Dark Matter with N-Body Numerical Simulations

TL;DR

This paper explains the fundamentals of N-body simulations for cosmological dark matter, introduces GADGET-2 software, and demonstrates large-scale structure formation results consistent with theoretical models.

Contribution

It provides a comprehensive guide to N-body simulation techniques, including code modification and analysis of dark matter structure formation in the $\Lambda$CDM model.

Findings

Matter power spectrum matches theoretical predictions

Successful simulation of large-scale structure formation

Guidance on GADGET-2 implementation and usage

Abstract

The development of numerical N -body simulations have allowed to study formation process and evolution of galaxies at different scales. This paper presents the fundamental concepts of N-body systems applied to the cosmological evolution of the $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model. In order to perform structure formation in the Universe, we provide an introduction to the basic equations and their implementation on the GADGET-2 software. We also present a simple guide to modify this code. First, we briefly describe the dark matter in the Universe as well as the theoretical and experimental basis of the $\Lambda$CDM model. Then, we focus on the simulation codes and provide the equations that govern most of the N-body simulations to model the dark matter. We describe the Smoothed Particle Hydrodynamics method used for simulating the gas, star dynamics and structure formation in these simulations. Then, cautiously, we guide the reader to the installation of GADGET-2 on a Linux-based computer, as well as to carry out a couple of examples to operate the code. Finally, by using a computational cluster, we show several results of a large structure simulation, analyse the outputs to display the matter power spectrum, and compare the outcome with theoretical predictions.