Search for gamma-ray line signals around the black hole at the galactic center with DAMPE observation

The adiabatic growth of a black hole (BH) may enhance the dark matter (DM) density surrounding it, causing a spike in the DM density profile. The spike around the supermassive BH at the center of the Milky Way may lead to a dramatic enhancement of the gamma-ray flux of DM annihilation from the galactic center (GC). In this work, we analyze the gamma-ray data of the innermost region (i.e., the inner 1$^\circ$) of the GC to search for potential line-like signals from the BH spike. Such line-like signals could be generated in the process of DM particles annihilating into double photons. We adopt the gamma-ray data from the Dark Matter Particle Explorer (DAMPE). Although the DAMPE has a much smaller effective area than the Fermi-LAT, the gamma-ray line search can benefit from its unprecedented high energy resolution. No significant line-like signals are found in our analysis. We derive upper limits on the cross section of the annihilation based on this non-detection. We find that despite the DAMPE's small effective area for photon detection, we can still place strong constraints on the cross section ($\left<\sigma v\right>\lesssim10^{-27}\,{\rm cm^3\,s^{-1}}$) in the spike scenario due to the very bright model-expected flux from the spike. Our results indicate that either DM does not annihilate primarily through the $\gamma\gamma$ channel in the mass range we considered or no sharp density spike is present at the GC.