Context :

Aims : We use N-body simulations to examine whether a characteristic turnaround radius , as predicted from the spherical collapse model in a \Lambda CDM 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 R _ { 200 } .
There , the turnaround radius can be unambiguously identified as the largest non-expanding scale around a center of gravity .

Results : 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 rather 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

Conclusions :