The ALFALFA H i velocity width function

We make the most precise determination to date of number density extragalactic 21-cm radio sources as a function their spectral line widths - HI velocity width (HIWF) based on 21827 from final 7000 deg$^2$ data release Arecibo Legacy Fast ALFA (ALFALFA) survey. The neutral hydrogen masses mass (HIMF) has previously been reported have significantly different low-mass slope and 'knee mass' in two sky regions surveyed during ALFALFA. In contrast with this, we find that shape HIWF same is remarkably similar, consistent being identical within confidence intervals implied by (but overall normalisation differs). spatial uniformity implies it likely stable tracer dark matter haloes, spite environmental processes which measured variation HIMF are attributed, at least for galaxies containing enough be detected. This insensitivity galaxy formation evolution can exploited turn into powerful constraint cosmological models future surveys yield increasingly measurements. also report possible influence overlooked systematic error affecting HIWF, may plausibly see its low-velocity steepen $\sim$40 per cent analyses future, deeper surveys. Finally, provide an updated estimate ALFALFA completeness limit.