A Mean-Field Approach to Simulating the Merging of Collisionless Stellar
  Systems Using a Particle-Based Method
  We present a mean-field approach to simulating merging processes of two
spherical collisionless stellar systems. This approach is realized with a
self-consistent field (SCF) method in which the full spatial dependence of the
density and potential of a system is expanded in a set of basis functions for
solving Poisson's equation. In order to apply this SCF method to a merging
situation where two systems are moving in space, we assign the expansion center
to the center of mass of each system, the position of which is followed by a
mass-less particle placed at that position initially. Merging simulations over
a wide range of impact parameters are performed using both an SCF code
developed here and a tree code. The results of each simulation produced by the
two codes show excellent agreement in the evolving morphology of the merging
systems and in the density and velocity dispersion profiles of the merged
systems. However, comparing the results generated by the tree code to those
obtained with the softening-free SCF code, we have found that in large impact
parameter cases, a softening length of the Plummer type introduced in the tree
code has an effect of advancing the orbital phase of the two systems in the
merging process at late times. We demonstrate that the faster orbital phase
originates from the larger convergence length to the pure Newtonian force.
Other application problems suitable to the current SCF code are also discussed.
