The effect of softening on dynamical simulations of galaxies

Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of parsecs. Generally, the spatial resolution is defined by (some multiple of) the softening length, whose value is set as a compromise between the desired resolution and the need for limiting small-scale noise. Several works have studied the question whether a softening scale fixed in space and time provides a good enough modelling of an astrophysical system. Here we address this question within the context of dynamical simulations and disc instabilities. We first follow the evolution of a galaxy-like object in isolation and then set up a simulation of an idealised merger event. Alongside a run using the standard fixed-softening approach, we performed simulations where the softening lengths were let to vary from particle to particle according to the evolution of the local density field in space and time. Even though during the most violent phases of the merging the fixed-softening simulation tends to underestimate the resulting matter densities, as far as the evolution of the disc component is concerned we found no significant differences among the runs. We conclude that using an appropriate fixed softening scale is a safe approach to the problem of modelling an N-body, non-cosmological disc galaxy system.