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 similar to 2 times larger than the universal MF in the 10(9) - 10(13) h(-1) M(circle dot) mass range. Imposing the field of view of the ongoing Hi 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 similar to 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 similar to 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.