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 (r) over bar, such that, close to (r) over bar, ( 2) the function w = -d log W/d log r has a maximum, while (3) the relation R((r) over bar) similar or equal to w((r) over bar) holds. BLs are set where these three properties are fulfilled, in halos found in simulations of tilted'' Einstein-de Sitter and LambdaCDM 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 similar to97% of the similar to300 clusters ( per model) we have with M > 4.2 x 10(14) h(-1) M-circle dot 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 (r) over bar = 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 Delta(c) for each virialized halo, which we compare with the virial'' density contrast Delta(v) similar or equal to 178Omega(m)(0.45) (where Omega(m) is the matter density parameter) obtained assuming a spherically symmetric and unperturbed fluctuation growth. As expected, for each mass scale, Delta(v) is within the range of values Delta(c). However, the spread in Delta(c) is wide, while the average Delta(c) is similar to25% smaller than the corresponding Delta(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 Delta(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.