The HI Column Density Distribution Function at z=0: the Connection to Damped Ly alpha Statistics

We present a measurement of the HI column density distribution function, f(N), at the present epoch for column densities log N > 20 cm^-2. These high column densities compare to those measured in damped Ly alpha lines seen in absorption against background quasars. Although observationally rare, it appears that the bulk of the neutral gas in the Universe is associated with these damped Ly alpha systems. In order to obtain a good anchor point at z=0 we determine f(N) in the local Universe by using 21cm synthesis observations of a complete sample of spiral galaxies. We show that f(N) for damped Ly alpha systems has changed significantly from high z to the present and that change is greatest for the highest column densities. The measurements indicate that low surface brightness galaxies make a minor contribution to the cross section for HI, especially for log N > 21^-2.