Sensitivity of CTA to dark matter signals from the Galactic Center

(abridged) The Galactic Center is one of the most promising targets for indirect detection of dark matter with gamma rays. We investigate the sensitivity of the upcoming Cherenkov Telescope Array (CTA) to dark matter annihilation and decay in the Galactic Center. As the inner density profile of the Milky Ways dark matter halo is uncertain, we study the impact of the slope of the Galactic density profile, inwards of the Sun, on the prospects for detecting a dark matter signal with CTA. We find that the sensitivity achieved by CTA to annihilation signals is strongly dependent on the inner profile slope, whereas the dependence is more mild in the case of dark matter decay. Surprisingly, we find that the optimal choice of signal and background regions is virtually independent of the assumed density profile. For the fiducial case of a Navarro-Frenk-White profile, we find that CTA will be able to probe annihilation cross sections well below the canonical thermal relic value for dark matter masses from a few tens of GeV up to $sim 5$ TeV for annihilation to $tau^{+}tau^{-}$, and will achieve only a slightly weaker sensitivity for annihilation to $bbar{b}$ or $mu^{+}mu^{-}$. CTA will improve significantly on current sensitivity to annihilation signals for dark matter masses above $sim 100$ GeV, covering parameter space that is complementary to that probed by searches with the Fermi Large Area Telescope. The interpretation of apparent excesses in the measured cosmic-ray electron and positron spectra as signals of dark matter decay will also be testable with CTA observations of the Galactic Center. We demonstrate that both for annihilation and for decay, including spectral information for hard channels (such as $mu^{+}mu^{-}$ and $tau^{+}tau^{-}$) leads to enhanced sensitivity for dark matter masses above $m_{rm DM}sim 200$ GeV.