Statistical interpretation of the spatial distribution of current 130 GeV gamma-ray line signal within the dark matter annihilation scenario

Recently, several groups identified a tentative $\gamma$-ray line signal with energy $\sim 130$ GeV in the central Galaxy from the Fermi-LAT data. %The morphology study shows that the signal is consistent with dark matter %annihilation, but with an offset $\sim 220$ pc ($1.5^{\circ}$) of the %center from the Galactic center Sgr A$^{\star}$, Such a $\gamma-$ray line can be interpreted as the signal of dark matter annihilation. However, the offset $\sim 220$ pc ($1.5^{\circ}$) of the center of the most prominent signal region from the Galactic center Sgr A$^{\star}$ has been thought to challenge the dark matter annihilation interpretation. Considering the fact that such a 130 GeV $\gamma$-ray line signal consists of only $\sim14$ photons, we suggest that the "imperfect" consistency of these photons with the expected dark matter distribution is due to the limited statistics. The offset will be smaller as more signal photons have been collected in the near future. Our Monte Carlo simulation supports the above speculation.