Multi-TeV dark matter density in the inner Milky Way halo: spectral and dynamical constraints

We develop a comprehensive study of the gamma-ray flux observed by H.E.S.S. in 5 regions of the Galactic Center (GC). Motivated by previous works on a possible Dark Matter (DM) explanation for the TeV cut-off observed in the innermost $\sim 16$ pc of the Galaxy, we aim to constrain the DM density profile up to a radius $\sim 450$ pc from the GC. In this region, cosmological simulations and Galactic dynamics studies fail to produce a strong prediction of the DM profile. With our proof-of-concept analysis, we set upper limits on the density distribution of thermal multi-TeV WIMPs, compatible with the observed gamma-ray flux. The results agree with the hypothesis of a DM density enhancement in the GC with respect to the benchmark NFW profile ($\gamma=1$) and allow us to exclude profiles with a slope $\gamma \gtrsim 1.3$. We also investigate the possibility that such an enhancement could be related to the existence of a DM spike associated with the supermassive black hole Sgr A*. We find out that the existence of an adiabatic DM spike smoothed by the scattering off of WIMPs by the bulge stars may be consistent with the observed gamma-ray flux if the spike forms on an underlying generalized NFW profile with $\gamma \lesssim 0.8$, corresponding to a spike slope $\gamma_{sp-star}= 1.5$ and radius $R_\text{sp-stars} \sim 25$-$30$ pc. Instead, in the extreme case of the instantaneous growth of the black hole, the profile could have up to $\gamma \sim 1.2$, a corresponding $\gamma_{sp-inst}=1.4$ and $R_\text{sp-inst}\sim 15$-$25$ pc. Moreover, the results of our analysis of the total DM mass enclosed within the S2 orbit are less stringent than the spectral analysis. Our work aims to guide future studies of the GC region, with both current and next-generation telescopes, like the next Cherenkov Telescope Array, that will be able to scan the GC with improved flux sensitivity and angular resolution.