The Crab Pulsar: Origin of the Crab Nebula’s Radio Pairs

Previously, we constructed a model-essentially a plausibility argument-in which the Crab Pulsar produces a spatially separated ion dominated and pair plasma dominated, magnetically striped relativistic wind, with the ion wind's kinetic energy and electromagnetic Poynting fluxes being comparable. In this paper, the polar cap ionphoton pair production of that model is replaced with pair production by ion curvature synchrotron photons. The first primary ion curvature photons, and, contrary to conventional wisdom, also the first primary electron curvature photons, do not immediately convert into pairs. The primary beam particles continue to accelerate, and the actual photons that convert into pairs, which then short out the parallel electric field and terminate the acceleration, are produced by the further accelerated, higher energy particles. Simple estimates of the ensuing pair production cascade give pair multiplicities-the number of pairs per primary beam particle-of M-+/- approximate to 6-8 x 10(4), comparable to standard calculations, but much less than the 3 x 10(6) value deduced by Rees and Gunn in order to sustain the Crab Nebula's N-+/- approximate to 10(51) radio-emitting pairs against adiabatic expansion energy losses. Using a simple spindown evolution model for the pulsar's rotation frequency, the time-integrated pair cascade production driven by the primary ion beam can produce the N-+/- approximate to 10(51) radio pairs, whereas the primary electron beam produces about an order of magnitude fewer pairs.