SIMBAD references

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 7000 deg² 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.