Measuring the mass and concentration of dark matter halos from the
  velocity dispersion profile of their stars
  We use the IllustrisTNG (TNG) cosmological, hydrodynamical simulations of
galaxy formation to measure the velocity dispersion profiles of dark matter and
star particles in Milky Way-mass, galaxy group, and cluster-scale dark matter
halos. The mean profile calculated from both dark and luminous tracers are
similar in shape, exhibiting a large degree of halo-to-halo scatter around the
average profile. The so-called "splashback" radius demarcates the outer
boundary of the halo, and manifests as a kink in the velocity dispersion
profile, located on average between $\sim 1.0-1.5r_{200m}$, where $r_{200m}$ is
the radius within which the enclosed density of the halo equals 200 times the
mean background density of the universe at that redshift. Interestingly, we
find that this location may also be identified as the radius at which the
(stacked) velocity dispersion profile drops to 60% of its peak value (for
line-of-sight motions of stellar and dark matter particles in TNG halos). We
further show that the scatter in the velocity dispersion profiles may be
attributed to the variations in the assembly history of the host halos. In
particular, this segregates the profile into two regimes: one within
$\sim0.1r_{200m}$, where the scatter in the velocity dispersion within is set
by the early assembly history of the halo, and the other beyond this radius
where the scatter in the velocity dispersion is influenced more strongly by its
late-time assembly. Finally, we show that a two-parameter model can be used to
fit the measured velocity dispersion profiles and the fit parameters can be
related directly to two fundamental halo properties: mass and concentration. We
describe a simple model which allows us to express the stellar velocity
dispersion profile in terms of the mass and concentration of the host halo as
the only free parameters.
