The Arecibo Legacy Fast ALFA Survey. X. The H I Mass Function and Ω_(HI) from the 40% ALFALFA Survey

The Arecibo Legacy Fast ALFA (ALFALFA) survey has completed source extraction for 40% of its total sky area, resulting in the largest sample of H I-selected galaxies to date. We measure the H I mass function from a sample of 10,119 galaxies with 6.2 < log(M_(HI)/M_☉) < 11.0 and with well-described mass errors that accurately reflect our knowledge of low-mass systems. We characterize the survey sensitivity and its dependence on profile velocity width, the effect of large-scale structure, and the impact of radio frequency interference in order to calculate the H I mass function with both the 1/V_(max) and 2DSWML methods. We also assess a flux-limited sample to test the robustness of the methods applied to the full sample. These measurements are in excellent agreement with one another; the derived Schechter function parameters are φ* (h^(3)_(70) Mpc^(–3) dex^(–1)) = 4.8 ± 0.3 × 10^(–3), log (M*/M_☉) + 2 log h_(70) = 9.96 ± 0.02, and α = –1.33 ± 0.02. We find Ω_(HI) = 4.3 ± 0.3 ×10^(–4) h^(–1)_(70), 16% larger than the 2005 HIPASS result, and our Schechter function fit extrapolated to log (M_(HI)/M_☉) = 11.0 predicts an order of magnitude more galaxies than HIPASS. The larger values of Ω_(HI) and of M* imply an upward adjustment for estimates of the detection rate of future large-scale H I line surveys with, e.g., the Square Kilometer Array. A comparison with simulated galaxies from the Millennium Run and a treatment of photoheating as a method of baryon removal from H I-selected halos indicate that the disagreement between dark matter mass functions and baryonic mass functions may soon be resolved