Fireballs Loading and the Blast Wave Model of Gamma Ray Bursts

C. D. Dermer; J. Chiang; M. Boettcher

doi:10.1086/306871

paper

Fireballs Loading and the Blast Wave Model of Gamma Ray Bursts

arXiv:astro-ph/9804174 · doi:10.1086/306871

Abstract

A simple function for the spectral power $P (ε, t) \equiv ν L (ν)$ is proposed to model, with 9 parameters, the spectral and temporal evolution of the observed nonthermal synchrotron power flux from GRBs in the blast wave model. Here $ε = h ν /$ m $_{e}$ c $^{2}$ is the observed dimensionless photon energy and $t$ is the observing time. Assumptions and an issue of lack of self-consistency are spelled out. The spectra are found to be most sensitive to the baryon loading, expressed in terms of the initial bulk Lorentz factor $Γ_{0}$ , and an equipartition term $q$ which is assumed to be constant in time and independent of $Γ_{0}$ . Expressions are given for the peak spectral power $P_{p} (t) = P (ε_{p}, t)$ at the photon energy $ε = ε_{p} (t)$ of the spectral power peak. A general rule is that the total fireball particle kinetic energy $E_{0} \sim Π_{0} t_{d}$ , where $t_{d} \propto Γ_{0}^{- 8/3}$ is the deceleration time scale and $Π_{0} \equiv P (ε_{p}, t_{d}) \propto Γ_{0}^{8/3}$ is the maximum measured bolometric power output in radiation, during which it is carried primarily by photons with energy $E_{0} = ε_{p} (t_{d}) \propto q Γ_{0}^{4}$ .

26 pages, including 4 figures, uses epsf.sty, rotate.sty; submitted to ApJ; revised version with extended introduction, redrawn figures, and corrections

Fireballs Loading and the Blast Wave Model of Gamma Ray Bursts

Abstract

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