The Sigma Problem of the Crab Pulsar Wind

We investigate how rapidly Poynting flux can be converted into kinetic energy in the wind of the Crab pulsar by implementing into a global MHD model explicit prescriptions for the dissipation rate. A lower limit is given by limiting the maximum drift speed of the current carriers to that of light an upper limit follows from demanding that the dissipation zone expand only subsonically in the comoving frame. A further prescription is obtained by assuming that the expansion speed is limited by the growth rate of the relativistic tearing mode. In each case solutions are presented which give the Lorentz factor of the wind containing a transverse oscillating magnetic field component as a function of radius. We find that the Poynting flux can be dissipated before the wind reaches the inner edge of the Nebula if the pulsar emits electron positron pairs at a rate greater than 1.E40 per secon