Profiles of dark haloes: evolution, scatter and environment

We study dark matter halo density profiles in a high-resolution N-body simu lation of a Lambda CDM cosmology. Our statistical sample contains similar t o 5000 haloes in the range 10(11)-10(14) h(-1) M., and the resolution allow s 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 con centration is c(vir) proportional to (1 + z)(-1). This corresponds to r(s)( z) similar to constant, and is contrary to earlier suspicions that c(vir) d oes not vary much with redshift. The implications are that high-redshift ga laxies are predicted to be more extended and dimmer than expected before. S econdly, we find that the scatter in halo profiles is large, with a 1 sigma Delta (log c(vir)) = 0.18 at a given mass, corresponding to a scatter in m aximum rotation velocities of DeltaV(max)/V-max = 0.12. We discuss implicat ions 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. T hese results suggest that c(vir) is an essential parameter for the theory o f galaxy modelling, and we briefly discuss implications for the universalit y of the Tully-Fisher relation, the formation of low surface brightness gal axies, and the origin of the Hubble sequence. We present an improved analyt ic treatment of halo formation that fits the measured relations between hal o parameters and their redshift dependence, and can thus serve semi-analyti c studies of galaxy formation.