Analytical solutions for expanding fireballs

Li Chao*, Re'em Sari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Many models of gamma-ray bursts (GRBs) as well as of soft gamma repeaters (SGRs) involve a fireball - an optically thick concentration of radiation energy with a high ratio of energy density to rest mass. We study the asymptotic behavior of an ultrarelativistic fireball consisting of electron-positron pairs and photons. We show that in the ultrarelativistic limit, after photons decouple from the pairs, the photon distribution function remains a blackbody spectrum in some appropriate Lorentz frame, allowing us to define an effective Lorentz factor and temperature for the photon gas. We also study the freezing out of electron-positron pairs and their asymptotic Lorentz factor γ . The dependence of these quantities on initial conditions can be described by simple scaling laws. We apply our results to SGR 1806-20 and find that the energy carried by electron-positron pairs is higher than calculated by former estimates, but is still an order of magnitude short of the minimum energy required to produce the observed afterglow. A viable solution of the energy budget is that the fireball is loaded by baryons or electromagnetic flux.

Original languageAmerican English
Pages (from-to)425-431
Number of pages7
JournalAstrophysical Journal
Issue number1
StatePublished - 10 Apr 2008
Externally publishedYes


  • Gamma rays: bursts
  • Hydrodynamics
  • Radiative transfer


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