The generation, annihilation and re-radiation of e± pairs in fireballs of internal shock waves

Abstract

In the internal shock wave model of gamma-ray bursts (GRBs), the central energy source ejects a series of material envelopes with comparable masses but very different global Lorentz factors. Strong collisions of these envelopes with various velocities generate relativistic shock waves. The electrons in the envelopes are heated by the shock waves, and via synchrotron radiation as well as inverse Compton scattering they emit high-energy γ photons. Due to the electron pairs produced by γ — γ collisions, photons with energies on orders as high as GeV (in the observer's system) are absorbed by the fireball. As revealed by Pilla & Leob's numerical calculation, the number of electron pairs is much larger than that of electrons in the fireball. Recently, Li et al. obtained a similar result, which was used to interpret the deficiency of optical flashes in the early afterglow. From an analytical study of the time evolution of the processes of generation and annihilation of electron pairs, it is discovered that for a typical pulse the number of e ± pairs produced in the early phase in the high-energy part of synchrotron radiation is large and the rate of annihilation is high. However, in the late phase, owing to the limitation of the maximum frequency of the synchrotron radiation, the high-energy part no longer contributes to the generation of e ± pairs. Unlike this, the contribution of inverse Compton scattering to the production of e ±'s is approximately proportional to the time scale of the pulse duration. For typical parameter values, the number of electron pairs generated jointly by the two components of radiation may be as high as more than 10 times the number of electrons carried by the original fireball. Because the Lorentz factor of the generated e ±'s is rather small, the corresponding synchrotron radiation has no influence on the observed spectrum (this is so at least for the energy range of the BATSE detector). But after the secondary inverse Compton scattering, there is a possible influence on the observed spectrum. Because the mass of electron pair is far smaller than that of proton, the effect on the late phase of the dynamic evolution of the fireball is not large. At least for a uniform medium environment, the existence of electron pairs has no great influence on the optical radiation of afterglow in its early phase.