NIHAO X: Reconciling the local galaxy velocity function with cold dark matter via mock H i observations

We used 87 high-resolution hydrodynamical cosmological simulations from the NIHAO suite to investigate the relation between the maximum circular velocity (V^Dm _max) of a dark matter halo in a collisionless simulation and the velocity width of the H i gas in the same halo in the hydrodynamical simulation. These two quantities are normally used to compare theoretical and observational velocity functions and have led to a possible discrepancy between observations and predictions based on the cold dark matter (CDM) model. We show that below 100 km s^-1, there is clear bias between H i -based velocities and V^Dm _max, that leads to an underestimation of the actual circular velocity of the halo. When this bias is taken into account, the CDM model has no trouble in reproducing the observed velocity function and no lack of low-velocity galaxies is actually present. Our simulations also reproduce the linewidth-stellar mass (Tully-Fisher) relation and H i sizes, indicating that the H i gas in our simulations is as extended as observed. The physical reason for the lower than expected linewidths is that, in contrast to high-mass galaxies, low-mass galaxies no longer have extended thin H i rotating discs, as is commonly assumed.