The diversity and similarity of simulated cold dark matter haloes

We study the mass, velocity dispersion and anisotropy profiles of Lambda cold dark matter (Lambda CDM) haloes using a suite of N-body simulations of unprecedented numerical resolution. The Aquarius Project follows the formation of six different galaxy-sized haloes simulated several times at varying numerical resolution, allowing numerical convergence to be assessed directly. The highest resolution simulation represents a single dark matter halo using 4.4 billion particles, of which 1.1 billion end up within the virial radius. Our analysis confirms a number of results claimed by earlier work, and clarifies a few issues where conflicting claims may be found in the recent literature. The mass profile of Lambda CDM haloes deviates slightly but systematically from the form proposed by Navarro, Frenk & White. The spherically averaged density profile becomes progressively shallower inwards and, at the innermost resolved radius, the logarithmic slope is gamma equivalent to - d ln /d ln r less than or similar to 1. Asymptotic inner slopes as steep as the recently claimed proportional to r-1.2 are clearly ruled out. The radial dependence of gamma is well approximated by a power law, gamma proportional to r alpha (the Einasto profile). The shape parameter, alpha, varies slightly but significantly from halo to halo, implying that the mass profiles of Lambda CDM haloes are not strictly universal: different haloes cannot, in general, be rescaled to look identical. Departures from similarity are also seen in velocity dispersion profiles and correlate with those in density profiles so as to preserve a power-law form for the spherically averaged pseudo-phase-space density, /Sigma 3 proportional to r-1.875. The index here is identical to that of Bertschinger's similarity solution for self-similar infall on to a point mass from an otherwise uniform Einstein-de Sitter universe. The origin of this striking behaviour is unclear, but its robustness suggests that it reflects a fundamental structural property of Lambda CDM haloes. Our conclusions are reliable down to radii below 0.4 per cent of the virial radius, providing well-defined predictions for halo structure when baryonic effects are neglected, and thus an instructive theoretical template against which the modifications induced by the baryonic components of real galaxies can be judged.