Acceleration of X-Ray Emitting Electrons in the Crab Nebula

Abstract

Abstract We study particle acceleration at the termination shock of a striped pulsar wind by integrating trajectories in a prescribed model of the magnetic field and flow pattern. Drift motion on the shock surface maintains either electrons or positrons on “Speiser” orbits in a ring-shaped region close to the equatorial plane of the pulsar, enabling them to be accelerated to very high energy by the first-order Fermi mechanism. A power-law spectrum results: , where α e lies in the range −1.8 to −2.4 and depends on the downstream turbulence level. For sufficiently strong turbulence, we find α e ≃ −2.2, and both the photon index and the flux of 1–100 keV X-rays from the Crab Nebula, as measured by NuSTAR, can be reproduced. The particle spectrum hardens to α e ≃ −1.8 at lower turbulence levels, which may explain the hard photon index observed by the Chandra X-ray Observatory in the central regions of the Nebula.