Phase-space structure of protohalos: Vlasov versus particle-mesh

The phase-space structure of primordial dark matter halos is revisited using cosmological simulations with three sine waves and cold dark matter (CDM) initial conditions. The simulations are performed with the tessellation based Vlasov solver Co1DICE and a particle-mesh (PM) N-body code. The analyses include projected density, phase-space diagrams, radial density rho(r), and pseudo-phase space density: Q(r) = rho(r)/sigma(v)(r)(3) with sigma(v) the local velocity dispersion. Particular attention is paid to force and mass resolution. Because the phase-space sheet complexity, estimated in terms of total volume and simplex (tetrahedron) count, increases very quickly, Co1DICE can follow only the early violent relaxation phase of halo formation. During the violent relaxation phase, agreement between Co1DICE and PM simulations having one particle per cell or more is excellent and halos have a power-law density profile, rho(r) proportional to r(-alpha), alpha is an element of [1.5, 1.8]. This slope, measured prior to any merger, is slightly larger than in the literature. The phase-space diagrams evidence complex but coherent patterns with clear signatures of self-similarity in the sine wave simulations, while the CDM halos are somewhat scribbly. After additional mass resolution tests, the PM simulations are used to follow the next stages of evolution. The power law progressively breaks down with a convergence of the density profile to the well-known Navarro-Frenk-White universal attractor, irrespective of initial conditions, that is even in the three-sine-wave simulations. This demonstrates again that mergers do not represent a necessary condition for convergence to the dynamical attractor. Not surprisingly, the measured pseudo phase-space density is a power law Q(r) proportional to r(-alpha Q), with a Q close to the prediction of secondary spherical infall model, alpha(Q) similar or equal to 1.875. However this property is also verified during the early relaxation phase, which is non-trivial.

Automated summary

The structure of primordial dark matter halos was reexamined using cosmological simulations, revealing different density profiles at different stages and showcasing complex yet coherent patterns.