Mass of clusters in simulations

We show that dark matter halos in N-body simulations have a boundary layer (BL), which neatly separates dynamically bound mass from unbound materials. We define T(r) and W(r) as the differential kinetic and potential energy of halos and evaluate them in spherical shells. We notice that in simulated halos such differential quantities fulfill the following properties: (1) the differential virial ratio ℛ = -2T/W has at least one persistent (resolution-independent) minimum r̄, such that, close to r̄, (2) the function w = -d log W/d log r has a maximum, while (3) the relation ℛ(r̄) ≃ w(r̄) holds. BLs are set where these three properties are fulfilled, in halos found in simulations of "tilted" Einstein-de Sitter and ACDM models, run ad hoc, using the ART and GADGET codes; their presence is confirmed in larger simulations of the same models with a lower level of resolution. Here we find that ∼97% of the ∼300 clusters (per model) we have with M > 4.2 × 10¹⁴ h^-1 M_⊙ own a BL. Those clusters that appear not to have a BL are seen to be undergoing major merging processes and to grossly violate spherical symmetry. The radius r̄ ≡ r_c has significant properties. First of all, the mass M_c it encloses almost coincides with the mass M_dyn evaluated from the velocities of all particles within r_c, according to the virial theorem. Also, materials at r > r_c are shown not be in virial equilibrium. Using r_c we can then determine an individual density contrast Δ_c for each virialized halo, which we compare with the "virial" density contrast Δ_v ≃ 178Ω_m^0.45 (where Ω_m is the matter density parameter) obtained assuming a spherically symmetric and unperturbed fluctuation growth. As expected, for each mass scale, Δ_v is within the range of values Δ_c. However, the spread in Δ_c is wide, while the average Δ_c is ∼25% smaller than the corresponding Δ_v. We argue that the matching of properties derived under the assumption of spherical symmetry must be a consequence of an approximate sphericity, after violent relaxation destroyed features related to ellipsoidal nonlinear growth. On the contrary, the spread of the final Δ_c is an imprint of the different initial three-dimensional geometries of fluctuations and of the variable environment during their collapse, as suggested by a comparison of our results with the Sheth & Tormen analysis.