Optimal angular window for observing Dark Matter annihilation from the Galactic Center region: the case of gamma-ray lines

Although the emission of radiation from dark matter annihilation is expected to be maximized at the Galactic Center, geometric factors and the presence of point-like and diffuse backgrounds make the choice of the angular window size to optimize the chance of a signal detection a non-trivial problem. Contrarily to what is often assumed, we find that the best strategy is to focus on a window size around the Galactic Center of ~ 1 deg to >~ 30 deg, where the optimal size depends on the angular distribution of the signal and the backgrounds. Although our conclusions are general, we illustrate this point in the particular case of annihilation into two monochromatic photons in the phenomenologically most interesting range of energy 45 GeV < E < 80 GeV, which is of great interest for the GLAST satellite. We find for example that Dark Matter models with sufficiently strong line annihilation signals, like the Inert Doublet Model, may be detectable without or with very moderate boost factors.