Theory of “Jitter” Radiation from Small‐Scale Random Magnetic Fields and Prompt Emission from Gamma‐Ray Burst Shocks

We demonstrate that the radiation emitted by ultrarelativistic electrons in highly nonuniform, small-scale magnetic fields is different from synchrotron radiation if the electron's transverse deflections in these fields are much smaller than the beaming angle. A quantitative analytical theory of this radiation, which we refer to as jitter radiation, is developed. It is shown that the emergent spectrum is determined by statistical properties of the magnetic field. The jitter radiation theory is then applied to internal shocks of γ-ray bursts (GRBs). The model of a magnetic field in GRBs proposed by Medvedev & Loeb in 1999 is used. The spectral power distribution of radiation produced by the power-law-distributed electrons with a low-energy cutoff is well described by a sharply broken power law: P(ω) ∝ ω1 for ω ≲ ωjm and P(ω) ∝ ω-(p-1)/2 for ω ≳ ωjm, where p is the electron power-law index and ωjm is the jitter break frequency, which is independent of the field strength but depends on the electron density in the ejecta, ωjm ∝ n1/2, as well as on the shock energetics and kinematics. The total emitted power of jitter radiation is, however, equal to that of synchrotron radiation.