The velocity function in the local environment from LCDM and LWDM
  constrained simulations
  Using constrained simulations of the local Universe for generic cold dark
matter and for 1keV warm dark matter, we investigate the difference in the
abundance of dark matter halos in the local environment. We find that the mass
function within 20 Mpc/h of the Local Group is ~2 times larger than the
universal mass function in the 10^9-10^13 M_odot/h mass range. Imposing the
field of view of the on-going HI blind survey ALFALFA in our simulations, we
predict that the velocity function in the Virgo-direction region exceeds the
universal velocity function by a factor of 3. Furthermore, employing a scheme
to translate the halo velocity function into a galaxy velocity function, 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
velocity function in the 80-300 km/s velocity range, having a value ~10 times
larger than the universal velocity function in the Virgo-direction region. In
the low velocity regime, 35-80 km/s, the warm dark matter simulation reproduces
the observed flattening of the velocity function. On the contrary, the
simulation with cold dark matter predicts a steep rise in the velocity function
towards lower velocities; for V_max=35 km/s, 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 cold dark matter paradigm or
for the conventional assumptions about energetic feedback in dwarf galaxies.
