Shear Particle Acceleration in Structured Gamma-Ray Burst Jets. I. Physical Origin of the Band Function and Application to GRBs 090926A, 131108A, and 160509A

Abstract The radiation physics of gamma-ray bursts (GRBs) remains an open question. Based on the simulation analysis and recent observations, it was proposed that GRB jets are composed of a narrow ultrarelativistic core surrounded by a wide subrelativistic cocoon. We show that emission from the synchrotron radiations and the synchrotron self-Compton (SSC) process of shear-accelerated electrons in the mixed jet-cocoon (MJC) region and internal-shock-accelerated electrons in the jet core is potentially explained the spectral characteristics of the prompt gamma rays. Assuming an exponential-decay velocity profile, the shear flow in the MJC region can accelerate electrons up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> <mml:mo>,</mml:mo> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>4</mml:mn> </mml:msup> </mml:math> for injected electrons with γ e,inject = 3 × 10 2 if its magnetic field strength ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>cn</mml:mi> </mml:msub> </mml:math> ) is 100 G and its inner-edge velocity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mi>cn</mml:mi> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> ) is 0.9 c. The cooling of these electrons is dominated by the SSC process, and the emission flux peaks at the keV band. In addition, the energy flux of synchrotron radiations of internal-shock-accelerated electrons ( γ e = 10 4 ∼ 10 5 ) peaks at around the keV−MeV band, assuming a bulk Lorentz factor of 300, a magnetic field strength of ∼10 6 G for the jet core. Adding the flux from both the jet core and the MJC region, the total spectral energy distribution illustrates similar characteristics as the broadband observations of GRBs. The bimodal and Band cut spectra observed in GRBs 090926A, 131108A, and 160509A can be well fit with our model. The derived <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>cn</mml:mi> </mml:msub> </mml:math> varies from 54 G to 450 G and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mi>cn</mml:mi> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.83</mml:mn> <mml:mo>∼</mml:mo> <mml:mn>0.91</mml:mn> </mml:math> c.