Prospects for Galactic dark matter searches with the Cherenkov Telescope Array (CTA)

In the current understanding of structure formation in the Universe, the Milky Way is embedded in a clumpy halo of dark matter (DM). Regions of high DM density are expected to emit enhanced γ-radiation from the DM relic annihilation. This γ-radiation can possibly be detected by γ-ray observatories on Earth, like the forthcoming Cherenkov Telescope Array (CTA). This dissertation presents a semi-analytical density modeling of the subclustered Milky Way DM halo, and the γ-ray intensity at Earth from DM annihilation in Galactic subclumps is calculated for various substructure models. It is shown that the modeling approach is able to reproduce the γ-ray intensities obtained from extensive dynamical DM simulations, and that it is consistent with the DM properties derived from optical observations of dwarf spheroidal galaxies. A systematic confidence margin of plausible γ-ray intensities from Galactic DM annihilation is estimated, encompassing a variety of previous findings. The average distances, masses, and extended emission profiles of the γ-ray-brightest DM clumps are calculated. The DM substructure models are then used to draw reliable predictions for detecting Galactic DM density clumps with CTA, using the most recent benchmark calculations for the performance of the instrument. A Likelihood-based calculation with CTA analysis software is applied to find the instrumental sensitivity to detect the γ-ray-brightest DM clump in the projected CTA extragalactic survey. An alternative Likelihood-based analysis method is developed, to detect DM substructures as anisotropies in the angular power spectrum of the extragalactic survey data. The analyses predict that the CTA extragalactic survey will be able to probe annihilation cross sections of $⟨$σv$⟩$$\gtrsim$ 1 × 10${}^{-24}$ cm${}^3$ s${}^{-1}$ at the 95% confidence level for a DM particle mass of mχ ~ 500 GeV from DM annihilation in substructures. This sensitivity is compatible with long-term observations of single dwarf spheroidal galaxies with CTA. Independent of a particular source model, it is found that the CTA extragalactic survey will be able to detect anisotropies in the diffuse γ-ray background above 100 GeV at a relative amplitude of C${}_P^F$$\gtrsim$ 10${}^{-2}$.