Simulations of sinking satellites

The orbital decay of satellite galaxies can be investigated using simulation methods which follow the dynamical process in a variety of different approximations. A comparison of the results shows that the decay rate depends on the global response of the parent galaxy. It is artificially enhanced by fixing the center of the parent, and it is suppressed by neglecting the self-gravity of the response. Chandrasekhar's local dynamical friction formula cannot, therefore, be a complete description of the underlying physics, although it predicts decay rates which are approximately correct. A simulation method which calculates the galactic gravitational field to second order in a multipole expansion gives results in agreement with full N-body experiments, but it runs several hundred times faster for N = 5000; It is only a factor of 2 or 3 slower than methods based on a generalization of the restricted three-body problem.