The luminosity function and surface brightness distribution of HI selectedgalaxies

We measure the z = 0 B-band optical luminosity function (LF) for galaxies s elected in a blind Hi survey. The total LF of the Hi selected sample is fla t, with Schechter parameters M*= -19.38+(+1.02)(-0.62) + 5 log h(100) mag a nd alpha = -1.03(-0.15)(+0.25), in good agreement with LFs of optically sel ected late-type galaxies. Bivariate distribution functions of several galax y parameters show that the H I density in the local Universe is more widely spread over galaxies of different size, central surface brightness and lum inosity than the optical luminosity density is. The number density of very low surface brightness (LSB) (>24.0 mag arcsec (-2)) gas-rich galaxies is c onsiderably 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 l ocal cosmological gas and luminosity density is modest (18(-5)(+6) and 5(-2 )(+2) per cent respectively); their contribution to Omega (matter) is not w ell-determined, but probably <11 per cent. These values are in excellent ag reement with the low redshift results from the Hubble Deep Field.