Résumé
Microquasars have emerged as promising candidates to explain the cosmic-ray flux at petaelectronvolt energies. LHAASO observations revealed V4641~Sgr as the most extreme example so far. Using $\approx$100~h of H.E.S.S. data, we performed a spectro-morphological study of the gamma-ray emission around V4641~Sgr. We employed HI and dedicated CO observations of the region to infer the target material for cosmic-ray interactions. We detected multi-TeV emission around V4641~Sgr with a high significance. The emission region is elongated. We found a power-law spectrum with an index $\approx$1.8, and together with results from other gamma-ray instruments, this reveals a spectral energy distribution that peaks at energies of $\approx$100~TeV for the first time. We found indications (3$σ$) of a two-component morphology, with indistinguishable spectral properties. The position of V4641~Sgr is inconsistent with the best-fit position of the single-component model and with the dip between the two components. We found no significant evidence of an energy-dependent morphology. No dense gas was found at any distance towards V4641~Sgr. The peak of the SED at $\approx$100~TeV identifies V4641~Sgr as a candidate cosmic-ray accelerator beyond the so-called knee. The absence of dense target gas places stringent energetic constraints on hadronic interpretations, however. The H.E.S.S. measurement requires an unusually hard ($\approx 1.5$) spectral index for the protons. A leptonic scenario faces fewer obstacles if the particle transport is fast enough to avoid losses and to reproduce the observed energy-independent morphology. The absence of bright \xray emission across the gamma-ray emission region requires a magnetic field strength $\lesssim3$~$μ$G, however. Our findings favour a leptonic origin of the gamma-ray emission. This conclusion does not exclude hadron acceleration in the V4641~Sgr system.