Modelling gravity in N-body simulations of disc galaxies Optimal types of softening for given dynamical requirements

Modelling gravity is a fundamental problem that must be tackled in N -body simulations of stellar systems, and satisfactory solutions require a deep understanding of the dynamical effects of softening. In a previous paper (Romeo 1997), we have devised a method for exploring such effects, and we have focused on two applications that reveal the dynamical differences between the most representative types of softened gravity. In the present paper we show that our method can be applied in another, more fruitful, way: for developing new ideas about softening. Indeed, it opens a direct route to the discovery of optimal types of softened gravity for given dynamical requirements, and thus to the accomplishment of a physically consistent modelling of disc galaxies, even in the presence of a cold interstellar gaseous component and in situations that demand anisotropic resolution.