On the Detectability of Prompt Coherent GRB Radio Emission

Both induced Compton scattering and induced Raman scattering strongly limit the observability of the extremely bright (<< 10^21K), prompt coherent radio emission recently predicted to emanate from gamma-ray bursts. Induced Compton scattering is the main limiting factor when the region around the progenitor is not dense but when one still considers the scattering effect of the a tenuous circumburst ISM. For a medium of density 0.01 n_{0.01} cm^{-3} and a path length L_{kpc} kpc and emission that is roughly isotropic in its rest frame the brightness temperature is limited to < 3 x 10^18 Gamma_{100}^2 n_{0.01}^{-1} L_{\rm kpc}^{-1} K, where $100 Gamma_{100} is the Lorentz factor of the frame in which the emission occurs. Thus, for a burst at distance D the predicted emission is only visible if the jet is ultra-relativistic, with Gamma > 10^3 (D/100 Mpc), or if the intrinsic opening angle of the emission is extremely small. Thus the presence or absence of such radio emission provides an excellent constraint on the Lorentz factor of the GRB outflow during the very early stages of its outburst. Induced Raman scattering imposes an even more stringent limit independent of the emission opening angle, but only effective if GRB emission must propagate through a dense progenitor wind within ~ 10^{15} cm from the blast center.