The internal structure of Cold Dark Matter Haloes

Currently favoured cosmological models for structure formation of the Universe assume that a large fraction of the mass of the Universe is 'dark'. The evidence for dark matter comes from observations of its gravitational influence. Examples such as the flatness of rotation curves of spiral galaxies or the large velocities of galaxies in galaxy clusters are thought to be manifestations of its presence. Gravitational lensing can now also be used to map the dark matter distribution of the Universe. Despite the fact that the evidence for dark matter has existed for more than 75 years, it is still not clear what dark matter is made of. Particle physics provides some interesting and well-motivated candidates, but the elusive dark matter particles have not yet been detected. Therefore, the hunt for dark matter is one of the major joint efforts of cosmology and particle physics. The only way to prove the dark matter hypothesis is the direct detection of dark matter particles in a laboratory. Experiments exploit various techniques to detect dark matter particles. All of these experiments require as input the phase-space distribution of dark matter. This means they require information on the configuration-space and velocity-space distributions. These insights can only come from cosmology and the theory of structure formation in the Universe. The goal of this thesis is to predict the expected dark matter phase-space distribution near the solar system and in the dark matter halo of the Milky Way. A large part of this thesis is dedicated to a detailed analysis of the coarse-grained dark matter distribution near the Sun based on the Aquarius project, the currently largest set of Milky Way-like dark matter halo simulations. Based on these simulations we predict the local dark matter density distribution to be remarkably smooth: the density at the Sun differs from the mean over a best-fit ellipsoidal equidensity contour by less than 15% at the 99.9% confidence level. The local velocity distribution is also very smooth, but it differs systematically from a (multivariate) Gaussian distribution. This is not due to the presence of individual clumps or streams, but to broad features in the velocity modulus and energy distributions that are stable both in space and time and reflect the detailed assembly history of each halo. These features have a significant impact on the signals predicted for WIMP (weakly interacting massive particle) and axion searches. For example, WIMP recoil rates can deviate by ~10% from those expected from the best-fit multivariate Gaussian models. The axion spectra in the simulations typically peak at lower frequencies than in the case of multivariate Gaussian velocity distributions. Also in this case, the spectra show significant imprints of the formation of the halo. This implies that once direct dark matter detection has become routine, features in the detector signal will allow the study of the dark matter assembly history of the Milky Way. A new field, 'dark matter astronomy', will then emerge. The main part of this thesis focuses on the fine-grained phase-space structure of the dark matter distribution near the Sun. A new and completely general technique for calculating the fine-grained phase-space structure of dark matter throughout the Galactic halo is presented. Its goal is to understand dark matter structure on the scales relevant for direct and indirect detection experiments. The method is based on evaluating the geodesic deviation equation along the trajectories of individual dark matter simulation particles. It requires no assumptions about the symmetry or stationarity of the halo formation process. General static potentials that exhibit more complex behaviour than the separable potentials studied previously are discussed. 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 configuration-space density of the associated dark matter streams. A relevant analysis is made on the evolution of the 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 $10^5$ streams are expected near the Sun. The most novel aspect of the new approach is that general non-static systems can be studied through its implementation in cosmological N-body codes. The new scheme is embedded in a current state-of-the-art N-body code. Tests demonstrating that N-body discreteness effects can be kept under control in realistic configurations are presented. The new method also allows an analysis of caustics in the dark matter distribution and a detailed calculation of the annihilation radiation associated with them. Caustics are a generic feature of the nonlinear growth of structure in the dark matter distribution. If the dark matter were absolutely cold, its mass density would diverge at caustics, and the integrated annihilation probability would also diverge for individual particles participating in them. For realistic dark matter candidates, this behaviour is regularised by small but non-zero initial thermal velocities. A mathematical treatment of evolution from hot, warm or cold dark matter initial conditions is given. This scheme can be directly implemented in cosmological N-body codes. It allows the identification of caustics and the estimation of their annihilation radiation in fully general simulations of structure formation. The methods developed for the fine-grained phase-space and caustic analysis are applied to the growth of isolated dark matter haloes from self-similar and spherically symmetric initial conditions. A modified N-body code integrates the geodesic deviation equation in order to track the streams and caustics associated with individual simulation particles. The radial orbit instability causes the haloes to develop major-to-minor axis ratios approaching 10 to 1 in their inner regions. They grow similarly in time and have similar density profiles to the spherical similarity solution, but their detailed structure is very different. The higher dimensionality of the orbits causes their stream and caustic densities to drop much more rapidly than in the similarity solution. This results in a corresponding increase in the number of streams at each point. At 1\% of the turnaround radius (corresponding roughly to the Sun's position in the Milky Way) we find of order 10^6 streams in our simulations, as compared to 10^2 in the similarity solution. The number of caustics in the inner halo increases by a factor of several, because a typical orbit has six turning points rather than one, but caustic densities drop by a much larger factor. This reduces the caustic contribution to the annihilation radiation. For the region between 1% and 50% of the turnaround radius, this is 4% of the total in our simulated haloes, as compared to 6.5% in the similarity solution. Caustics contribute much less at smaller radii. These numbers assume a 100GeV/c^2 neutralino with present-day velocity dispersion 0.03cm/s, but reducing the dispersion by ten orders of magnitude only doubles the caustic luminosity. Therefore, caustics will be unobservable in the inner parts of haloes. Only the outermost caustic might potentially be detectable. Finally, we present results on the fine-grained phase-space structure of cold dark matter haloes growing in the concordance LCDM cosmology. We use the geodesic deviation technique to follow the local phase-space evolution of individual simulation particles, and we apply this method to three different resolutions of the Aq-A halo of the Aquarius project. We use a fixed softening length and only change the number of particles. Good convergence is achieved for all fine-grained properties of the halo: caustic passages, stream densities, number of streams and intra-stream annihilation radiation. At the virial radius we expect about 10^7 streams. We find caustic densities to be subdominant within the virial radius: at the virial radius the maximum caustic density is comparable to the mean halo density, whereas at 10% of the virial radius the caustic density is already a factor 10^6 smaller than the mean density. We attribute this to the very efficient phase-space mixing. The contribution of caustics to the annihilation radiation at the turnaround radius is about 10%, but well below 0.1% at 10% of the virial radius.