Robust constraints on the physics of the MeV emission line in GRB 221009A from optical depth arguments

The brightest-of-all-time gamma-ray burst (GRB), GRB 221009A, is the first GRB observed to have emission line (up to 37 MeV) in its prompt emission spectra. It is naturally explained as e-/e+ annihilation line that was Doppler boosted in the relativistic jet of the GRB. In this work, we repeatedly apply the simple optical depth argument to different physical processes necessary to produce an observable e-/e+ annihilation line. This approach results in robust constraints on the physics of the line: We conclude that in GRB 221009A, the e-/e+ pairs were produced at a radius greater than 4.3 x 1015 cm from the central engine, and annihilated in a region between 1.4 x 1016 and 4.3 x 1016 cm. From these constraints, we established a self-consistent picture of e-/e+ production, cooling, and annihilation. We also derived a criterion for pair production in the GRB prompt emission: Eiso less than or similar to 3.3 x 1053Epeak,100(1 + z)R( )(prod,16 )(2)erg. Using this criterion, we find tens of candidate GRBs that could have produced e-/e+ in prompt emissions to annihilate. GRB 221009A is with the highest likelihood according to this criterion. We also predict the presence of a thermal radiation, with a time-evolving blackbody temperature, sweeping through soft X-ray during the prompt emission phase