THE ARECIBO LEGACY FAST ALFA SURVEY. X. THE H I MASS FUNCTION AND ΩH I 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 Hi-selected galaxies to date. We measure the Hi mass function from a sample of 10,119 galaxies with 6.2 < log(M-H I/M-circle dot) < 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 Hi 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 phi(*) (h(70)(3) Mpc(-3) dex(-1)) = 4.8 +/- 0.3 x 10(-3), log(M-*/M-circle dot) + 2 log h(70) = 9.96 +/- 0.02, and alpha = -1.33 +/- 0.02. We find Omega(H I) = 4.3 +/- 0.3 x 10(-4) h(70)(-1), 16% larger than the 2005 HIPASS result, and our Schechter function fit extrapolated to log(M-H I/M-circle dot) = 11.0 predicts an order of magnitude more galaxies than HIPASS. The larger values of Omega(H I) 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.