Abstract
We present here, follow-up observations of four Binary black hole BBH events performed with the High Energy Stereoscopic System (H.E.S.S.) in the Very High Energy (VHE) gamma-ray domain during the second and third LIGO/Virgo observation runs. Detailed analyses of the obtained data did not show significant VHE emission. We derive integral upper limit maps considering a generic $E^{-2}$ source spectrum in the most sensitive H.E.S.S energy interval ranging from 1 to 10 TeV. We also consider Extragalactic Background Light absorption effects and derive integral upper limits over the full accessible energy range. We finally derive upper limits of the VHE luminosity for each event and compare them with the expected VHE emission from GRBs. These comparisons allow us to assess the H.E.S.S. gravitational wave follow-up strategies. For the fourth GW observing run O4, we do not expect to fundamentally alter our observing strategy, and will continue to prioritize sky coverage like for the previous runs
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