We use a set of large cosmological N-body simulations to study the internal structure of dark matter haloes which form in scale-free hierarchical clustering models ( initial power spectra P ( k ) \propto k ^ { n } with n = 0 , -1 and -2 ) in an \Omega = 1 universe .
We find that the radius r _ { 178 } in a halo corresponding to a mean interior overdensity of 178 accurately delineates the quasi-static halo interior from the surrounding infalling material , in agreement with the simple spherical collapse model .
The interior velocity dispersion correlates with mass , again in good agreement with the spherical collapse model .
Interior to the virial radius \r { 1 } 78 , the spherically averaged density , circular velocity and velocity dispersion profiles are well fit by a simple two-parameter analytical model proposed by Navarro \etal ( 1995a ) .
This model has \rho \propto r ^ { -1 } at small radii , steepening to \rho \propto r ^ { -3 } at large radii , and fits our haloes to the resolution limit of the simulations .
The two model parameters , scalelength and mass , are tightly correlated .
Lower mass haloes are more centrally concentrated , and so have scalelengths which are a smaller fraction of their virial radius than those of their higher mass counterparts .
This reflects the earlier formation times of low mass haloes .
The haloes are moderately aspherical , with typical axial ratios 1 : 0.8 : 0.65 at their virial radii , becoming gradually more spherical towards their centres .
The haloes are generically triaxial , but with a slight preference for prolate over oblate configurations , at least for n = -1 and 0 .
These shapes are maintained by an anisotropic velocity dispersion tensor .
The median value of the spin parameter is \lambda \approx 0.04 , with a weak trend for lower \lambda at higher halo mass .
We also investigate how the halo properties depend on the algorithm used to identify them in the simulations , using both friends-of-friends and spherical overdensity methods .
We find that for groups selected at mean overdensities \sim 100 - 400 by either method , the properties are insensitive to how the haloes are selected , if the halo centre is taken as the position of the most bound particle .