Time-Dependent Electron Acceleration in Pulsar-Wind Termination Shocks: Application to the 2011 April Crab Nebula Gamma-Ray Flare

摘要

The $\gamma$-ray flares from the Crab nebula observed by {\it AGILE} and {\itFermi}-LAT between 2007-2013 reached GeV photon energies and lasted severaldays. The strongest emission, observed during the 2011 April "super-flare,"exceeded the quiescent level by more than an order of magnitude. Theseobservations challenge the standard models for particle acceleration in pulsarwind nebulae, because the radiating electrons have energies exceeding theclassical radiation-reaction limit for synchrotron. Particle-in-cellsimulations have suggested that the classical synchrotron limit can be exceededif the electrons also experience electrostatic acceleration due to shock-drivenmagnetic reconnection. In this paper, we revisit the problem using an analyticapproach based on solving a fully time-dependent electron transport equationdescribing the electrostatic acceleration, synchrotron losses, and escapeexperienced by electrons in a magnetically confined plasma "blob" as itencounters and passes through the pulsar-wind termination shock. We show thatour model can reproduce the $\gamma$-ray spectra observed during the rising anddecaying phases of each of the two sub-flare components of the 2011 Aprilsuper-flare. We integrate the spectrum for photon energies $\ge 100\,$MeV toobtain the light curve for the event, which agrees with the observations. Wefind that strong electrostatic acceleration occurs on both sides of thetermination shock, driven by magnetic reconnection. We also find that thedominant mode of particle escape changes from diffusive escape to advectiveescape as the blob passes through the shock.