeness, and consequences of LSS. We derive results for the large Arecibo Dual Beam Survey which indicate that the field mass function does rise steeply, while within the Virgo Cluster environs, the slope appears to be much shallower. Dependence on the local density of galaxies may partially explain differences between surveys.