A matter of measurement: rotation velocities and the velocity function of dwarf galaxies

The velocity function derived from large scale surveys can be compared with the predictions of ΛCDM cosmology, by matching the measured rotation velocities Vrot of galaxies to the maximum circular velocity of dark matter (DM) halos Vmax. For Vrot<50 kms−1, a major discrepancy arises between the observed and ΛCDM velocity functions. However, the manner in which different observational measures of Vrot are associated with Vmax is not straight forward in dwarf galaxies. We instead relate galaxies to DM halos using the empirical baryonmass to halo-mass relation, and show that different observational measures of Vrot result in very different velocity functions. We show how the W50 velocity function, i.e. using the HI profile line width at 50% of peak HI flux to measure Vrot, can be reconciled with a ΛCDM cosmology. Our semi-empirical methodology allows us to determine the region of rotation curves that are probed by HI measurements (RHI), and shows that the Vrot of dwarfs are generally measured at a fraction of Rmax, explaining their tendency to have rising rotation curves. We provide fitting formulae for relating RHI and Reff (the effective radius) to the virial radius of DM halos. To continue to use velocity functions as a probe of ΛCDM cosmology, it is necessary to be precise about how the different measures of rotation velocity are probing the mass of the DM halos, dropping the assumption that any measure of rotational velocity can be equally used as a proxy for Vmax.