Relativistic Wind Bubbles and Afterglow Signatures

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Abstract
Highly magnetized, rapidly rotating compact objects are widely argued as central energy sources of $\gamma$-ray bursts (GRBs). After the GRB, such a magnetar-like object may directly lose its rotational energy through some magnetically-driven processes, which produce an ultrarelativistic wind dominated possibly by the energy flux of electron-positron pairs. The interaction of such a wind with an outward-expanding fireball leads to a relativistic wind bubble, being regarded as a relativistic version of the well-studied Crab Nebula. We here explore the dynamics of this wind bubble and its emission signatures. We find that when the injection energy significantly exceeds the initial energy of the fireball, the bulk Lorentz factor of the wind bubble decays more slowly than before, and more importantly, the reverse-shock emission could dominate the afterglow emission, which yields a bump in afterglow light curves. In addition, high polarization of the bump emission would be expected if a toroidal magnetic field in the shocked wind dominates over the random component.