Low-frequency spectra of gamma-ray bursts

Particles with energies below the mean energy $E_0$ in relativistic shocked plasmas should assume an equilibrium energy distribution. This leads to a synchrotron spectrum $F_ u propto u^{1/3}$ up to approximately the critical frequency $ u_0$ of an electron with the energy $E_0$. Application to GRBs implies that a burst with $10^{-5}$ erg/cm$^2$s of soft gamma-rays and $h u_0 = 300$ KeV should be about 18th magnitude in visible light and a few $mu$Jy at 1 GHz (less if self-absorbed).Comment: 10pp, Tex, WU-JIK-93-