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.