The ultimate halo mass in a ΛCDM universe

Abstract In the far future of an accelerating ΛCDM cosmology, the cosmic web of large-scale structure consists of a set of increasingly isolated haloes in dynamical equilibrium. We examine the approach of collisionless dark matter to hydrostatic equilibrium using a large N-body simulation evolved to scale factor a= 100, well beyond the vacuum—matter equality epoch, aeq= 0.75, and 53 h−1 Gyr into the future for a concordance model universe (Ωm= 0.3, ΩΛ= 0.7). The radial phase-space structure of haloes — characterized at a≲aeq by a pair of zero-velocity surfaces that bracket a dynamically active accretion region — simplifies at a≳ 10 aeq when these surfaces merge to create a single zero-velocity surface, clearly defining the halo outer boundary, rhalo, and its enclosed mass, Mhalo. This boundary approaches a fixed physical size encompassing a mean interior density ∼5 times the critical density, similar to the turnaround value in a classical Einstein—de Sitter model. We relate Mhalo to other scales currently used to define halo mass (M200, Mvir, M180b) and find that M200 is approximately half of the total asymptotic cluster mass, while M180b follows the evolution of the inner zero-velocity surface for a≲ 2 but becomes much larger than the total bound mass for a≳ 3. The radial density profile of all bound halo material is well fit by a truncated Hernquist profile. An NFW profile provides a somewhat better fit interior to r200 but is much too shallow in the range r200 r rhalo.