Collective processes in relativistic plasma and their implications for gamma-ray burst afterglows

We consider the effects of collective plasma processes on synchrotron emission from highly relativistic electrons. We find, in agreement with Sazonov (1970), that strong effects are possible also in the absence of a non-relativistic plasma component, due to the relativistic electrons (and protons) themselves. In contrast with Sazonov, who infers strong effects only in cases where the ratio of plasma frequency to cyclotron frequency is much larger than the square of the characteristic electron Lorentz factor, nu_p/nu_B >> gamma^2, we find strong effects also for 1 << nu_p/nu_B << gamma^2. The modification of the spectrum is prominent at frequencies nu < nu_{R*} = nu_p min[gamma, (nu_p/nu_B)^(1/2)], where nu_{R*} generalizes the Razin-Tsytovich frequency, nu_R = gamma nu_p, to the regime nu_p/nu_B << gamma^2. Applying our results to gamma-ray burst (GRB) plasmas, we predict a strong modification of the radio spectrum on minute time scale following the GRB, at the onset of fireball interaction with its surrounding medium, in cases where the ratio of the energy carried by the relativistic electrons to the energy carried by the magnetic field exceeds ~ 10^5. Plausible electron distribution functions may lead to negative synchrotron reabsorption, i.e to coherent radio emission, which is characterized by a low degree of circular polarization. Detection of these effects would constrain the fraction of energy in the magnetic field, which is currently poorly determined by observations, and, moreover, would provide a novel handle on the properties of the environment into which the fireball expands.