The dynamical structure of dark matter haloes

Thanks to the ever increasing computational power and the development of more sophisticated algorithms, numerical N -body simulations are now uncovering several phenomenological relations between the physical properties of dark matter haloes in position and velocity space. It is the aim of the present work to investigate in detail the dynamical structure of dark matter haloes, as well as its possible dependence on mass and its evolution with redshift up to z = 5. We use high-resolution cosmological simulations of individual objects to compute the radially-averaged profiles of several quantities, scaled by the radius Rmax at which the circular velocity attains its maximum value, Vmax. We investigate the circular velocity profile, the dark matter density and its logarithmic slope, the position and velocity of the centre of mass on different scales, the radial infall around the halo, its spin parameter, the radial and tangential components of the velocity dispersion, and the coarse-grained phase-space density. It is found that all the physical properties considered display a similar structure when expressed in terms of Rmax and Vmax. No systematic dependence on mass or cosmic epoch are found within Rmax, and all the different radial profiles are well fit by simple analytical models. However, our results suggest that several properties are not ‘universal’ outside this radius. In particular, dark matter haloes should not be assumed to be in equilibrium beyond Rmax, especially at high redshift, where significant infall velocities can be measured. We therefore conclude that the whole dynamical structure of haloes, rather than just their density profile, is ‘universal’ within Rmax at least up to z = 5, and that some dynamical process yet to be identified is responsible for such universality, rather than the details of the merger history of the halo. Memory of the initial conditions is only retained in the outer regions, where there is significant scatter from object to object, as well as clear systematic trends with mass and time. Thus, we argue that Rmax and Vmax provide a well-motivated, model-independent choice to characterize dark matter haloes, especially in comparison with the so-called ‘virial’ mass or radius.