  We determine the dark matter pair-wise relative velocity distribution in a
set of Milky Way-like halos in the Auriga and APOSTLE simulations. Focusing on
the smooth halo component, the relative velocity distribution is well-described
by a Maxwell-Boltzmann distribution over nearly all radii in the halo. We
explore the implications for velocity-dependent dark matter annihilation,
focusing on four models which scale as different powers of the relative
velocity: Sommerfeld, s-wave, p-wave, and d-wave models. We show that the
J-factors scale as the moments of the relative velocity distribution, and that
the halo-to-halo scatter is largest for d-wave, and smallest for Sommerfeld
models. The J-factor is strongly correlated with the dark matter density in the
halo, and is very weakly correlated with the velocity dispersion. This implies
that if the dark matter density in the Milky Way can be robustly determined,
one can accurately predict the dark matter annihilation signal, without the
need to identify the dark matter velocity distribution in the Galaxy.
