Cooling Time Scales and Temporal Structure of Gamma-Ray Bursts

Abstract

A leading mechanism for producing cosmological gamma-ray bursts (GRBs) is via ultra-relativistic particles in an expanding fireball. The kinetic energy of the particles is converted into thermal energy in a forward shock and a reverse shock, when the outward flowing particles encounter the interstellar medium. The thermal energy is radiated via synchrotron emission and Comptonization. We estimate the synchrotron cooling time scale of the shocked regions 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 magnetic energy density in the shocked material must be greater than about 1\% of the thermal energy density. Additionally, the electrons must be nearly in equipartition with the protons, otherwise the radiative efficiency is low. 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, 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 characteristic break energy in GRB spectra.