Bar-halo Friction in Galaxies I: Scaling Laws
  It has been known for some time that rotating bars in galaxies slow due to dynamical friction against the halo. However, recent attempts to use this process to place constraints on the dark matter density in galaxies and possibly also to drive dark matter out of the center have been challenged. This paper uses simplified numerical experiments to clarify several aspects of the friction mechanism. I explicitly demonstrate the Chandrasekhar scaling of the friction force with bar mass, halo density, and halo velocity dispersion. I present direct evidence that exchanges between the bar and halo orbits at major resonances are responsible for friction and study both individual orbits and the net changes at these resonances. I also show that friction alters the phase space density of particles in the vicinity of a major resonance, which is the reason the magnitude of the friction force depends on the prior evolution. I demonstrate that bar slow down can be captured correctly in simulations having modest spatial resolution and practicable numbers of particles. Subsequent papers in this series delineate the dark matter density that can be tolerated in halos of different density profiles. 
J. A. Sellwood (Rutgers University)