The ALFALFA HI mass function: A dichotomy in the low-mass slope and a locally suppressed 'knee' mass

We present the most precise measurement of the $z = 0$ HI mass function (HIMF) to date based on the final catalogue of the ALFALFA (Arecibo Legacy Fast ALFA) blind HI survey of the nearby Universe. The Schechter function fit has a `knee' mass $\log (M_{*}\,h^{2}_{70}/\mathrm{M_{\odot}}) = 9.94 \pm 0.01 \pm 0.05$, a low-mass slope parameter $\alpha = -1.25 \pm 0.02 \pm 0.1$, and a normalisation $\phi_{*} = (4.5 \pm 0.2 \pm 0.8) \times 10^{-3} \; h^{3}_{70}\,\mathrm{Mpc^{-3}\,dex^{-1}}$, with both random and systematic uncertainties as quoted. Together these give an estimate of the HI content of the $z = 0$ Universe as $\Omega_{\mathrm{HI}} = (3.9 \pm 0.1 \pm 0.6) \times 10^{-4} \, h^{-1}_{70}$ (corrected for HI self-absorption). Our analysis of the uncertainties indicates that the `knee' mass is a cosmologically fair measurement of the $z = 0$ value, with its largest uncertainty originating from the absolute flux calibration, but that the low-mass slope is only representative of the local Universe. We also explore large scale trends in $\alpha$ and $M_{*}$ across the ALFALFA volume. Unlike with the 40 per cent sample, there is now sufficient coverage in both of the survey fields to make an independent determination of the HIMF in each. We find a large discrepancy in the low-mass slope ($\Delta \alpha = 0.14 \pm 0.03$) between the two regions, and argue that this is likely caused by the presence of a deep void in one field and the Virgo cluster in the other. Furthermore, we find that the value of the `knee' mass within the Local Volume appears to be suppressed by $0.18 \pm 0.04$ dex compared to the global ALFALFA value, which explains the lower value measured by the shallower HIPASS. We discuss possible explanations and interpretations of these results and how they can be expanded on with future surveys.