2024ApJ...972L..25Z

Gamma-ray bursts (GRBs) are believed to launch relativistic jets, which generate prompt emission by internal processes, and produce long-lasting afterglows by driving external shocks into the surrounding medium. However, how the jet powers the external shock is poorly known. The unprecedented observations of the keV-MeV emission with Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor and the TeV emission with LHAASO of the brightest-of-all-time GRB 221009A offer a great opportunity to study the prompt-to-afterglow transition and the impact of jet on the early dynamics of external shock. In this Letter, we find that the cumulative light curve of keV-MeV emission could well fit the rising stage of the TeV light curve of GRB 221009A, with a time delay, ${4.45}_{-0.26}^{+0.26}$ s, of TeV emission. Moreover, both the rapid increase in the initial stage and the excess from about T_ref + 260 s to 270 s in the TeV light curve are tracking the light-curve bumps in the prompt keV-MeV emission. The close relation between the keV-MeV and TeV emission reveals the continuous energy injection into the external shock. Assuming an energy injection rate exactly following the keV-MeV flux of GRB 221009A, including the very early precursor, we build a continuous energy injection model where the jet Lorentz factor is derived from the TeV time delay, and the TeV data are well fitted, with the TeV excesses interpreted by inverse-Compton scatterings of the inner-coming prompt emission by the energetic electrons in external shock.