Dissipation in Poynting‐Flux–dominated Flows: The σ‐Problem of the Crab Pulsar Wind

Flows in which energy is transported predominantly as Poynting flux arethought to occur in pulsars, gamma-ray bursts and relativistic jets fromcompact objects. The fluctuating component of the magnetic field in such a flowcan in principle be dissipated by magnetic reconnection, and used to acceleratethe flow. We investigate how rapidly this transition can take place, byimplementing into a global MHD model, that uses a thermodynamic description ofthe plasma, explicit, physically motivated prescriptions for the dissipationrate: a lower limit on this rate is given by limiting the maximum drift speedof the current carriers to that of light, an upper limit follows from demandingthat the dissipation zone expand only subsonically in the comoving frame and afurther prescription is obtained by assuming that the expansion speed islimited by the growth rate of the relativistic tearing mode. In each case,solutions are presented which give the Lorentz factor of a spherical windcontaining a transverse, oscillating magnetic field component as a function ofradius. In the case of the Crab pulsar, we find that the Poynting flux can bedissipated before the wind reaches the inner edge of the Nebula if the pulsaremits electron positron pairs at a rate >1.E40 per second, thus providing apossible solution to the sigma-problem.Comment: Accepted for publication in Ap