The 1000 Brightest HIPASS Galaxies: HI Mass Function and Omega_HI

We present a new accurate measurement of the HI mass function of galaxies from the HIPASS Bright Galaxy Catalog, a sample of 1000 galaxies with the highest HI peak flux densities in the southern hemisphere (Koribalski et al. 2003). This sample spans nearly four orders of magnitude in HI mass (from log M_HI/M_sun=6.8 to 10.6, H0=75) and is the largest sample of HI selected galaxies to date. We develop a bivariate maximum likelihood technique to measure the space density of galaxies, and show that this is a robust method, insensitive to the effects of large scale structure. The resulting HI mass function can be fitted satisfactorily with a Schechter function with faint-end slope alpha=-1.30. This slope is found to be dependent on morphological type, with later type galaxies giving steeper slopes. We extensively test various effects that potentially bias the determination of the HI mass function, including peculiar motions of galaxies, large scale structure, selection bias, and inclination effects, and quantify these biases. The large sample of galaxies enables an accurate measurement of the cosmological mass density of neutral gas: Omega_HI=(3.8 +/- 0.6) x 10^{-4}. Low surface brightness galaxies contribute only 15% to this value, consistent with previous findings.