The origin of very-high-energy gamma-rays from GRB 221009A: implications for reverse shock proton synchrotron emission

Recently, GRB 221009A, known as the brightest of all time (BOAT), has been observed across an astounding range of $\sim 18$ orders of magnitude in energy, spanning from radio to VHE bands. Notably, the Large High Altitude Air Shower Observatory (LHAASO) recorded over $60000$ photons with energies exceeding $0.2\rm~TeV$, including the first-ever detection of photons above $10\rm~TeV$. However, explaining the observed energy flux evolution in the VHE band alongside late-time multi-wavelength data poses a significant challenge. Our approach involves a two-component structured jet model, consisting of a narrow core dominated by magnetic energy and a wide jet component dominated by matter. We show that the combination of the forward shock electron synchrotron self-Compton emission from both jets and reverse shock proton synchrotron emission from the wide jet could account for both the energy flux and spectral evolution in the VHE band, and the early TeV lightcurve may be influenced by prompt photons which could explain the initial steep rising phase. We noticed the arrival time of the highest energy photons detected by LHAASO-KM2A coincident with the peak of the reverse shock proton synchrotron emission, especially a minor flare occurring about $\sim500-800$ seconds after the trigger, coinciding with the observed spectral hardening and arrival time of the $\sim 13\rm~TeV$ photons detected by LHAASO. These findings imply that the GRB reverse shock may serve as a potential accelerator of ultra-high-energy cosmic rays, a hypothesis that could be tested through future multimessenger observations.