A universal angular momentum profile for dark matter haloes
  The angular momentum distribution in dark matter haloes and galaxies is a key
ingredient in understanding their formation. Especially, the internal
distribution of angular momenta is closely related to the formation of disk
galaxies. In this article, we use haloes identified from a high-resolution
simulation, the Bolshoi simulation, to study the spatial distribution of
specific angular momenta, $j(r,\theta)$. We show that by stacking haloes with
similar masses to increase the signal-to-noise ratio, the profile can be fitted
as a simple function, $j(r,\theta)=j_s \sin^2(\theta/\theta_s)
(r/r_s)^2/(1+r/r_s)^4 $, with three free parameters, $j_s, r_s$, and
$\theta_s$. Specifically, $j_s$ correlates with the halo mass $M_\mathrm{vir}$
as $j_s\propto M_\mathrm{vir}^{2/3}$, $r_s$ has a weak dependence on the halo
mass as $r_s \propto M_\mathrm{vir}^{0.040}$, and $\theta_s$ is independent of
$M_\mathrm{vir}$. This profile agrees with that from a rigid shell model,
though its origin is unclear. Our universal specific angular momentum profile
$j(r,\theta)$ is useful in modelling haloes' angular momenta. Furthermore, by
using an empirical stellar mass - halo mass relation, we can infer the averaged
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.
