The Luminosity Function and Surface Brightness Distribution of HI Selected Galaxies

We measure the z=0 B-band optical luminosity function (LF) for galaxies selected in a blind HI survey. The total LF of the HI selected sample is flat, with Schechter parameters M*=-19.38_{-0.62}^{+1.02} + 5 log h mag and alpha=-1.03_{-0.15}^{+0.25}, in good agreement with LFs of optically selected late-type galaxies. Bivariate distribution functions of several galaxy parameters show that the HI density in the local Universe is more widely spread over galaxies of different size, central surface brightness, and luminosity than is the optical luminosity density. The number density of very low surface brightness (>24.0 mag/arcsec^2) gas-rich galaxies is considerably lower than that found in optical surveys designed to detect dim galaxies. This suggests that only a part of the population of LSB galaxies is gas rich and that the rest must be gas poor. However, we show that this gas-poor population must be cosmologically insignificant in baryon content. The contribution of gas-rich LSB galaxies (>23.0 mag/arcsec^2) to the local cosmological gas and luminosity density is modest (18_{-5}^{+6} and 5_{-2}^{+2} per cent respectively); their contribution to Omega_matter is not well-determined, but probably < 11 per cent. These values are in excellent agreement with the low redshift results from the Hubble Deep Field.