Synchrotron model for the infrared, optical, and X-ray emission of the Crab pulsar

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(gamma) proportional to gamma (-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 gamma similar to 10(7). 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 gamma similar to 10(2). 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 L-X similar to 10(-3) L-sd found by Becker & Trumper.