The theory of spectral evolution of the GRB prompt emission

Abstract

We develop the theory of jitter radiation from GRB shocks containing small-scale magnetic fields and propagating at an angle with respect to the line of sight. We demonstrate that the spectra vary considerably: the low-energy photon index, $α$, ranges from 0 to -1 as the apparent viewing angle goes from 0 to $π/2$. Thus, we interpret the hard-to-soft evolution and the correlation of $α$ with the photon flux observed in GRBs as a combined effect of temporal variation of the viewing angle and relativistic aberration of an individual thin, instantaneously illuminated shell. The model predicts that about a quarter of time-resolved spectra should have hard spectra, violating the synchrotron $α=-2/3$ line of death. The model also naturally explains why the peak of the distribution of $α$ is at $α\approx-1$. The presence of a low-energy break in the jitter spectrum at oblique angles also explains the appearance of a soft X-ray component in some GRBs and a relatively small number of them. We emphasize that our theory is based solely on the first principles and contains no {\it ad hoc} (phenomenological) assumptions.