A universal angular momentum profile for dark matter haloes

Abstract

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.

arXiv comment10 pages, 8 figures, accepted version by ApJ, Figure 5 is added to address the r_s - c relation, Section 5 is updated

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