We make the most precise determination to date of the number density of extragalactic 21-cm radio sources as a function of their spectral line widths – the H I velocity width function (H I WF) – based on 21 827 sources from the final 7000deg2 data release of the Arecibo Legacy Fast ALFA (ALFALFA) survey. The number density of sources as a function of their neutral hydrogen masses – the H I mass function (H I MF) – has previously been reported to have a significantly different low-mass slope and ‘knee mass’ in the two sky regions surveyed during ALFALFA. In contrast with this, we find that the shape of the H I WF in the same two sky regions is remarkably similar, consistent with being identical within the confidence intervals implied by the data (but the overall normalization differs). The spatial uniformity of the H I WF implies that it is likely a stable tracer of the mass function of dark matter haloes, in spite of the environmental processes to which the measured variation in the H I MF are attributed, at least for galaxies containing enough neutral hydrogen to be detected. This insensitivity of the H I WF to galaxy formation and evolution can be exploited to turn it into a powerful constraint on cosmological models as future surveys yield increasingly precise measurements. We also report on the possible influence of a previously overlooked systematic error affecting the H I WF, which may plausibly see its low-velocity slope steepen by ∼40 per cent in analyses of future, deeper surveys. Finally, we provide an updated estimate of the ALFALFA completeness limit.
Oman, K. A. (2022). The ALFALFA HI velocity width function. Monthly Notices of the Royal Astronomical Society, 509(3), 3268-3284. https://doi.org/10.1093/mnras/stab3164