Afterglow light curves from misaligned structured jets

Abstract

GRB 170817A/GW 170817 is the first gamma-ray burst (GRB) clearly viewed far from the GRB jet's symmetry axis. Its afterglow was densely monitored over a wide range of frequencies and times. It has been modelled extensively, primarily numerically, and although this endeavour was very fruitful, many of the underlying model parameters remain undetermined. We provide analytic modelling of GRB afterglows observed off-axis, considering jets with a narrow core (of half-opening angle θ_c) and power-law wings in energy per unit solid angle (ϵ = ϵ_cΘ^(−a)) where Θ = [1 + (θ/θ_c)²]^(1/2)) and initial specific kinetic energy (Γ₀ − 1 = [Γ_(c, 0) − 1]Θ^(−b)), as well as briefly discuss Gaussian jets. Our study reveals qualitatively different types of light curves that can be viewed in future off-axis GRBs, with either single or double peaks, depending on the jet structure and the viewing angle. Considering the light-curve shape rather than the absolute normalizations of times and/or fluxes, removes the dependence of the light curve on many of the highly degenerate burst parameters. This study can be easily used to determine the underlying jet structure, significantly reduce the effective parameter space for numerical fitting attempts and provide physical insights. As an illustration, we show that for GRB 170817A, there is a strong correlation between the allowed values of Γ_(c, 0) and b, leading to a narrow strip of allowed solutions in the Γ_(c, 0)–b plane above some minimal values Γ_(c, 0) ≳ 40, b ≳ 1.2. Furthermore, the Lorentz factor of the material dominating the early light curve can be constrained by three independent techniques to be Γ₀ (θ_(min, 0)) ≈ 5–7.

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