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 _ { HI } / M _ { \odot } ) < 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 HIMF 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 \pm .3 \times 10 ^ { -3 } , \log ( M _ { * } / M _ { \odot } ) + 2 \log h _ { 70 } = 9.96 \pm 0.02 and \alpha = -1.33 \pm 0.02 .
We find \Omega _ { HI } = 4.3 \pm 0.3 \times 10 ^ { -4 } h ^ { -1 } _ { 70 } , 16 \% larger than the 2005 HIPASS result , and our Schechter function fit extrapolated to \log ( M _ { HI } / M _ { \odot } ) = 11.0 predicts an order of magnitude more galaxies than HIPASS .
The larger values of \Omega _ { HI } and of M _ { * } imply an upward adjustment for estimates of the detection rate of future large-scale HI 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 HI-selected halos indicates that the disagreement between dark matter mass functions and baryonic mass functions may soon be resolved .