Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

TL;DR

This paper extends Particle Linear Theory to various perturbed cubic Bravais lattices to better understand and quantify discreteness effects in N-body simulations of self-gravitating systems.

Contribution

It develops the implementation of Particle Linear Theory for different perturbed cubic Bravais lattices, enabling comparison of discreteness effects in N-body simulations.

Findings

Quantifies discreteness effects in linear regime

Provides implementation details for multiple lattice types

Facilitates comparison of initial condition discretizations

Abstract

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called "Particle Linear Theory" (PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects -- in the linear regime -- of N-body simulations for which initial conditions have been set-up using these different lattices.