Acceleration of X-ray Emitting Electrons in the Crab Nebula

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: $d{N}_{\mathrm{e}}/d\gamma \propto {\gamma }^{{\alpha }_{\mathrm{e}}}$, where ${\alpha }_{\mathrm{e}}$ lies in the range $-1.8$ to $-2.4$ and depends on the downstream turbulence level. For sufficiently strong turbulence, we find ${\alpha }_{\mathrm{e}}\simeq -2.2$, 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 ${\alpha }_{\mathrm{e}}\simeq -1.8$ 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.

14 pages, 8 figures, 2 tables. Accepted for publication in The Astrophysical Journal

References in corpus (7)

• Broadband X-ray Imaging and Spectroscopy of the Crab Nebula and Pulsar with NuSTAR
• Constraints on particle acceleration sites in the Crab Nebula from relativistic MHD simulations
• Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions
• Modelling Jets, Tori and Flares in Pulsar Wind Nebulae
• Inductive spikes in the Crab Nebula - a theory of gamma-ray flares
• Electron acceleration at pulsar wind termination shocks
• Relativistic MHD modeling of magnetized neutron stars, pulsar winds, and their nebulae

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