Present and Future constraints on Secluded Dark Matter in the Galactic Halo with TeV Gamma-ray Observatories

The dark matter relic density may be governed by the presence of new mediators that connect the dark matter field with the Standard Model particles. When the dark matter particle mass is larger than the mediator's, the pair production of mediators is kinematically open. This setup is known in the literature as secluded dark matter. Motivated by the appearance of secluded dark matter in several model building endeavours, we investigate the sensitivity of TeV gamma-ray instruments in the Southern Hemisphere namely, H.E.S.S., CTA, and SWGO to secluded dark matter annihilating in the Galactic Halo. We exploit the complementarity aspects of these detectors to find restrictive bounds on the annihilation cross-section for different annihilation channels. In particular, for a dark matter particle mass of $2$~TeV, H.E.S.S. is able to constraint $\langle \sigma v \rangle \geq 4 \times 10^{-26}\,\, {\rm cm}^3\, {\rm s}^{-1}$ at 95\% confidence level for the $4q$ and $4\tau$ channel, while CTA will be sensitive to $\langle \sigma v \rangle \geq 7 \times 10^{-27}\,\, {\rm cm}^3\, {\rm s}^{-1}$ and SWGO $\langle \sigma v \rangle \geq 6 \times 10^{-27}\,\, {\rm cm}^3\, {\rm s}^{-1}$ for the $4\tau$ channel, both well below the thermal relic cross-section. In fact, the combination of CTA and SWGO will be able to probe cross-sections below the thermal relic value for dark matter particles in the whole mass range between 100 GeV and 100 TeV in the $4q$ and $4\tau$ channels, and between 100 GeV and $\sim$40 TeV in the $4b$ channel.