Bars in Cuspy Dark Halos
  We examine the bar instability in models with an exponential disk and a cuspy NFW-like dark matter (DM) halo inspired by cosmological simulations. Bar evolution is studied as a function of numerical resolution in a sequence of models spanning 10K to 100M DM particles - including a multi-mass model with an effective resolution of 10G. The goal is to find convergence in dynamical behaviour. We characterize the bar growth, the buckling instability, pattern speed decay through resonant transfer of angular momentum, and possible destruction of the DM halo cusp. Overall, most characteristics converge in behaviour in detail for halos containing more than 10M particles. Notably, the formation of the bar does not destroy the density cusp in this case. These higher resolution simulations clearly illustrate the importance of discrete resonances in transporting angular momentum from the bar to the halo. 
John Dubinski, Ingo Berentzen, and Isaac Shlosman