On the Onset of Stochasticity in $\Lambda$CDM Cosmological Simulations

TL;DR

This paper investigates the onset of stochasticity in $\Lambda$CDM cosmological simulations, identifying a critical scale and mass where chaos emerges, affecting certain properties of cosmic structures while others remain robust.

Contribution

It introduces a novel measurement of chaos onset in cosmological simulations and links it to specific scales and masses, enhancing understanding of non-linear structure formation.

Findings

Chaos appears at small, non-linear scales (~3.5 Mpc/h).

Critical mass for sensitivity scales as perturbation amplitude to the 0.15 power.

Some halo properties are sensitive to initial conditions, others are robust.

Abstract

The onset of stochasticity is measured in $\Lambda$CDM cosmological simulations using a set of classical observables. It is quantified as the local derivative of the logarithm of the dispersion of a given observable (within a set of different simulations differing weakly through their initial realization), with respect to the cosmic growth factor. In an Eulerian framework, it is shown here that chaos appears at small scales, where dynamic is non-linear, while it vanishes at larger scales, allowing the computation of a critical transition scale corresponding to ~ 3.5 Mpc/h. This picture is confirmed by Lagrangian measurements which show that the distribution of substructures within clusters is partially sensitive to initial conditions, with a critical mass upper bound scaling roughly like the perturbation's amplitude to the power 0.15. The corresponding characteristic mass, $M_{\rm crit}=2 10^{13} M_{\odot}$, is roughly of the order of the critical mass of non linearities at z=1 and accounts for the decoupling induced by the dark energy triggered acceleration. The sensitivity to detailed initial conditions spills to some of the overall physical properties of the host halo (spin and velocity dispersion tensor orientation) while other "global" properties are quite robust and show no chaos (mass, spin parameter, connexity and center of mass position). This apparent discrepancy may reflect the fact that quantities which are integrals over particles rapidly average out details of difference in orbits, while the other observables are more sensitive to the detailed environment of forming halos and reflect the non-linear scale coupling characterizing the environments of halos.