Radiative Acceleration and X-ray Spectrum of Outflowing Pure Electron-Positron Pair Fireball in Magnetar Bursts

An X-ray short burst associated with a Galactic fast radio burst was observed in 2020, distinguished by its X-ray cut-off energy significantly exceeding that of other X-ray short bursts. X-ray photons of these short bursts are believed to originate from fireballs within the magnetospheres of magnetars. If a fireball forms near a magnetic pole, it expands along the magnetic field lines, subsequently emitting photons and generating plasma outflows that may account for the observed radio bursts. We numerically study the radiative acceleration and X-ray spectrum of such outflowing fireballs consisting of pure electron-positron pairs and radiation, employing spherically symmetric relativistic radiation hydrodynamics calculations with the effects of strong magnetic fields. Using Monte-Carlo scheme in the radiation calculation, we consistently incorporate both the acceleration of the fluid by radiation and the scattering of radiation by the fluid, both of which are enhanced by the cyclotron resonant scattering. Our calculation reveals that cyclotron resonant scattering accelerates the plasma outflow significantly and broadens the X-ray spectrum. The plasma outflow is accelerated up to ultra-relativistic velocities, with Lorentz factors exceeding 100. The calculated X-ray spectrum broadened due to the scattering is similar to the observed X-ray spectrum in the Galactic fast radio burst.