The inner structure of  CDM haloes -- I. A numerical convergence study

We present a comprehensive set of convergence tests which explore the role of various numerical parameters on the equilibrium structure of a simulated dark matter halo. We report on results obtained with two independent, state-of-the-art, multi-stepping, parallel <it>N</it>-body codes: <scp>pkdgrav</scp> and <scp>gadget</scp>. We find that convergent mass profiles can be obtained for suitable choices of the gravitational softening, time-step, force accuracy, initial redshift, and particle number. For softenings chosen so that particle discreteness effects are negligible, convergence in the circular velocity is obtained at radii where the following conditions are satisfied:…