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The X-ray light curves of the early afterglow phase from gamma-ray burstspresent a puzzling variability, including flares. The origin of these flares isstill debated, and often associated with a late activity of the central engine.We discuss an alternative scenario where the central engine remains short-livedand flares are produced by the propagation of a long-lived reverse shock in astratified ejecta. Here we focus on the hydrodynamics of the shockinteractions. We perform one-dimensional ultrarelativistic hydrodynamicsimulations with different initial internal structure in the gamma-ray burstejecta. We use them to extract bolometric light curves and compare with aprevious study based on a simplified ballistic model. We find a good agreementbetween both approaches, with similar slopes and variability in the lightcurves, but identify several weaknesses in the ballistic model: the density isunderestimated in the shocked regions, and more importantly, late shockreflections are not captured. With accurate dynamics provided by ourhydrodynamic simulations, we confirm that internal shocks in the ejecta lead tothe formation of dense shells. The interaction of the long-lived reverse shockwith a dense shell then produces a fast and intense increase of the dissipatedpower. Assuming that the emission is due to the synchrotron radiation fromshock-accelerated electrons, and that the external forward shock is radiativelyinefficient, we find that this results in a bright flare in the X-raylightcurve, with arrival times, shapes, and duration in agreement with theobserved properties of X-ray flares in GRB afterglows.

Relativistic simulations of long-lived reverse shocks in stratified ejecta: the origin of flares in GRB afterglows