GRB 221009A is the brightest gamma-ray burst (GRB) ever detected. To probe the very-high-energy (VHE; >100 GeV) emission, the High Energy Stereoscopic System (H.E.S.S.) began observations 53 hr after the triggering event, when the brightness of the moonlight no longer precluded observations. We derive differential and integral upper limits using H.E.S.S. data from the third, fourth, and ninth nights after the initial GRB detection, after applying atmospheric corrections. The combined observations yield an integral energy flux upper limit of above E thr = 650 GeV. The constraints derived from the H.E.S.S. observations complement the available multiwavelength data. The radio to X-ray data are consistent with synchrotron emission from a single electron population, with the peak in the spectral energy distribution occurring above the X-ray band. Compared to the VHE-bright GRB 190829A, the upper limits for GRB 221009A imply a smaller gamma-ray to X-ray flux ratio in the afterglow. Even in the absence of a detection, the H.E.S.S. upper limits thus contribute to the multiwavelength picture of GRB 221009A, effectively ruling out an IC-dominated scenario.
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