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 ultrarelativisticelectrons in highly nonuniform, small-scale magnetic fields is different fromsynchrotron radiation if the electron's transverse deflections in these fieldsare much smaller than the beaming angle. A quantitative analytical theory ofthis radiation, which we refer to as jitter radiation, is developed. It isshown that the emergent spectrum is determined by statistical properties of themagnetic field. As an example,we then use the model of a magnetic field ininternal shocks of GRBs. The spectral power distribution of radiation producedby the power-law electrons is well described by a sharply broken power-law withindices 1 and -(p-1)/2 and the jitter break frequency is independent of thefield strength but depends on the electron density in the ejecta. Sincelarge-scale fields may also be present in the ejecta, we construct atwo-component, jitter+synchrotron spectral model of the prompt $\gamma$-rayemission. Quite surprisingly, this model seems to be readily capable ofexplaining several properties of time-resolved spectra of some GRBs, such as(i) the violation of the constraint on the low-energy spectral index called thesynchrotron ``line of death'', (ii) the sharp spectral break at the peakfrequency, inconsistent with the broad synchrotron bump, (iii) the evidence fortwo spectral sub-components, and (iv) possible existence of emission featurescalled ``GRB lines''. We believe these facts strongly support both theexistence of small-scale magnetic fields and the proposed radiation mechanismfrom GRB shocks. As an example, we use the composite model to analyze GRB910503 which has two spectral peaks.