THE ARECIBO LEGACY FAST ALFA SURVEY: THE α.40 H I SOURCE CATALOG, ITS CHARACTERISTICS AND THEIR IMPACT ON THE DERIVATION OF THE H I MASS FUNCTION

We present a current catalog of 21 cm H I line sources extracted from the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA) survey over ~2800 deg^2 of sky: the α.40 catalog. Covering 40% of the final survey area, the α.40 catalog contains 15,855 sources in the regions 07^h30^m < R.A. < 16^h30^m, +04° < decl. <+16°, and +24° < decl. <+28° and 22^h < R.A. < 03^h, +14° < decl. <+16°, and +24° < decl. < + 32°. Of those, 15,041 are certainly extragalactic, yielding a source density of 5.3 galaxies per deg^2, a factor of 29 improvement over the catalog extracted from the H I Parkes All-Sky Survey. In addition to the source centroid positions, H I line flux densities, recessional velocities, and line widths, the catalog includes the coordinates of the most probable optical counterpart of each H I line detection, and a separate compilation provides a cross-match to identifications given in the photometric and spectroscopic catalogs associated with the Sloan Digital Sky Survey Data Release 7. Fewer than 2% of the extragalactic H I line sources cannot be identified with a feasible optical counterpart; some of those may be rare OH megamasers at 0.16 < z < 0.25. A detailed analysis is presented of the completeness, width-dependent sensitivity function and bias inherent of the α.40 catalog. The impact of survey selection, distance errors, current volume coverage, and local large-scale structure on the derivation of the H I mass function is assessed. While α.40 does not yet provide a completely representative sampling of cosmological volume, derivations of the H I mass function using future data releases from ALFALFA will further improve both statistical and systematic uncertainties.