High-Resolution Numerical Calculations of GRB Afterglow Plateaus arising from Stratified Ejecta

Abstract

Since the discovery of plateaus in GRB afterglows by Swift, they have been modeled predominantly by late-time energy injection. However, many studies have suggested that the plateau may be modeled by an early phase before reverse shock crossing (either coasting with constant Lorentz factor or decelerating very slowly as the reverse shock crosses the ejecta). The slope of the early plateau provides some constraints the stratification of the fastest-moving ejecta, which could be the ejecta responsible for the prompt emission. However, numerical studies typically do not model the jet as a stratified outflow; the reason being the extremely high resolution required in order to accurately evolve this tiny amount of highly relativistic material. In this study, we perform high-resolution numerical calculations ($Δr/r \lesssim 10^{-5}$) verifying that a stratified ejecta structure can indeed produce an afterglow plateau in both wind ($k=2$) and ISM ($k=0$) environments, and computing break times explicitly. We evolve the relativistic hydrodynamics using the JET code, and post-process this to compute the afterglow using the Firefly code. Our results show that a stratified ejecta structure (which should generically be present in GRB jets) is sufficient to explain GRB afterglows, and the plateau slopes can be used to constrain the ejecta stratification. We additionally provide precise measured scalings for the plateau duration as a function of the characteristic Lorentz factor of the ejecta. The long duration of typical plateaus requires a very modest characteristic Lorentz factor for the ejecta ($γ_0 \sim 10-50$), in agreement with other afterglow plateau models.