On the polarization properties of magnetar giant flare pulsating tails

Abstract

Three giant flares have been detected so far from soft gamma-ray repeaters, each characterized by an initial short hard spike and a pulsating tail. The observed pulsating tails are characterized by a duration of $\sim100\,\rm{s}$, an isotropic energy of $\sim 10^{44}\,\rm{erg}$, and a pulse period of a few seconds. The pulsating tail emission likely originates from the residual energy after the intense energy release during the initial spike, which forms a trapped fireball composed of a photon-pair plasma in a closed field line region of the magnetars. Observationally the spectra of pulsating tails can be fitted by the superposition of a thermal component and a power-law component, with the thermal component dominating the emission in the early and late stages of the pulsating tail observations. In this paper, assuming that the trapped fireball is from a closed field line region in the magnetosphere, we calculate the atmosphere structure of the optically-thick trapped fireball and the polarization properties of the trapped fireball. By properly treating the photon propagation in a hot, highly magnetized, electron-positron pair plasma, we tally photons in two modes (O mode and E mode) at a certain observational angle through Monte Carlo simulations. Our results suggest that the polarization degree depends on the viewing angle with respect to the magnetic axis of the magnetar, and can be as high as $\Pi\simeq30\%$ in the $1-30\,\rm{keV}$ band, and $\Pi\simeq10\%$ in the $30-100\,\rm{keV}$ band, if the line of sight is perpendicular to the magnetic axis.