External Inverse-Compton and Proton Synchrotron Emission from the Reverse Shock as the Origin of VHE Gamma-Rays from the Hyper-Bright GRB 221009A

The detection of the hyper-bright gamma-ray burst (GRB) 221009A enables us to explore the nature of GRB emission and the origin of very-high-energy (VHE) gamma-rays. We analyze the ${\it Fermi}$-LAT data and investigate GeV-TeV emission in the framework of the external reverse shock model. We show that early $\sim1-10$ GeV emission can be explained by the external inverse-Compton mechanism via upscattering MeV gamma-rays by electrons accelerated at the reverse shock, in addition to the synchrotron self-Compton component. The predicted early optical flux could have been brighter than the naked-eye GRB 080319B. We also show that proton synchrotron emission from accelerated ultra-high-energy cosmic rays (UHECRs) is detectable, and could potentially explain $\gtrsim \rm TeV$ photons detected by LHAASO or UHECR acceleration can be constrained. Our model suggests that the detection of $\mathcal{O}(10\rm~TeV)$ photons with energy up to $\sim18$ TeV is possible for reasonable models of the extragalactic background light without invoking new physics, and predicts anti-correlations between MeV photons and TeV photons, which can be tested with the LHAASO data.