Stability of Fireballs and $\gamma$-Ray Bursts

Abstract

Fireballs are an essential part of any cosmological $\gamma$-ray burst. We drive here a stability criterion for fireballs and show that fireballs are Rayleigh-Taylor unstable in any region in which the entropy decreases outward. The instability begins to operate when the fireball becomes matter dominated. Among the possible implication of the instability are: (i) Conversion of a fraction of the radiation energy to a convective energy expressed in the motion of bubbles relative to each other. (ii) Penetration of fast bubbles through slower ones and creation of high $\gamma$ regimes which are essential for efficient conversion of the energy to $\gamma$-rays. (iii) Formation of rapid variation (of the scale of the bubbles) in the observed $\gamma$-rays.