Electron Acceleration in Pulsar-Wind Termination Shocks: An Application to the Crab Nebula Gamma-Ray Flares
(Oct 14, 2016)Abstract
The \gamma-ray flares from the Crab nebula observed by AGILE and Fermi-LAT
reaching GeV energies and lasting several days challenge the standard models
for particle acceleration in pulsar wind nebulae, because the radiating
electrons have energies exceeding the classical radiation-reaction limit for
synchrotron. Previous modeling has suggested that the synchrotron limit can be
exceeded if the electrons experience electrostatic acceleration, but the
resulting spectra do not agree very well with the data. As a result, there are
still some important unanswered questions about the detailed particle
acceleration and emission processes occurring during the flares. We revisit the
problem using a new analytical approach based on an electron transport equation
that includes terms describing electrostatic acceleration, stochastic
wave-particle acceleration, shock acceleration, synchrotron losses, and
particle escape. An exact solution is obtained for the electron distribution,
which is used to compute the associated \gamma-ray synchrotron spectrum. We
find that in our model the \gamma-ray flares are mainly powered by
electrostatic acceleration, but the contributions from stochastic and shock
acceleration play an important role in producing the observed spectral shapes.
Our model can reproduce the spectra of all the Fermi-LAT and AGILE flares from
the Crab nebula, using magnetic field strengths in agreement with the
multi-wavelength observational constraints. We also compute the spectrum and
duration of the synchrotron afterglow created by the accelerated electrons,
after they escape into the region on the downstream side of the pulsar wind
termination shock. The afterglow is expected to fade over a maximum period of
about three weeks after the \gamma-ray flare.