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

Abstract

The velocity function derived from large-scale surveys can be compared with the predictions of ∧ cold dark matter (∧CDM) cosmology, by matching the measured rotation velocities Vrot of galaxies to the maximum circular velocity of dark matter (DM) haloes Vmax. For Vrot < 50 kms-1, a major discrepancy arises between the observed and ∧CDM velocity functions. However, the manner in which different observational measures of Vrot are associated with Vmax is not straightforward in dwarf galaxies. We instead relate galaxies to DM haloes using the empirical baryon-mass 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 H I profile linewidth at 50 per cent of peak H I 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 H I 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 haloes. To continue to use velocity functions as a probe of ∧CDM cosmology, it is necessary to be precise about how the different measures of rotation velocity are probing the mass of the DM haloes, dropping the assumption that any measure of rotational velocity can be equally used as a proxy for Vmax.