Gravitational softening as a smoothing operation

TL;DR

This paper explains gravitational softening in N-body simulations as a smoothing operation on mass distribution, offering advantages for setting up initial conditions and understanding the method.

Contribution

It clarifies the equivalence between softening and smoothing, highlighting benefits for initial condition setup in collisionless system simulations.

Findings

Softening can be exactly described as a smoothing operation.

Smoothing approach aids in creating near-equilibrium initial conditions.

Mathematically, softening and smoothing are equivalent descriptions.

Abstract

In self-consistent N-body simulations of collisionless systems, gravitational interactions are modified on small scales to remove singularities and simplify the task of numerically integrating the equations of motion. This `gravitational softening' is sometimes presented as an ad-hoc departure from Newtonian gravity. However, softening can also be described as a smoothing operation applied to the mass distribution; the gravitational potential and the smoothed density obey Poisson's equation precisely. While `softening' and `smoothing' are mathematically equivalent descriptions, the latter has some advantages. For example, the smoothing description suggests a way to set up N-body initial conditions in almost perfect dynamical equilibrium.