Shear Particle Acceleration in Structured Gamma-Ray Burst Jets: II. Viewing Angle Effect on the Prompt Emission and Application to GRB 170817A

Abstract: Multi-messenger observations suggest that the gamma-ray burst on Aug. 17, 2017 (GRB 170817A) resulted from off-axial observations of its structured jet, which consists of a narrow ultra-relativistic jet core surrounded by a wide mild-relativistic cocoon. In a serious paper, we explore the emission of shear-accelerated electrons in the mixed jet-cocoon (MJC) region in a series of papers. This paper focuses on the viewing angle effect for a structured jet by considering the emission from the shear-accelerated electrons. It is found that the observed synchrotron emission peaks at the Infrared band and the synchrotron self-Compton (SSC) emission peaks at the band of hundreds of keV. They are not sensitive to the viewing angle. In the off-axis observations scenario, the prompt emission spectrum is dominated by the emission of the shear-accelerated electrons. The prompt gamma-ray spectrum of GRB 170817A can be well explained with our model by setting the velocity of the inner edge of the cocoon region as 0.9c, the magnetic field strength as 21 G, the injected initial electron Lorentz factor as $10^3$, and the viewing angle as 0.44 rad. We argue that the joint observations in the Infrared/optical and X-ray bands are critical to verify our model.