Spectral Shapes of Pair Annihilation Line Emission in Magnetar Giant Flares

We investigate the gamma-ray spectrum in the MeV range arising from electron-positron pair annihilation in fireballs associated with magnetar giant flares (MGFs), motivated by the recent observation of a MeV gamma-ray line feature in a bright gamma-ray burst, GRB~221009A. We develop an analytic model of line emission, demonstrating that relativistic beaming results in a broadened, power-law spectral feature with photon index -1. We then perform Monte Carlo radiative transfer simulations incorporating electron-positron pair production, annihilation, and Compton scattering. The dependence of the emergent spectrum on the baryon loading is also examined, showing that a baryon-poor fireball is more favorable for the detection of MeV gamma rays. We further assess the detectability of the line component. The simulation results indicate that a power-law MeV component from the initial spike of a Galactic MGFs could be observed with current instruments, such as Fermi/GBM, and will be well within the reach of upcoming MeV gamma-ray satellites, which are expected to detect O(100) photons from such events.