We investigate a novel mechanism of bulk acceleration of relativistic outflows of pure electron-positron pairs both analytically and numerically. The steady and spherically symmetric flow is assumed to start from a Wien equilibrium state between pure pairs and photons in a compact region that is optically thick to electron scattering at a relativistic temperature. Inside the photosphere where the optical thickness becomes unity, pairs and photons behave as a single fuid and are thermally accelerated. Outside the photosphere, pairs and photons behave separately, and we assume the free-streaming approximation for photons, which are emitted from the relativistically moving photosphere. Pairs are shown to be thermally accelerated further even outside the photosphere because the photospheric temperature is at least mildly relativistic. It is to be noted that the mean energy of photons is higher than that of pairs in the comoving frame of pairs and that Compton interaction leads to additional heating and radiative acceleration of pairs. For a reasonable range of the boundary temperature and optical thickness, the terminal Lorentz factor of pair outflows turns out be more than 10 and the terminal kinetic power accounts for more than 2/3 of the total luminosity. While the total luminosity should be at least larger than the Eddington luminosity, the real luminosity can be modest if the outflow is collimated by some unknown mechanism. This mechanism successfully avoids the difficulties of pair annihilation and radiation drag owing to pair production by accompanying high-energy photons and the strong beaming of the radiation field. It is seen that most pairs injected at the boundary survive to infinity. The radiation from the photosphere should be observed as MeV peaked emission at infinity with an order of kinetic power of jets.
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