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 $F_{\nu }\propto {\nu }^{1\mathrm{/}3}$ up to approximately the critical frequency ${\nu }_0$ 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 $h \nu_0 = 300$KeVshouldbeabout18thmagnitudeinvisiblelightandafew$\mu$Jy at 1 GHz (less if self-absorbed).