  We use the hydrodynamical galaxy formation simulations from the Illustris
suite to study the origin and properties of galaxy velocity bias, i.e., the
difference between the velocity distributions of galaxies and dark matter
inside halos. We find that galaxy velocity bias is a decreasing function of the
ratio of galaxy stellar mass to host halo mass. In general, central galaxies
are not at rest with respect to dark matter halos or the core of halos, with a
velocity dispersion above 0.04 times that of the dark matter. The central
galaxy velocity bias is found to be mostly caused by the close interactions
between the central and satellite galaxies. For satellite galaxies, the
velocity bias is related to their dynamical and tidal evolution history after
being accreted onto the host halos. It depends on the time after the accretion
and their distances from the halo centers, with massive satellites generally
moving more slowly than the dark matter. The results are in broad agreements
with those inferred from modeling small-scale redshift-space galaxy clustering
data, and the study can help improve models of redshift-space galaxy
clustering.
