The Arecibo Galaxy Environment Survey - IV. The NGC 7448 region and the H I mass function

In this paper we describe results from the Arecibo Galaxy Environments Survey (AGES). The survey reaches column densities of similar to 3 x 10(18) cm(-2) and masses of similar to 10(7) M-circle dot, over individual regions of order 10 deg(2) in size, out to a maximum velocity of 18 000 km s(-1). Each surveyed region is centred on a nearby galaxy, group or cluster, in this instance the NGC 7448 group. Galaxy interactions in the NGC 7448 group reveal themselves through the identification of tidal tails and bridges. We find similar to 2.5 times more atomic gas in the intergalactic medium than in the group galaxies. We identify five new dwarf galaxies, two of which appear to be members of the NGC 7448 group. This is too small, by roughly an order of magnitude, a number of dwarf galaxies to reconcile observation with theoretical predictions of galaxy formation models. If they had observed this region of the sky in previous wide-area blind H I surveys, HIPASS and ALFALFA, they would have detected only 5 and 43 per cent, respectively, of the galaxies we have detected, missing a large fraction of the atomic gas in this volume. We combine the data from this paper with that from our other AGES papers (370 galaxies) to derive an H I mass function with the following Schechter function parameters: alpha = -1.52(+/- 0.05), M* = 5.1(+/- 0.3) x 10(9) h(72)(-2) M-circle dot, phi = 8.6(+/- 1.1) x 10(-3) h(72)(3) Mpc(-3) dex(-1). Integrating the mass function leads to a cosmic mass density of atomic hydrogen of Omega(H I) = 5.3(+/- 0.8) x 10(-4) h(72)(-1). Our mass function is steeper than that found by both HIPASS and ALFALFA (alpha = 1.37 and 1.33, respectively), while our cosmic mass density is consistent with ALFALFA, but 1.7 times larger than found by HIPASS.