Dissipation in Poynting-flux Dominated Flows: the Sigma-Problem of the Crab Pulsar Wind

Flows in which energy is transported predominantly as Poynting flux are thought to occur in pulsars, gamma-ray bursts and relativistic jets from compact objects. The fluctuating component of the magnetic field in such a flow can in principle be dissipated by magnetic reconnection, and used to accelerate the flow. We investigate how rapidly this transition can take place, by implementing into a global MHD model, that uses a thermodynamic description of the plasma, explicit, physically motivated prescriptions for the dissipation rate: a lower limit on this rate 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 and 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 a spherical wind containing a transverse, oscillating magnetic field component as a function of radius. In the case of the Crab pulsar, 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 >1.E40 per second, thus providing a possible solution to the sigma-problem.