The ultimate halo mass in ΛCDM universe

In the far future of an accelerating Lambda CDM 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, a(eq) = 0.75, and 53 h(-1) Gyr into the future for a concordance model universe (Omega(m) = 0.3, Omega(Lambda) = 0.7). The radial phase-space structure of haloes - characterized at a less than or similar to a(eq) by a pair of zero-velocity surfaces that bracket a dynamically active accretion region - simplifies at a greater than or similar to 10 a(eq) when these surfaces merge to create a single zero-velocity surface, clearly defining the halo outer boundary, r(halo), and its enclosed mass, M-halo. This boundary approaches a fixed physical size encompassing a mean interior density similar to 5 times the critical density, similar to the turnaround value in a classical Einstein-de Sitter model. We relate M-halo to other scales currently used to define halo mass (M-200, M-vir, M-180b) and find that M-200 is approximately half of the total asymptotic cluster mass, while M-180b follows the evolution of the inner zero-velocity surface for a less than or similar to 2 but becomes much larger than the total bound mass for a greater than or similar to 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 r(200) but is much too shallow in the range r(200) < r < r(halo).