Exact versus approximate beaming formulas in Gamma-Ray Burst afterglows

Abstract

We present the exact analytic expressions to compute, assuming the emitted Gamma-Ray Burst (GRB) radiation is not spherically symmetric but is confined into a narrow jet, the value of the detector arrival time at which we start to "see" the sides of the jet, both in the fully radiative and adiabatic regimes. We obtain this result using our exact analytic expressions for the EQuiTemporal Surfaces (EQTSs) in GRB afterglows. We re-examine the validity of three different approximate formulas currently adopted for the adiabatic regime in the GRB literature. We also present an empirical fit of the numerical solutions of the exact equations, compared and contrasted with the three above approximate formulas. The extent of the differences is such as to require a reassessment on the existence and entity of beaming in the cases considered in the current literature, as well as on its consequences on the GRB energetics.

4 pages, 4 figures, to appear on ApJ Lett

References in corpus (13)

• The Physics of Gamma-Ray Bursts
• Beaming in Gamma-Ray Bursts: Evidence for a Standard Energy Reservoir
• Jets in GRBs
• The collimation--corrected GRB energies correlate with the peak energy of their $\nu F_{\nu }$ spectrum
• The afterglow of GRB050709 and the nature of the short-hard gamma-ray bursts
• Dynamical Evolution, Light-Curves and Spectra of Spherical and Collimated Gamma-Ray Burst Remnants
• The Energetics and Environment of the Short-GRB Afterglows 050709 and 050724
• On the exact analytic expressions for the equitemporal surfaces in Gamma-Ray Burst afterglows
• Exact versus approximate solutions in Gamma-Ray Burst afterglows
• On the instantaneous spectrum of Gamma-Ray Bursts
• Exact versus approximate equitemporal surfaces in Gamma-Ray Burst afterglows
• Theoretical interpretation of luminosity and spectral properties of GRB 031203
• GRB 980425, SN1998bw and the EMBH model

Cited by in corpus (5)

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• On the ultra-relativistic Prompt Emission (UPE), the Hard and Soft X-ray Flares, and the extended thermal emission (ETE) in GRB 151027A
• Fundamental physics from black holes, neutron stars and gamma-ray bursts
• The luminosity evolution over the EQuiTemporal Surfaces in the prompt emission of Gamma-Ray Bursts