Theory of "Jitter" Radiation from Small-Scale Random Magnetic Fields and Prompt Emission from Gamma-Ray Burst Shocks

Abridged.-- 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. As an example,we then use the model of a magnetic field in internal shocks of GRBs. The spectral power distribution of radiation produced by the power-law electrons is well described by a sharply broken power-law with indices 1 and -(p-1)/2 and the jitter break frequency is independent of the field strength but depends on the electron density in the ejecta. Since large-scale fields may also be present in the ejecta, we construct a two-component, jitter+synchrotron spectral model of the prompt $\gamma$-ray emission. Quite surprisingly, this model seems to be readily capable of explaining several properties of time-resolved spectra of some GRBs, such as (i) the violation of the constraint on the low-energy spectral index called the synchrotron ``line of death'', (ii) the sharp spectral break at the peak frequency, inconsistent with the broad synchrotron bump, (iii) the evidence for two spectral sub-components, and (iv) possible existence of emission features called ``GRB lines''. We believe these facts strongly support both the existence of small-scale magnetic fields and the proposed radiation mechanism from GRB shocks. As an example, we use the composite model to analyze GRB 910503 which has two spectral peaks.