We compute the sensitivity to dark matter annihilations for the forthcoming large Cherenkov Telescope Array (CTA) in several primary channels and over a range of dark matter masses from 30 GeV up to 80 TeV. For all channels, we include inverse Compton scattering of e$^pm$ by dark matter annihilations on the ambient photon background, which yields substantial contributions to the overall gamma-ray flux. We improve the analysis over previous work by: i) implementing a spectral and morphological analysis of the gamma-ray emission; ii) taking into account the most up-to-date cosmic ray background obtained from a full CTA Monte Carlo simulation and a description of the diffuse astrophysical emission; and iii) including the systematic uncertainties in the rich observational CTA datasets. We find that our spectral and morphological analysis improves the CTA sensitivity by roughly a factor 2. For the hadronic channels, CTA will be able to probe thermal dark matter candidates over a broad range of masses if the systematic uncertainties in the datasets will be controlled better than the percent level. For the leptonic modes, the CTA sensitivity will be well below the thermal value of the annihilation cross-section. In this case, even with larger systematics, thermal dark matter candidates up to masses of a few TeV will be easily studied.
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