  The evolution of a dilute electron-positron fireball is calculated in the
regime of strong magnetization and very high compactness (l ~10^3-10^8).
Heating is applied at a low effective temperature (< 25 keV), and the fireball
is allowed to expand, so that the formation of a black-body spectral
distribution is inhibited by pair annihilation. The diffusion equation for
Compton scattering is coupled to a single-temperature pair gas and an exact
(trans-relativistic) cyclo-synchrotron photon source. We find that the photon
spectrum develops a quasi-thermal peak, with a power-law slope below it that is
characteristic of gamma-ray bursts. The formation of a thermal high-frequency
spectrum is checked using the full kinetic equations at l ~ 10^3. These results
have several implications for the central engine of GRBs, and the mechanism of
energy transport. 1. Baryon rest mass carries less than ~ 10^{-5} of the energy
flux at jet breakout inside ~ 10^{12} cm from the engine, with most carried by
the magnetic field. 2. This degree of baryon purity points to the presence of
an event horizon in the engine, and neutrons play a negligible role in the
prompt emission mechanism. 3. X-ray flashes are emitted by outflows carrying
enough baryons that the photosphere is pair-depleted, which we show results in
faster thermalization. 4. The relation between observed peak frequency and
burst luminosity is bounded below by the observed Amati et al. relation if jet
Lorentz factor ~ 1/(opening angle) at breakout. 5. Stellar models are used to
demonstrate an inconsistency between the highest observed GRB energies, and a
hydrodynamic nozzle: magnetic collimation is required. 6. The magnetized pair
gas is dilute enough that high-frequency Alfven waves may become charge
starved. Finally, we suggest that limitations on magnetic reconnection from
plasma collisionality have been overestimated.
