  We study the effects of inelastic dark matter self-interactions on the
internal structure of a simulated Milky Way (MW)-size halo. Self-interacting
dark matter (SIDM) is an alternative to collisionless cold dark matter (CDM)
which offers a unique solution to the problems encountered with CDM on
sub-galactic scales. Although previous SIDM simulations have mainly considered
elastic collisions, theoretical considerations motivate the existence of
multi-state dark matter where transitions from the excited to the ground state
are exothermic. In this work, we consider a self-interacting, two-state dark
matter model with inelastic collisions, implemented in the Arepo code. We find
that energy injection from inelastic self-interactions reduces the central
density of the MW halo in a shorter timescale relative to the elastic scale,
resulting in a larger core size. Inelastic collisions also isotropize the
orbits, resulting in an overall lower velocity anisotropy for the inelastic MW
halo. In the inner halo, the inelastic SIDM case (minor-to-major axis ratio $s
\equiv c/a \approx 0.65$) is more spherical than the CDM ($s \approx 0.4$), but
less spherical than the elastic SIDM case ($s \approx 0.75$). The speed
distribution $f(v)$ of dark matter particles at the location of the Sun in the
inelastic SIDM model shows a significant departure from the CDM model, with
$f(v)$ falling more steeply at high speeds. In addition, the velocity kicks
imparted during inelastic collisions produce unbound high-speed particles with
velocities up to 500 km s$^{-1}$ throughout the halo. This implies that
inelastic SIDM can potentially leave distinct signatures in direct detection
experiments, relative to elastic SIDM and CDM.
