Gamma-Ray Burst Afterglows in Pulsar-Wind Bubbles

Abstract

We propose to identify pulsar-wind bubbles (PWBs) as the environment in which the afterglow emission in at least some gamma-ray bursts (GRBs) originates. Such bubbles could naturally account for the high fraction of the internal energy residing in relativistic electrons/positrons ($ε_e$) and the high magnetic-to-internal energy ratio ($ε_B$) that have been inferred in a number of sources. GRBs might occur within PWBs under a number of scenarios: in particular, in the supranova model of GRB formation a prolonged (months to years) period of intense pulsar-type wind from the GRB progenitor precedes the burst. Focusing on this scenario, we construct a simple model of the early-time structure of a plerionic supernova remnant. The model is based on the assumption of an ``equipartition'' upper bound on the electromagnetic- to-thermal pressure ratio in the bubble and takes into account synchrotron- radiation cooling. We derive an expression for the effective hydrogen number density $n_{H,equiv}$ of the shocked pulsar wind in terms of the comoving particle pressure and electromagnetic fields. We show that, for plausible parameter values, $n_{H,equiv}$ spans the range inferred from spectral fits to GRB afterglows and that its radial profile varies within the bubble and may resemble a uniform interstellar medium or a stellar wind. We consider how the standard expressions for the characteristic synchrotron spectrum are modified when the afterglow-emitting shock propagates inside a PWB and demonstrate that the predictions for the empirically inferred values of $ε_e$ and $ε_B$ are compatible with the observations. Finally, we outline a self-consistent interpretation of the X-ray emission features detected in sources like GRB 991216 in the context of the supranova/PWB picture.