Cooling timescales and temporal structure of gamma-ray bursts

A leading mechanism for producing cosmological gamma-ray bursts (GRBs) is via ultrarelativistic particles in an expanding fireball. The kinetic energy of the particles is converted into thermal energy in two shocks, a forward shock and a reverse shock, when the outward flowing particles encounter the interstellar medium. The thermal energy is then radiated via synchrotron emission and Comptonization. We estimate the synchrotron cooling timescale of the shocked material in the forward and reverse shocks for electrons of various Lorentz factors, focusing in particular on those electrons whose radiation falls within the energy detection range of the BATSE detectors. We find that in order to produce the rapid variability observed in most bursts, the energy density of the magnetic field in the shocked material must be greater than about 1% of the thermal energy density. In addition, the electrons must be nearly in equipartition with the protons, since otherwise we do not have reasonable radiative efficiencies of GRBs. Inverse Compton scattering can increase the cooling rate of the relevant electrons, but the Comptonized emission itself is never within the BATSE range. These arguments allow us to pinpoint the conditions within the radiating regions in GRBs and to determine the important radiation processes. In addition, they provide a plausible explanation for several observations. The model predicts that the duty cycle of intensity variations in GRB light curves should be nearly independent of burst duration and should scale inversely as the square root of the observed photon energy. Both correlations are in agreement with observations. The model also provides a plausible explanation for the bimodal distribution of burst durations. There is no explanation, however, for the presence of a characteristic break energy in GRB spectra.