Stability of the Forward/Reverse-Shock System Formed by the Impact of a Relativistic Fireball on an Ambient Medium

We analyze the stability of a relativistic double (forward/reverse)-shock system that forms when the fireball of a gamma-ray burst (GRB) impacts on the surrounding medium. We find this shock system to be stable to linear global perturbations for either a uniform or a wind (r-2) density profile of the ambient medium. For the wind case, we calculate analytically the frequencies of the normal modes that could modulate the early short-term variability of GRB afterglows. We find that perturbations in the double-shock system could induce damped oscillatory fluctuations in the observed flux on short timescales during the early phase of an afterglow.