### Abstract

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 × 10^{14} 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.

Original language | English (US) |
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Pages (from-to) | 35-49 |

Number of pages | 15 |

Journal | Astrophysical Journal |

Volume | 588 |

Issue number | 1 I |

DOIs | |

State | Published - May 1 2003 |

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### Keywords

- Cosmology: theory
- Dark matter
- Galaxies: clusters: general
- Large-scale structure of universe
- Methods: N-body simulations

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*588*(1 I), 35-49. https://doi.org/10.1086/373944