The spatial distribution of dark matter annihilation originating from a gamma-ray line signal

The GeV–TeV γ-ray line signal is the smoking gun signature of dark matter annihilation or decay. The detection of such a signal is one of the main targets of some space-based telescopes, including Fermi-LAT and the upcoming missions CALET, DAMPE and Gamma-400. An important feature of γ-ray line photons that originate from dark-matter-annihilation is that they are concentrated at the center of the Galaxy. So far, no reliable γ-ray line has been detected by Fermi-LAT, and the upper limits on the cross section of annihilation into γ-rays have been reported. We use these upper limits to estimate the "maximal" number of γ-ray line photons detectable for Fermi-LAT, DAMPE and Gamma-400, and then investigate the spatial distribution of these photons. We show that the center of the distribution will usually be offset from the Galactic center (Sgr A*) due to the limited statistics. Such a result is almost independent of models of the dark matter distribution, and will render the reconstruction of the dark matter distribution with the γ-ray line signal very challenging for foreseeable space-based detectors.