Cooling waves in pair plasma

We consider structure and emission properties of a pair plasma fireball that cools due to radiation. At temperatures $T\ge 0.5m_e{c}^2$ the cooling takes a form of clearly defined cooling wave, whereby the temperature and pair density experience a sharp drop within a narrow region. The surface temperature, corresponding to the location where the optical depth to infinity reaches unity, never falls much below $0.1m_e{c}^2\approx 50$ keV. The propagation velocity of the cooling wave is much smaller than the speed of light and decreases with increasing bulk temperature.