THE ARECIBO LEGACY FAST ALFA SURVEY. X. THE H I MASS FUNCTION AND ₇\, ₈ 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 H i /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 * (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 = -1.33 0.02. We find