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.