We use $\Lambda$CDM numerical simulations to model the density profiles and substructure populations in a set of sixteen dark matter halos with resolutions of up to seven million particles within the virial radius. These simulations allow us to follow robustly the formation and evolution of the central cusp over a large mass range of 10$^{11}$ to 10$^{14}$$\msun$ down to approximately 0.5% of the virial radius, and from redshift 5 to the present. The cusp of the density profile is set at redshifts of two or greater and remains remarkably stable to the present time, when considered in non-comoving coordinates.

We fit our halos to a 2 parameter profile where the steepness of the asymptotic cusp is given by $\gamma$, and its radial extent is described by the concentration, $c_{\gamma}$. In our simulations, we find $\gamma$ = 1.4 - 0.08Log($M/M_*$) for halos of 0.01$M_*$ to 1000$M_*$, with a large scatter of $\Delta\gamma \sim \pm 0.3$; and $c_{\gamma} = 8(M/M_*)^{-0.15}$ with a large $M/M_*$ dependent scatter roughly equal to $\pm c_{\gamma}$. Our redshift zero halos have inner slope parameters ranging approximately from r$^{-1}$ to r$^{-1.5}$, with a median of roughly r$^{-1.3}$. This two parameter profile fit works well for all halo types present in our simulations, whether or not they show evidence of a steep asymptotic cusp.

The substructure population is independent of host halo mass and redshift with halo to halo scatter in the substructure velocity distribution function of a factor of roughly two to four. The radial distribution of substructure halos (subhalos) is consistent with the mass profile over the radial range where the possibility of artificial numerical disruption of subhalos can be most reliably excluded, r$\simgt$0.3 r$_{vir}$, although a weakly shallower subhalo profile is favored by the data. We discuss the implications that our results have on gravitational lensing studies of halo structure.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html