Synchrotron Model for the Infrared, Optical, and X‐Ray Emission of the Crab Pulsar

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Abstract
We develop a model for the infrared, optical, and soft X-ray emission of the Crab pulsar in terms of anisotropic synchrotron emission by relativistic particles in an outer gap scenario with a single energy distribution N(γ) ∝ γ-2. It is shown that such a distribution is naturally produced in an efficient pair cascade and that the energy of the primary particles is limited by synchrotron radiation to γ ~ 107. It is further shown that this synchrotron model is able to reproduce the spectral shape between the infrared and soft X-rays and also the corresponding luminosities. In particular, the long-standing problem of the rapid spectral decline toward infrared frequencies is understandable as emission at very small pitch angles from low-energy particles with γ ~ 102. Finally, we show that the scaling of our synchrotron model explains the observed correlation between the X-ray luminosity and the spin-down luminosity of the neutron star LX ~ 10-3Lsd found by Becker & Trümper.
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