The luminosity function and surface brightness distribution of H i selected galaxies

We measure the     B -band optical luminosity function (LF) for galaxies selected in a blind H  i survey. The total LF of the H  i selected sample is flat, with Schechter parameters     and     , in good agreement with LFs of optically selected late-type galaxies. Bivariate distribution functions of several galaxy parameters show that the H  i density in the local Universe is more widely spread over galaxies of different size, central surface brightness and luminosity than the optical luminosity density is. The number density of very low surface brightness (LSB ) (>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     and     per cent respectively); their contribution to Ω_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.