The halo mass function of late-type galaxies from HI kinematics

We present an empirical method to measure the halo mass function (HMF) of galaxies. We determine the relation between the \hi\ line-width from single-dish observations and the dark matter halo mass ($M_{200}$) inferred from rotation curve fits in the SPARC database, then we apply this relation to galaxies from the \hi\ Parkes All Sky Survey (HIPASS) to derive the HMF. This empirical HMF is well fit by a Schecther function, and matches that expected in $Λ$CDM over the range $10^{10.5} < M_{200} < 10^{12}\;\mathrm{M}_{\odot}$. More massive halos must be poor in neutral gas to maintain consistency with the power law predicted by $Λ$CDM. We detect no discrepancy at low masses. The lowest halo mass probed by HIPASS, however, is just greater than the mass scale where the Local Group missing satellite problem sets in. The integrated mass density associated with the dark matter halos of \hi-detected galaxies sums to $Ω_{\rm m,gal} \approx 0.03$ over the probed mass range.

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