Did Swift measure GRB prompt emission radii?

Abstract

The Swift X-Ray Telescope often observes a rapidly decaying X-ray emission stretching to as long as $ t \sim 10^3$ seconds after a conventional prompt phase. This component is most likely due to a prompt emission viewed at large observer angles $\theta > 1/\Gamma$, where $\theta\sim 0.1$ is a typical viewing angle of the jet and$\Gamma\geq 100$ is the Lorentz factor of the flow during the prompt phase. This can be used to estimate the prompt emission radii, $r_{em} \geq 2 t c/\theta^2 \sim 6 \times 10^{15}$ cm. These radii are much larger than is assumed within a framework of a fireball model. Such large emission radii can be reconciled with a fast variability, on time scales as short as milliseconds, if the emission is beamed in the bulk outflow frame, e.g. due to a random relativistic motion of ''fundamental emitters''. This may also offer a possible explanation for X-ray flares observed during early afterglows.