We study steady and spherically symmetric outflows of pure electron-positron pair plasma as a possible acceleration mechanism of relativistic jets up to a bulk Lorentz factor of greater than 10. We assume that at the inner boundary a "Wien fireball" is realized, which is optically thick to Compton scattering but thin to absorption and in a Wien equilibrium state between pairs and photons at a relativistic temperature. As was shown by approximate treatments in our previous paper, the Wien fireball results in a relativistic outflow by thermal expansion, and thus problems with pair annihilation and radiation drag can be avoided. In this paper we present numerical solutions obtained with a Monte Carlo simulation of radiative transfer in a relativistic flow. Compton scattering, pair annihilation, and pair creation processes are considered in simulating the photon trajectories, and we evaluate the photon distribution function, pair creation rate, and radiative force. The dynamics of the outflow of pairs are consistently solved with radiative force and pair processes by iteration. The numerical results basically confirm our previous finding that the formation of powerful relativistic outflows can be obtained by the Wien fireball. Pair plasma is relativistically accelerated, and the radiative force does not work as a drag force but as an accelerating one because of the relativistic beaming effects. Radiation emitted from the photosphere should be observed as MeV peaked emission at infinity with a luminosity on the order of the kinetic power of jets.
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