Physics

Lorentz factor

Energy (signal processing)

Mathematics

Lorentz transformation

Mechanics

Parameter space

Jet (fluid)

Optics

Liquid-crystal display

Light curve

Kinetic energy

Composite material

Solid angle

Gamma-ray burst

Materials science

Range (aeronautics)

Geometry

Viewing angle

Afterglow

Astrophysics

Quantum mechanics

Classical mechanics

Detector

Monthly Notices of the Royal Astronomical Society

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 θc) and power-law wings in energy per unit solid angle (ϵ = ϵcΘ−a where Θ = [1 + (θ/θc)2]1/2) and initial specific kinetic energy (Γ0 − 1 = [Γc, 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 Γc, 0 and b, leading to a narrow strip of allowed solutions in the Γc, 0–b plane above some minimal values Γc, 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(θmin, 0) ≈ 5–7.

Afterglow light curves from misaligned structured jets