The graininess of dark matter haloes

We use the recently completed one billion particle Via Lactea II Λ cold dark matter simulation to investigate local properties like density, mean velocity, velocity dispersion, anisotropy, orientation and shape of the velocity dispersion ellipsoid, as well as the structure in velocity space of dark matter haloes. We show that at the same radial distance from the halo centre, these properties can deviate by orders of magnitude from the canonical, spherically averaged values, a variation that can only be partly explained by triaxiality and the presence of subhaloes. The mass density appears smooth in the central relaxed regions but spans four orders of magnitude in the outskirts, both because of the presence of subhaloes as well as of underdense regions and holes in the matter distribution. In the inner regions, the local velocity dispersion ellipsoid is aligned with the shape ellipsoid of the halo. This is not true in the outer parts where the orientation becomes more isotropic. The clumpy structure in local velocity space of the outer halo cannot be well described by a smooth multivariate normal distribution. Via Lactea II also shows the presence of cold streams made visible by their high 6D phase space density. Generally, the structure of dark matter haloes shows a high degree of graininess in phase space that cannot be described by a smooth distribution function.     

The distribution function of dark matter in massive haloes

We study the distribution function (DF) of dark matter particles in haloes of mass range  10¹⁴–10¹⁵ M_⊙  . In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard Λ cold dark matter (ΛCDM) model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L , a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form     . This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (β₀ and  β_∞  ) and the scale of transition between them ( L ₀). The energy part   f _E ( E )  is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase-space density   Q =ρ( r )/σ³( r )  .     

The fine-grained phase-space structure of cold dark matter haloes

We present a new and completely general technique for calculating the fine-grained phase-space structure of dark matter (DM) throughout the Galactic halo. Our goal is to understand this structure on the scales relevant for direct and indirect detection experiments. Our method is based on evaluating the geodesic deviation equation along the trajectories of individual DM particles. It requires no assumptions about the symmetry or stationarity of the halo formation process. In this paper we study general static potentials which exhibit more complex behaviour than the separable potentials studied previously. For ellipsoidal logarithmic potentials with a core, phase mixing is sensitive to the resonance structure, as indicated by the number of independent orbital frequencies. Regions of chaotic mixing can be identified by the very rapid decrease in the real-space density of the associated DM streams. We also study the evolution of stream-density in ellipsoidal NFW haloes with radially varying isopotential shape, showing that if such a model is applied to the Galactic halo, at least 10⁵ streams are expected near the Sun. The most novel aspect of our approach is that general non-static systems can be studied through implementation in a cosmological N -body code. Such an implementation allows a robust and accurate evaluation of the enhancements in annihilation radiation due to fine-scale structure such as caustics. We embed the scheme in the current state-of-the-art code gadget -3 and present tests which demonstrate that N -body discreteness effects can be kept under control in realistic configurations.