The location of the Crab pulsar emission region: restrictions on synchrotron emission models

Abstract

Recent observations of the Crab pulsar show no evidence for a spectral break in the infrared regime. It is argued that the observations are consistent with a power-law spectrum in the whole observable infrared - optical range. This is taken as the starting point for an evaluation of how self-consistent incoherent synchrotron models fare in a comparison with observations. Inclusion of synchrotron self-absorption proves important as does the restriction on the observed size of the emission region imposed by the relativistic beaming thought to define the pulse profile. It is shown that the observations can be used to derive two independent constraints on the distance from the neutron star to the emission region; in addition to a direct lower limit, an indirect measure is obtained from an upper limit to the magnetic field strength. Both of these limits indicate that the emission region is located at a distance considerably larger than the light cylinder radius. The implications of this result are discussed and it is emphasized that, in order for standard incoherent synchrotron models to fit inside the light cylinder, rather special physical conditions need to be invoked.