Stability of Fireballs and $γ$-Ray Bursts

Abstract

Fireballs are an essential part of any cosmological $γ$-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 $γ$ regimes which are essential for efficient conversion of the energy to $γ$-rays. (iii) Formation of rapid variation (of the scale of the bubbles) in the observed $γ$-rays.