Softening in N-body simulations of collisionless systems

The standard Plummer softening force law is physically inconsistent: the force on a particle is calculated as if it were a point mass, but its contribution to the gravitational field for other particles is that of an extended mass. The use of uniform density spheres as models for the particles leads to a consistent force and is physically more reasonable. For a King model with W(0) = 5, the optimal size of uniform density spheres is approximately three times the optimal Plummer softening length. This allows a larger time step to be used and thus uniform density sphere softening is more efficient. The relaxation rate is smaller for the optimal uniform density sphere softening.