Gravitational collapse from cold uniform asymmetric initial conditions

TL;DR

This study uses N-body simulations to explore how initial asymmetries and fluctuations influence the final structure of collapsing systems, revealing different density profiles and slow convergence with particle number.

Contribution

It demonstrates the competing roles of finite N fluctuations and anisotropic perturbations in gravitational collapse, highlighting challenges in simulating cosmological structure formation.

Findings

Density profile decays as r^{-4} when fluctuations dominate

Density profile decays as r^{-3} when anisotropic perturbations dominate

Convergence of macroscopic properties with increasing N is very slow

Abstract

Using controlled numerical N-body experiments, we show how, in the collapse dynamics of an initially cold and uniform distribution of particles with a generic asymmetric shape, finite $N$ fluctuations and perturbations induced by the anisotropic gravitational field compete to determine the physical properties of the asymptotic quasi-stationary state. When finite $N$ fluctuations dominate the dynamics, the particle energy distribution changes greatly and the final density profile {decays outside its core} as $r^{-4}$ with an $N$-dependent amplitude. On the other hand, in the limit where the anisotropic perturbations dominate, the collapse is softer and the density profile shows a decay as $r^{-3}$, as is typical of halos in cosmological simulations. However, even in this limit, convergence with $N$ of the macroscopic properties of the virialized system, such as the particle energy distributions, the bound mass, and the density profile, is very slow and not clearly established, including for our largest simulations (with $N \sim 10^6$). Our results illustrate the challenges of accurately simulating the first collapsing structures in standard-type cosmological models