Aims. We use N-body simulations to examine whether a characteristic turnaround radius, as predicted from the spherical collapse model in a ΛCDM Universe, can be meaningfully identified for galaxy clusters in the presence of full three-dimensional effects.
Methods. 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 R200. There, the turnaround radius can be unambiguously identified as the largest nonexpanding scale around a center of gravity.
Results. We find that: (a) a single turnaround scale can meaningfully describe strongly nonspherical structures. (b) For halos of masses M200 > 1013 M⊙, the turnaround radius Rta scales with the enclosed mass Mta as Mta1/3, as predicted by the spherical collapse model. (c) The deviation of Rta in simulated halos from the spherical collapse model prediction is relatively insensitive to halo asphericity. Rather, it is sensitive to the tidal forces due to massive neighbors when these 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 (Ωm ∼ 0.3; ΩΛ ∼ 0.7) turnaround structures exhibit a density contrast with the matter density of the background Universe of δ ∼ 11. Thus, Rta is equivalent to R11 – in a way that is analogous to defining the “virial” radius as R200 – with the advantage that R11 is shown in this work to correspond to a kinematically relevant scale in N-body simulations.
The anisotropy of the power spectrum in periodic cosmological simulations