The Growth and Structure of Dark Matter Haloes

In this paper, we analyse in detail the mass-accretion histories and structural properties of dark haloes in high-resolution N-body simulations. We model the density distribution in individual haloes using the NFW profile. For a given halo, there is a tight correlation between its inner scale radius rs and the mass within it, Ms, for all its main progenitors, which is the basic reason why halo structural properties are closely related to their mass-accretion histories. This correlation can be used to predict the structural properties of a dark halo at any time in its history. The build-up of dark haloes in CDM models generally consists of an early phase of fast accretion [where the halo mass Mh increases with time much faster than the expansion rate of the universe] and a late phase of slow accretion [where Mh increases with time approximately as the expansion rate]. These two phases are separated at a time when the halo concentration parameter c ∼ 5 and the binding energy of the halo is approximately equal to that of a singular isothermal sphere with the same circular velocity. Haloes in the two accretion phases show systematically different properties, for example, the circular velocity vh increases rapidly with time in the fast accretion phase but remain almost constant in the slow accretion phase, the inner properties of a halo, such as rs and Ms increase rapidly with time in the fast accretion phase but change only slowly in the slow accretion phase, the inner circular velocity vs is approximately equal to vh in the fast accretion phase but is larger in the slow accretion phase. The potential well associated with a halo is built up mainly in the fast accretion phase, while a large amount of mass can be accreted in the slow accretion phase without