The velocity function in the local environment from λcdm and λwdm constrained simulations

Using constrained simulations of the local universe for generic cold dark matter (CDM) and for 1 keV warm dark matter (WDM), we investigate the difference in the abundance of dark matter halos in the local environment. We find that the mass function (MF) within 20 h ^-1 Mpc of the Local Group is 2 times larger than the universal MF in the 10⁹-10¹³ h ^-1 M mass range. Imposing the field of view of the ongoing H I blind survey Arecibo Legacy Fast ALFA (ALFALFA) in our simulations, we predict that the velocity function (VF) in the Virgo-direction region (VdR) exceeds the universal VF by a factor of 3. Furthermore, employing a scheme to translate the halo VF into a galaxy VF, we compare the simulation results with a sample of galaxies from the early catalog release of ALFALFA. We find that our simulations are able to reproduce the VF in the 80-300 km s^-1 velocity range, having a value 10 times larger than the universal VF in the VdR. In the low-velocity regime, 35-80 km s^-1, the WDM simulation reproduces the observed flattening of the VF. In contrast, the simulation with CDM predicts a steep rise in the VF toward lower velocities; for V _max = 35 km s^-1, it forecasts 10 times more sources than the ones observed. If confirmed by the complete ALFALFA survey, our results indicate a potential problem for the CDM paradigm or for the conventional assumptions about energetic feedback in dwarf galaxies.