The H I mass function of galaxies from a deep survey in the 21 centimeter line

The H I mass function (HIMF) for galaxies in the local universe is constructed from the results of the Arecibo H I Strip Survey, a blind extragalactic survey in the 21 cm line. The survey, consisting of two strips covering in total similar to 65 deg(2) of sky, with a depth of cz = 7400 km s(-1) was optimized to detect column densities of neutral gas N-HI > 10(18) cm(-2) (5 sigma). The survey yielded 66 significant extragalactic signals, of which approximately 50% are cataloged galaxies. No free-floating H I clouds without stars are found. VLA follow-up observations of all signals have been used to obtain better measurements of the positions and fluxes and to allow an alternate determination of the achieved survey sensitivity. The resulting HIMF has a shallow faint-end slope (alpha approximate to 1.2) and is consistent-with earlier estimates computed for the population of optically selected gas-rich galaxies. This implies that there is not a large population of gas-rich low-luminosity or low-surface brightness galaxies that has gone unnoticed by optical surveys. The influence of large-scale structure on the determination of the HIMF from the Arecibo H I Strip Survey was tested by numerical experiments and was not found to affect the resulting HIMF significantly. The cosmological mass density of H I at the present time, determined from the survey, Omega(HI)(z = 0) = (2.0 +/- 0.5) x 10(-4) h(-1), is in good agreement with earlier estimates. We determine lower limits for the average column densities (N-HI) of the galaxies detected in the survey and find that none of the galaxies have (N-HI) <10(19.7) cm(-2), although there are no observational selection criteria against finding lower density systems. Eight percent of the signals detected in the original survey originated in groups of galaxies whose signals chanced to coincide in frequency.