The Diversity and Similarity of Simulated Cold Dark Matter Halos

We study the mass, velocity dispersion, and anisotropy profiles of $\Lambda$CDM halos using a suite of N-body simulations of unprecedented numerical resolution (the {\it Aquarius Project}). 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 spherically-averaged density profile becomes progressively shallower inwards and, at the innermost resolved radius, the logarithmic slope is $\gamma \equiv -$d$\ln\rho/$d$\ln r \simlt 1$. Asymptotic inner slopes as steep as the recently claimed $\rho \propto r^{-1.2}$ are clearly ruled out. The radial dependence of $\gamma$ is well approximated by a power-law, $\gamma \propto r^{\alpha}$ (the Einasto profile). The shape parameter, $\alpha$, varies slightly but significantly from halo to halo, implying that the mass profiles of $\Lambda$CDM halos are not strictly universal: different halos 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, $\rho/\sigma^3\propto r^{-1.875}$. Our conclusions are reliable down to radii below 0.4% 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.