An Analytic Particle Acceleration Model in Pulsar Wind Termination Shocks Applied to the Crab Nebula Gamma-Ray Flares

The Crab nebula is a persistent source of gamma-rays up to about 100 MeV due to synchrotron radiation from electrons/positrons emitting in an ambient magnetic field thought to be of magnitude B~200 μG. The radiating electrons are limited by radiation-reaction forces which place an upper limit of about 100 MeV on the gamma-ray photons it can produce. This normally quiescent nebula has been observed by AGILE and Fermi to undergo bright transients lasting about a week and characterized by a significant increase in gamma-ray flux far above the classical radiation-reaction limit, with energies often reaching 3 GeV. The flares imply a population of PeV electrons accelerated on sub-day timescales. The very short acceleration timescales and the observed emission above the radiation-reaction limit place severe constraints on contemporary shock acceleration models such as diffusive shock acceleration which cannot account for the temporal and energetic properties of the gamma-ray flares. In this component of my dissertation research, I revisit the problem and find an analytic solution to the Fokker-Planck equation which incorporates a variety of acceleration and loss terms. I find that the model can reproduce the various Fermi-LAT flare spectra well and that electrostatic acceleration is the most significant contributor to the underlying mechanisms responsible for the most energetic astrophysical particle population ever observed. I find that the spectra of all the Fermi-LAT flares from the Crab nebula can be reproduced with this model using magnetic fields that are in agreement with multi-wavelength observations.