The H I mass function of the Local Universe: Combining measurements from HIPASS, ALFALFA, and FASHI

We present the first H <ns0:sc>I</ns0:sc> mass function (HIMF) measurement for the recent FAST All Sky H <ns0:sc>I</ns0:sc> (FASHI) survey and the most complete measurements of the HIMF in the Local Universe thus far. We obtained these results by combining the H <ns0:sc>I</ns0:sc> catalogues from H <ns0:sc>I</ns0:sc> Parkes All Sky Survey (HIPASS), Arecibo Legacy Fast ALFA (ALFALFA), and FASHI surveys at a redshift of 0 < z < 0.05, covering 76% of the entire sky. We adopted the same methods to estimate the distances, calculate the sample completeness, and determine the HIMF for all three surveys. The best-fit Schechter function for the total HIMF shows a low-mass slope parameter of α = −1.30 ± 0.01 and a ‘knee’ mass of $ \log (M_s/h_{70}^{-2}\,M_{{\odot}}) = 9.86 \pm 0.01, $ along with a normalisation of ϕs = (6.58 ± 0.23)×10−3 h703 Mpc−3 dex−1. This gives us the cosmic H <ns0:sc>I</ns0:sc> abundance: $ \Omega_{{\mathrm{{H}} \,\textsc{i}}} = (4.54 \pm 0.20)\times 10^{-4}\,h_{70}^{-1} $. We find that a double Schechter function with the same slope α better describes our HIMF, where the two different ‘knee’ masses are $ \log(M_{s_1}/h_{70}^{-2}\,M_{{\odot}}) = 9.96 \pm 0.03 $ and $ \log(M_{s_2}/h_{70}^{-2}\,M_{{\odot}}) = 9.65 \pm 0.07 $. We verify that the measured HIMF is marginally affected by the choice of distance estimates. The effect of cosmic variance is significantly suppressed by combining the three surveys and this provides a unique opportunity to obtain an unbiased estimate of the HIMF in the Local Universe.