Dark matter substructure modelling and sensitivity of the Cherenkov Telescope Array to Galactic dark halos

Hierarchical structure formation leads to a clumpy distribution of dark matter in the Milky Way. These clumps are possible targets to search for dark matter annihilation with present and future $\gamma$-ray instruments. Many uncertainties exist on the clump distribution, leading to disputed conclusions about the expected number of detectable clumps and the ensuing limits that can be obtained from non-detection. In this paper, we use the $\tt{CLUMPY}$ code to simulate thousands of skymaps for several clump distributions. This allows us to statistically assess the typical properties (mass, distance, angular size, luminosity) of the detectable clumps. Varying parameters of the clump distributions allows us to identify the key quantities to which the number of detectable clumps is the most sensitive. Focusing our analysis on two extreme clump configurations, yet consistent with results from numerical simulations, we revisit and compare various calculations made for the $\textit{Fermi}$-LAT instrument, in terms of number of dark clumps expected and the angular power spectrum for the Galactic signal. We then focus on the prospects of detecting dark clumps with the future CTA instrument, for which we make a detailed sensitivity analysis using open-source CTA software. Based on a realistic scenario for the foreseen CTA extragalactic survey, and accounting for a post-trial sensitivity in the survey, we show that we obtain competitive and complementary limits to those based on long observation of a single bright dwarf spheroidal galaxy.