# Numerical Discreteness Errors in Multi-Species Cosmological N-body Simulations

## TL;DR

This paper analyzes numerical discreteness errors in multi-species cosmological N-body simulations, identifying their sources and proposing mitigation strategies to improve the accuracy of large-scale power spectrum predictions.

## Contribution

It provides a detailed analysis of discreteness errors in two-species cosmological simulations and introduces two effective mitigation methods to reduce these errors.

## Key findings

- Discreteness errors cause biased small-scale power growth.
- Large-scale power offsets persist even with equal particle masses.
- Mitigation strategies significantly reduce power spectrum offsets.

## Abstract

We present a detailed analysis of numerical discreteness errors in two-species, gravity-only, cosmological simulations using the density power spectrum as a diagnostic probe. In a simple setup where both species are initialized with the same total matter transfer function, biased growth of power forms on small scales when the solver force resolution is finer than the mean interparticle separation. The artificial bias is more severe when individual density and velocity transfer functions are applied. In particular, significant large-scale offsets in power are measured between simulations with conventional offset grid initial conditions when compared against converged high-resolution results where the force resolution scale is matched to the interparticle separation. These offsets persist even when the cosmology is chosen so that the two particle species have the same mass, indicating that the error is sourced from discreteness in the total matter field as opposed to unequal particle mass. We further investigate two mitigation strategies to address discreteness errors: the frozen potential method and softened interspecies short-range forces. The former evolves particles under the approximately "frozen" total matter potential in linear theory at early times, while the latter filters cross-species gravitational interactions on small scales in low density regions. By modeling closer to the continuum limit, both mitigation strategies demonstrate considerable reductions in large-scale power spectrum offsets.