  We study the effects of dark matter self-interactions on the local dark
matter distribution in selected Milky Way-like galaxies in the EAGLE
hydrodynamical simulations. The simulations were run with two different
self-interacting dark matter models, a constant and velocity-dependent
self-interaction cross-section. We find that the local dark matter velocity
distribution of the Milky Way-like halos in the simulations with dark matter
self-interactions and baryons are generally similar to those extracted from
cold collisionless dark matter simulations with baryons. In both cases, the
local dark matter speed distributions agree well with their best fit Maxwellian
distributions. Including baryons in the simulations with or without dark matter
self-interactions increases the local dark matter density and shifts the dark
matter speed distributions to higher speeds. To study the implications for
direct detection, we compute the dark matter halo integrals obtained directly
from the simulations and compare them to those obtained from the best fit
Maxwellian velocity distribution. We find that a Maxwellian distribution
provides a good fit to the halo integrals of most halos, without any
significant difference between the results of different dark matter
self-interaction models.
