Ultra-relativistic winds: Pairs, radiation, and magnetic fields

Cosmological {dollar}gamma{dollar}-ray bursts (GRBs) are thought to involve relativistically expanding fireballs. We explore how conditions at the GRB source affect the evolution of the fireball and compute the spectrum emerging from such a highly relativistic flow.; First we consider a simple ultra-relativistic wind consisting of electron-positron pairs and photons. The wind is assumed to originate at radius {dollar}rsb{lcub}i{rcub}{dollar} where it has a Lorentz factor {dollar}gammasb{lcub}i{rcub}{dollar} and a temperature {dollar}Tsb{lcub}i{rcub}{dollar} sufficiently high to maintain pair equilibrium. As r increases, T decreases and becomes less than the temperature corresponding to the electron mass {dollar}msb{lcub}e{rcub},{dollar} after which non-equilibrium effects become important. The pairst which carry only a small fraction of the total energy, may be accelerated by the photons until {dollar}tau{dollar} falls below {dollar}tausim 2times 10sp{lcub}-5{rcub}gammasbsp{lcub}i{rcub}{lcub}3/4{rcub}.{dollar} The acceleration of the pairs increases {dollar}gamma{dollar} by a factor {dollar}sim{dollar}45 as compared to its value at the photosphere; it is shown to approach {dollar}gammasb{lcub}infty{rcub}sim 1.4times 10sp3(rsb{lcub}i{rcub}/10sp6{dollar}cm){dollar}sp{lcub}1/4{rcub}gammasbsp{lcub}i{rcub}{lcub}3/4{rcub}Tsb{lcub}i{rcub}/msb{lcub}e{rcub}.{dollar}; Based on the approximation {dollar}gammagg 1{dollar} and the assumption of spherical symmetry, we convert the equation of radiative transfer into an integral equation of the Volterra type. In the special case of the baryon-free wind discussed above, the equation of radiative transfer simplifies considerably and is solved by a blackbody distribution function. Since the emitting region is moving relativistically relative to the observer, the corresponding spectrum observed in the laboratory frame will not be blackbody, but it also differs from a typical power-law GRB spectra.; The fireballs discussed above were assumed to be spherically symmetric. If the emitted energy instead is beamed into a solid angle {dollar}Omegasb{lcub}gamma{rcub},{dollar} the required burst energy is smaller by a factor {dollar}Omegasb{lcub}gamma{rcub}/4pi{dollar} than for isotropic emission. We show that by including magnetic fields in the fireball model, one can get jet-like outflows with high Lorentz factors. This is true for a baryon-dominated flow, in which the initial magnetic energy is transferred into kinetic energy of the flow, and also for a radiation dominated flow, where a strong magnetic field appears to restrict the acceleration of the flow.