A Universal Angular Momentum Profile for Dark Matter Halos

The angular momentum distribution in dark matter halos and galaxies is a key ingredient in understanding their formation. Specifically, the internal distribution of angular momenta is closely related to the formation of disk galaxies. In this article, we use halos identified from a high-resolution simulation, the Bolshoi simulation, to study the spatial distribution of specific angular momenta, j(r,θ ). We show that by stacking halos with similar masses to increase the signal-to-noise ratio, the profile can be fitted as a simple function, j{(r,θ )={j}_s{\sin }²{(θ /{θ }_s)(r/{r}_s)}²/(1+r/{r}_s)}⁴, with three free parameters, {j}_s,{r}_s, and {θ }_s. Specifically, j _s correlates with the halo mass M _vir as {j}_s\propto {M}_{vir}^2/3, r _s has a weak dependence on the halo mass as {r}_s\propto {M}_{vir}^0.040, and {θ }_s is independent of M _vir. This profile agrees with that from a rigid shell model, though its origin is unclear. Our universal specific angular momentum profile j(r,θ ) is useful in modeling the angular momenta of halos. Furthermore, by using an empirical stellar mass-halo mass relation, we can infer the average angular momentum distribution of a dark matter halo. The specific angular momentum-stellar mass relation within a halo computed from our profile is shown to share a similar shape as that from the observed disk galaxies.