• MHD;
  • radiation mechanisms: non-thermal;
  • relativistic processes;
  • shock waves;
  • ISM: supernova remnants;
  • gamma-rays: ISM


The oblique geometry of the pulsar wind termination shock ensures that the Doppler beaming has a strong impact on the shock emission. We illustrate this using the recent relativistic magnetohydrodynamic (MHD) simulations of the Crab nebula and the analysis of oblique shocks. We also show that the observed size, shape and distance from the Crab pulsar of the Crab nebula inner knot are consistent with its interpretation as a Doppler-boosted emission from the termination shock. If the electrons responsible for the synchrotron gamma-rays are accelerated only at the termination shock, then their short lifetime ensures that these gamma-rays originate close to the shock and are also strongly affected by the Doppler beaming. As a result, the bulk of the observed synchrotron gamma-rays of the Crab nebula around 100 MeV may come from its inner knot. This hypothesis is consistent with the observed optical flux of the inner knot, provided its optical-gamma spectral index is the same as the injection spectral index found in the Kennel & Coroniti model of the nebula spectrum. The observed variability of synchrotron gamma-ray emission on the time-scale of the wisp production can be caused by the instability of the termination shock discovered in recent numerical simulations. Given the small size of the knot, it is also possible that the 2010 September gamma-ray flare of the Crab nebula also came from the knot, though the actual mechanism remains unclear. The model predicts correlation of the temporal variability of the synchrotron gamma-ray flux in the Fermi and Astro-revilatore Gamma a Immagini LEggero (AGILE) windows with the variability of the un-pulsed optical flux from within 1 arcsec of the Crab pulsar.