Time-Dependent Electron Acceleration in Pulsar Wind Termination Shocks: Application to the 2007 September Crab Nebula Gamma-Ray Flare

In 2007 September, the Crab Nebula exhibited a bright gamma-ray flare in the GeV energy range that was detected by AGILE. The observed emission at >160 MeV indicates that the radiating electrons had energies above the classical synchrotron radiation-reaction limit, thus presenting a serious challenge to classical models for electron acceleration in astrophysical environments. In this paper, we apply our recently developed time-dependent self-similar analytical model describing electrostatic acceleration in the explosive reconnection region around the pulsar wind termination shock to the 2007 September flare. This event was unique in that it displayed both long-duration "wave" and short-duration "sub-flare" features. The unusual temporal variation makes this flare an especially interesting test for our model. We demonstrate that our model can reproduce the time-dependent gamma-ray spectrum for this event, as well as the associated gamma-ray light curve, obtained by integrating the spectrum for photon energies >100 MeV. This establishes that our time-dependent electrostatic acceleration model can explain both wave and sub-flare transients, which lends further support to the theoretical framework we have developed. We also further examine the validity of the self-similar electric and magnetic field evolution implied by our model. We conclude that strong electrostatic acceleration driven by shock-induced magnetic reconnection is able to power the Crab Nebula gamma-ray flares by energizing the electrons on sub-Larmor timescales.
Comment: 13 pages, 5 figures, 2 tables