Gamma-ray burst afterglows in pulsar-wind bubbles

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 n_H,equiv = [4p + (B′ + ℰ′) ²/4π]/m_pc², where B′ and ℰ′ are, respectively, the comoving magnetic and electric fields, and p is the particle pressure. 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, a stellar wind, or a molecular cloud. We consider how the standard expressions for the characteristic synchrotron spectral quantities are modified when the after-glow-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.