A Self-consistent Scenario for the External-shock Emission in Density Jump Environments

Abstract The standard external-shock model, assuming a homogeneous turbulent downstream, has been widely used to decipher the afterglows of gamma-ray bursts. However, such assumption is invalid when the shock encounters a density jump. In this paper, we propose a self-consistent scenario to model the external forward shock emission, involving the advection and decaying behaviors of the shock-generated magnetic fields (sgMFs) in the downstream as found in particle-in-cell simulations. In an interstellar medium, our model is almost returned to the standard model but with ϵ B ∝ ( 1 + t dyn / t B ) α t . Here, ϵ B describes the sgMFs’ fraction of shock energy in the standard model, t dyn is the shock dynamic time, and t B together with α t depicts the sgMFs’ decaying behavior in our model. The situation is the same for the wind medium but with weak deviation in the early phase. When the shock encounters the density rise/dip, a shallower/deeper decay appears in the light curve. These behaviors are obvious for high-frequency emission or at the phase after the jet break. The GeV emission in the afterglow can serve to probe the circumburst density jump. We apply our model to decipher the later afterglows of the giant flare from SGR 1806-20. It is shown that a fireball propagating into a magnetar bow shock environment can well reproduce the observed peculiar steep decay in the radio light curve at ∼10 days from the burst.