Density profiles and substructure of dark matter halos: Converging resultsat ultra-high numerical resolution

Can dissipationless N-body simulations be used to reliably determine the st ructural and substructure properties of dark matter halos? A large simulati on of a galaxy cluster in a cold dark matter universe is used to increase t he force and mass resolution of current "high-resolution simulations" by al most an order of magnitude to examine the convergence of the important phys ical quantities. The cluster contains similar to5 million particles within the final virial radius, R-vir similar or equal to 2 MPC (with H-0 = 50 km s(-1) Mpc(-1)), and is: simulated using a force resolution of 1.0 kpc (equi valent to 0.05% of R-vir); the final virial mass is 4.3 x 10(14) M-., equiv alent to a circular velocity of v(circ) (GM/R)(1/2) similar or equal to 100 0 km s(-1) at the virial radius. The central density profile has a logarith mic slope of -1.5, identical to lower resolution studies of the same halo, indicating that the profiles measured from simulations of this resolution h ave converged to the "physical" limit down to scales of a few kpc (similar to0.2% of R-vir). In addition, the abundance and properties of substructure are consistent with those derived from lower resolution runs; from small t o large galaxy scales (v(circ) > 100 km s(-1), m > 10(11) M-.), the circula r velocity function and the mass function of substructures can be approxima ted by power laws with slopes of similar to -4 and similar to -2, respectiv ely. At the current resolution, overmerging (a numerical effect that leads to structureless virialized halos in low-resolution N-body simulations) see ms to be globally unimportant for substructure halos with circular velociti es of v(circ) > 100 km s(-1) (similar to 10% of the cluster's v(circ)). We can identify subhalos orbiting in the very central region of the cluster (R less than or similar to 100 kpc), and we can trace most of the cluster pro genitors from high redshift to the present. The object at the cluster cente r (the dark matter analog of a cD galaxy) is assembled between z = 3 and z = 1 from the merging of a dozen halos with v(circ) greater than or similar to 300 km s(-1). Tidal stripping and halo-halo collisions decrease the mean circular velocity of the substructure halos by approximate to 20% over a 5 billion yr period. We use the sample of 2000 substructure halos to explore the possibility of biases using galactic tracers in clusters: the velocity dispersions of the halos globally agree with the dark matter within less t han or similar to 10%, but the halos are spatially antibiased, and in the v ery central region of the cluster (R/R-vir < 0.3) they show positive veloci ty bias (b(v) <equivalent to> sigma (v3D,halos)/sigma (v3D,DM) similar or e qual to 1.2-1.3); however, this effect appears to depend on numerical resol ution.