2017ApJ...839...74Z

We discuss the synchrotron emission of fast cooling electrons in shocks. The fast cooling electrons behind the shocks can generate a position-dependent inhomogeneous electron distribution if they do not have enough time to mix homogeneously. This can lead to a very different synchrotron spectrum in low-frequency bands from that in the homogeneous case, due to the synchrotron absorption. In this paper, we calculate the synchrotron spectrum in the inhomogeneous case in a gamma-ray burst (GRB). Both the forward shock and the reverse shock are considered. We find that for the reverse shock dominated case, we would expect a "reverse shock bump" in the low-frequency spectrum. The spectral bump is due to the combination of synchrotron absorption in both the forward and reverse shock regions. In the low frequencies the forward shock spectrum has two unconventional segments, with spectral slopes of 1 and 11/8. The slope of 11/8 has been found by some authors, while the slope of 1 is new and due to the approximately constant electron temperature in the optically thick region. In the future, simultaneous observations in multiple bands (especially in the low-frequency bands) in the GRB early afterglow or prompt emission phases will possibly reveal these spectral characteristics and enable us to identify the reverse shock component and distinguish between the forward and reverse shock emissions. This also may be a method with which to diagnose the electron distribution status (homogeneous or inhomogeneous) after fast cooling in the relativistic shock region.