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 Way ’ s 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 .
Adopting the Ring Method to define the signal and background regions in an ON-OFF analysis approach , 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 b \bar { 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 _ { DM } \sim 200 GeV .