Adaptive Refinement Tree: A New High-Resolution N-Body Code for Cosmological Simulations

We present a new high-resolution N-body algorithm for cosmological simulations. The algorithm employs a traditional particle-mesh technique on a cubic grid and successive multilevel relaxations on the finer meshes, introduced recursively in a fully adaptive manner in the regions where the density exceeds a predefined threshold. The mesh is generated to effectively match an arbitrary geometry of the underlying density field—a property particularly important for cosmological simulations. In a simulation the mesh structure is not created at every time step but is properly adjusted to the evolving particle distribution. The algorithm is fast and effectively parallel: the gravitational relaxation solver is approximately half as fast as the fast Fourier transform solver on the same number of mesh cells. The required CPU time scales with the number of cells, N_c, as ~O(N_c). The code allows us to improve considerably the spatial resolution of the particle-mesh code without loss in mass resolution. We present a detailed description of the methodology, implementation, and tests of the code.

We further use the code to study the structure of dark matter halos in high-resolution (~2 h^-1 kpc) simulations of standard CDM (Ω = 1, h = 0.5, σ₈ = 0.63) and ΛCDM (Ω_Λ = 1 - Ω₀ = 0.7, h = 0.7, σ₈ = 1.0) models. We find that halo density profiles in both CDM and ΛCDM models are well fitted by the analytical model presented recently by Navarro et al., which predicts a singular [ρ(r) ∝ r^-1] behavior of the halo density profiles at small radii. We therefore conclude that halos formed in the ΛCDM model have structure similar to that of CDM halos and thus cannot explain the dynamics of the central parts of dwarf spiral galaxies, as inferred from the galaxies' rotation curves.