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 the 1970 work of Sazonov, that strong effects are also possible in the absence of a nonrelativistic plasma component, due to the relativistic electrons (and protons) themselves. In contrast with Sazonov, who infers strong effects only in cases in which the ratio of plasma frequency to cyclotron frequency is much larger than the square of the characteristic electron Lorentz factor, νp/νB γ, we also find strong effects for 1 νp/νB γ. The modification of the spectrum is prominent at frequencies ν ≤ ν ≡ νp min{γe, (νp/νB)1/2}, where ν generalizes the "Razin-Tsytovich" frequency νR ≡ γeνp to the regime νp/νB γ. Applying our results to gamma-ray burst (GRB) plasmas, we predict a strong modification of the radio spectrum on a minute timescale following the GRB at the onset of fireball interaction with its surrounding medium, in cases in which the ratio of the energy carried by the relativistic electrons to the energy carried by the magnetic field exceeds ~105. 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.