The statistics of   CDM halo concentrations

We use the Millennium Simulation (MS) to study the statistics of LCDM halo concentrations at z = 0. Our results confirm that the average halo concentration declines monotonically with mass; a power-law fits well the concentration-mass relation for over 3 decades in mass, up to the most massive objects to form in a LCDM universe (~ 10¹5 h^-1 Msol). This is in clear disagreement with the predictions of the model proposed by Bullock et al. for these rare objects, and agrees better with the original predictions of Navarro, Frenk, & White. The large volume surveyed, together with the unprecedented numerical resolution of the MS, allow us to estimate with confidence the distribution of concentrations and, consequently, the abundance of systems with unusual properties. About one in a hundred cluster haloes (M200 >~ 3x10¹4 h^-1 Msol) have concentrations exceeding c200 = 7. 5, a result that may be used to interpret the likelihood of unusually strong massive gravitational lenses, such as Abell 1689, in the LCDM cosmogony. A similar fraction (1 in 100) of galaxy-sized haloes (M200 ~ 10¹2 h^-1 Msol) have c200 < 4. 5, an important constraint on models that attempt to reconcile the rotation curves of low surface-brightness galaxies by appealing to haloes of unexpectedly low concentration. We find that halo concentrations are independent of spin once haloes manifestly out of equilibrium are removed from the sample. Compared to their relaxed brethren, the concentrations of out-of-equilibrium haloes tend to be lower and to have more scatter, while their spins tend to be higher. . . (continue)