How to Reconcile the Observed Velocity Function of Galaxies with Theory

Within a Λ cold dark matter (ΛCDM) scenario, we use high-resolution cosmological simulations spanning over four orders of magnitude in galaxy mass to understand the deficit of dwarf galaxies in observed velocity functions (VFs). We measure velocities in as similar a way as possible to observations, including generating mock H i data cubes for our simulated galaxies. We demonstrate that this apples-to-apples comparison yields an “observed” VF in agreement with observations, reconciling the large number of low-mass halos expected in a ΛCDM cosmological model with the low number of observed dwarfs at a given velocity. We then explore the source of the discrepancy between observations and theory and conclude that the dearth of observed dwarf galaxies is primarily explained by two effects. The first effect is that galactic rotational velocities derived from the H i linewidth severely underestimate the maximum halo velocity. The second effect is that a large fraction of halos at the lowest masses are too faint to be detected by current galaxy surveys. We find that cored DM density profiles can contribute to the lower observed velocity of galaxies but only for galaxies in which the velocity is measured interior to the size of the core (∼3 kpc).