A search for a consistent model for the electromagnetic spectrum of the Crab nebula

An attempt is made to search for a consistent model to explain the electromagnetic spectrum of the Crab nebula (Tau A). It is assumed that there is a continuous injection of electrons at the centre of the nebula with an energy spectrum E^-1.54 as evidenced by radio data. This spectrum must steepen to a slope larger than 2 at some energy E_i in order to ensure that the energy input into electrons remains finite. The spectrum must also steepen beyond an energy E_c depending on the magnetic field because of synchrotron energy losses. Two types of models are considered: Class I, in which the whole nebula is characterised by a uniform magnetic field, and Class II, in which besides the general field H₀, small filamentary regions of strong field H_s are postulated. In models of Class I, the best fit to the observed data is obtained when E_t>E_c and H₀≃5×10^-4 gauss. However, this predicts a decrease in X-ray source size beyond ∼40 KeV. There are two possibilities of Class II model depending on the residence time of electrons in strong field regions being small or large. The former case explains the flattening in the optical spectrum. Experiments to distinguish between the various models are indicated.