Turnaround radius of galaxy clusters in N-body simulations
  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.
