Systematic Error in Approximate Models of the GRB Early Afterglow

Abstract

Gamma-ray burst (GRB) afterglows are thought to arise when relativistic ejecta launched by a compact central engine drive a blast wave into the surrounding circumburst medium, producing broadband synchrotron emission. We present a rigorous assessment, based on high-resolution special relativistic hydrodynamics simulations, of a widely adopted `two-zone model' for approximating the dynamics of the early afterglow phase. Before the onset of the Blandford-McKee (BMK) self-similar solution, the outflow generally produces two emission components, associated with the forward-shocked circumburst medium and the reverse-shocked ejecta. The subsequent evolution depends on whether the reverse shock significantly decelerates the ejecta as it crosses the shell, separating the so-called relativistic and Newtonian reverse shock regimes. We show that when the reverse shock is Newtonian, it crosses the ejecta shell long before BMK self-similarity is established, leaving a prolonged interval that can span $\sim$ hours in observer time in which the true hydrodynamic evolution is not captured by standard semi-analytic prescriptions. We demonstrate that this mismatch can substantially overpredict the reverse-shock emission from radio through ultraviolet frequencies, or overpredict the forward-shock emission at X-ray frequencies, depending on how the transition away from the two-zone model is prescribed.