Profiles of dark haloes: Evolution, scatter and environment

We study dark matter halo density profiles in a high-resolution N-body simulation of a ΛCDM cosmology. Our statistical sample contains ∼5000 haloes in the range 10¹¹-10¹⁴ h^-1 M⊙, and the resolution allows a study of subhaloes inside host haloes. The profiles are parametrized by an NFW form with two parameters, an inner radius r_s and a virial radius R_vir, and we define the halo concentration c_vir ≡ R_vir/r_s. First, we find that, for a given halo mass, the redshift dependence of the median concentration is c_vir ∝ (1 + z)^-1. This corresponds to r_s(z) ∼ constant, and is contrary to earlier suspicions that c_vir does not vary much with redshift. The implications are that high-redshift galaxies are predicted to be more extended and dimmer than expected before. Secondly, we find that the scatter in halo profiles is large, with a 1σ Δ(log c_vir) = 0.18 at a given mass, corresponding to a scatter in maximum rotation velocities of ΔV_max/V_max = 0.12. We discuss implications for modelling the Tully-Fisher relation, which has a smaller reported intrinsic scatter. Thirdly, subhaloes and haloes in dense environments tend to be more concentrated than isolated haloes, and show a larger scatter. These results suggest that c_vir is an essential parameter for the theory of galaxy modelling, and we briefly discuss implications for the universality of the Tully-Fisher relation, the formation of low surface brightness galaxies, and the origin of the Hubble sequence. We present an improved analytic treatment of halo formation that fits the measured relations between halo parameters and their redshift dependence, and can thus serve semi-analytic studies of galaxy formation.