Distribution of Gamma-ray Burst Ejecta Energy with Lorentz Factor

Jonathan Granot; Pawan Kumar

doi:10.1111/j.1745-3933.2005.00121.x

paper

Distribution of Gamma-ray Burst Ejecta Energy with Lorentz Factor

arXiv:astro-ph/0511049 · doi:10.1111/j.1745-3933.2005.00121.x

Abstract

The early X-ray afterglow for a significant number of gamma-ray bursts detected by the Swift satellite is observed to have a phase of very slow flux decline with time ( $F_{ν} \propto t^{- α}$ with $0.2 ≲ α ≲ 0.8$ ) for $1 0^{2.5} s ≲ t ≲ 1 0^{4}$ s, while the subsequent decline is the usual $1 ≲ α_{3} ≲ 1.5$ behavior, that was seen in the pre-Swift era. We show that this behavior is a natural consequence of a small spread in the Lorentz factor of the ejecta, by a factor of $\sim 2 - 4$ , where the slower ejecta gradually catch-up with the shocked external medium, thus increasing the energy of forward shock and delaying its deceleration. The end of the ``shallow'' flux decay stage marks the beginning of the Blandford-McKee self similar external shock evolution. This suggests that most of the energy in the relativistic outflow is in material with a Lorentz factor of $\sim 30 - 50$ .

arXiv comment9 pages, 1 figure, 1 table; accepted for publication in MNRAS Letters

Distribution of Gamma-ray Burst Ejecta Energy with Lorentz Factor

Abstract

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