Abstract
ABSTRACT 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 $7000\, \mathrm{deg}^2$ 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.
Highlights
Predictions of the CDM model, especially at the low-mass end where the predictions of other dark matter models differ
The expected structure of cold dark matter haloes implies that their circular velocity1 profiles vcirc, related to the enclosed mass within radius r as vc2irc = GM (< r)/r, have a broad plateau whose amplitude vmax is tightly correlated with the halo mass (Navarro et al 1996, 1997)
We note that the importance of the measurement uncertainties relative to the counting uncertainties is much greater for the H I WF than it is for the H I MF (e.g. J18, table 1) – this is because the w50 uncertainties have a negligible influence on the H I MF, but contribute significantly to the H I WF uncertainty budget
Summary
As the HMF is not directly measurable we must instead rely on the kinematics of visible tracers orbiting in dark matter haloes, or other gravitational effects such as lensing, to provide indirect constraints. FALFA) survey, and the H I Parkes All-Sky Survey (H I PASS), respectively It was immediately recognized (and had been anticipated, from indirect estimates) that the observed lowvelocity width slope would be very difficult to reconcile with theoretical expectations – there is an apparently severe overabundance of haloes predicted to exist which, apparently, fail to host observable galaxies. This result has been confirmed repeatedly (Papastergis et al 2011; Klypin et al 2015; P15), including by the measurement we present below, and possible means to reconcile theory and measurement further discussed in the literature
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