2010ApJ...723.1359M

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 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 ³₇₀Mpc^–3.dex^–1) = 4.8±0.3x10^–3, log (M_*/M_☉) + 2 log h₇₀= 9.96±0.02, and α = -1.33±0.02. We find 4.3±0.3 x10^–4 h.^–1₇₀, 16% larger than the 2005 HIPASS result, and our Schechter function fit extrapolated to = 11.0 predicts an order of magnitude more galaxies than HIPASS. The larger values of 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.