Turnaround radius of galaxy clusters in N-body simulations

TL;DR

This study uses N-body simulations to investigate the turnaround radius of galaxy clusters, confirming its scaling with mass and its insensitivity to asphericity, while highlighting the influence of tidal forces and cosmology.

Contribution

It demonstrates that the turnaround radius can be reliably identified in simulations and follows theoretical predictions, extending the spherical collapse model to realistic, non-spherical structures.

Findings

Turnaround radius scales as M^{1/3} for halos above 10^{13} M_sun.

The deviation from the spherical collapse prediction is mainly due to tidal forces.

The characteristic density within the turnaround radius is about 11 times the background density.

Abstract

We use N-body simulations to examine whether a characteristic turnaround radius, as predicted from the spherical collapse model in a $\rm {\Lambda CDM}$ Universe, can be meaningfully identified for galaxy clusters, in the presence of full three-dimensional effects. We use The Dark Sky Simulations and Illustris-TNG dark-matter--only cosmological runs to calculate radial velocity profiles around collapsed structures, extending out to many times the virial radius $R_{200}$. There, the turnaround radius can be unambiguously identified as the largest non-expanding scale around a center of gravity. We find that: (a) Indeed, a single turnaround scale can meaningfully describe strongly non-spherical structures. (b) For halos of masses $M_{200}>10^{13}M_\odot$, the turnaround radius $R_{ta}$ scales with the enclosed mass $M_{ta}$ as $M_{ta}^{1/3}$, as predicted by the spherical collapse model. (c) The deviation of $R_{ta}$ in simulated halos from the spherical collapse model prediction is insensitive to halo asphericity. Rather, it is sensitive to the tidal forces due to massive neighbors when such are present. (d) Halos exhibit a characteristic average density within the turnaround scale. This characteristic density is dependent on cosmology and redshift. For the present cosmic epoch and for concordance cosmological parameters ($\Omega_m \sim 0.7$; $\Omega_\Lambda \sim 0.3$) turnaround structures exhibit an average matter density contrast with the background Universe of $\delta \sim 11$. Thus $R_{ta}$ is equivalent to $R_{11}$ -- in a way analogous to defining the "virial" radius as $R_{200}$ -- with the advantage that $R_{11}$ is shown in this work to correspond to a kinematically relevant scale in N-body simulations.