Velocity bias in the distribution of dark matter halos
  The standard formalism for the co-evolution of halos and dark matter predicts
that any initial halo velocity bias rapidly decays to zero. We argue that, when
the purpose is to compute statistics like power spectra etc., the coupling in
the momentum conservation equation for the biased tracers must be modified. Our
new formulation predicts the constancy in time of any statistical halo velocity
bias present in the initial conditions, in agreement with peak theory. We test
this prediction by studying the evolution of a conserved halo population in
N-body simulations. We establish that the initial simulated halo density and
velocity statistics show distinct features of the peak model and, thus, deviate
from the simple local Lagrangian bias. We demonstrate, for the first time, that
the time evolution of their velocity is in tension with the rapid decay
expected in the standard approach.
