On the 545 keV Line in the Spectrum of the Crab Nebula

The GRANAT group (R. Sunyaev {\it et al.\/}, Central Bureau of Astronomical Telegrams, International Astronomical Union, Circular No.~5481) recently reported the observation of a $(545 \pm 11)$ keV line in the spectrum of the Crab Nebula. It is tempting to associate this with the positron-electron annihilation line at 511 keV. If this line originates from some transition at the surface of the neutron star in the Crab, we expect a red shift of around 10\% rather then the observed blue shift of $\sim 35$ keV; in fact, this gravitational red shift implies that the natural frequency of the observed line is also 10\% higher, or around 600 keV. In this article we shall present a mechanism for generating such a split from 511 keV. For this mechanism to be successful we require: (a) surface magnetic fields, in the annihilation region, to be $(3-8)\times 10^{12}$~G and to point in our direction, (b) surface densities of $(10^5-10^6)$ g/cc. Both of these assumptions are consistent with pulsar models.