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 burst (GRB) sources originates. Such bubbles could naturally account for both the high fraction of the internal energy residing in relativistic electrons and positrons (e) and the high magnetic-to-internal energy ratio (B) that have been inferred in a number of sources from an interpretation of the afterglow emission as synchrotron radiation. 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 (SNR), guided by recent results on the Crab and Vela SNRs. 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 argue that the effective upstream hydrogen number density for a relativistic shock propagating into the bubble is given by nH,equiv = [4p + (B' + ')2/4π]/mpc2, where B' and ' are, respectively, the comoving magnetic and electric fields, and p is the particle pressure. We show that, for plausible parameter values, nH,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, a stellar wind, or a molecular cloud. We consider how the standard expressions for the characteristic synchrotron spectral quantities are modified when the afterglow-emitting shock propagates inside a PWB instead of in a uniform interstellar medium and demonstrate that the predictions for the empirically inferred values of e and B are consistent with the observations. Finally, we outline a self-consistent interpretation of the X-ray emission features detected in sources such as GRB 991216 in the context of the supranova/PWB picture.