A theory of photospheric emission from relativistic, collimated outflows

C. Lundman, A. Pe'er, F. Ryde

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124 Scopus citations


Relativistic outflows in the form of jets are common in many astrophysical objects. By their very nature, jets have angle-dependent velocity profiles, Γ=Γ(r, Θ, φ), where Γ is the outflow Lorentz factor. In this work we consider photospheric emission from non-dissipative jets with various Lorentz factor profiles, of the approximate form Γ ≈ Γ0/[(Θ/Θj)p + 1], where Θj is the characteristic jet opening angle. In collimated jets, the observed spectrum depends on the viewing angle, Θv. We show that for narrow jets (ΘjΓ0 < few), the obtained low-energy photon index is α ≈-1 (dN/dE / Eα), independent of viewing angle, and weakly dependent on the Lorentz factor gradient (p). A similar result is obtained for wider jets observed at Θv ≈ Θj. This result is surprisingly similar to the average low-energy photon index seen in gamma-ray bursts. For wide jets (ΘjΓ0 > few) observed at Θv > Θj, a multicolour blackbody spectrum is obtained. We discuss the consequences of this theory on our understanding of the prompt emission in gamma-ray bursts.

Original languageEnglish
Pages (from-to)2430-2442
Number of pages13
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
StatePublished - Jan 2013
Externally publishedYes


  • Gamma-ray burst: general.
  • Plasmas
  • Radiation mechanisms: thermal
  • Radiative transfer
  • Scattering


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