A critical analysis of ideal magnetohydrodynamic models for crab-like pulsar winds

We present a critical examination of the ideal MHD model far the stationary Crab pulsar wind, which has a terminal flow Lorentz factor gamma(infinity) similar to 10(6) and may have a terminal ratio of Poynting flux to kinetic energy flux as low as sigma similar to 10(-2)-10(-3). We first show that t ransitions to a low-sigma configuration cannot occur gradually in regions w ell beyond the light cylinder where the flow has already become ultrarelati vistic. This is because the poloidal field lines do not expand sufficiently beyond the fast critical point to convert the electromagnetic energy into flow kinetic energy. As an alternative, we consider whether the acceleratio n may proceed abruptly, with the flow rapidly passing through the fast crit ical point and expanding into a low-sigma configuration. Such rapid expansi on of held lines, analogous to that in a de Laval nozzle, requires the polo idal fields to be highly compressed upstream of the fast critical point. We categorize the rapid field expansion generally into two prototypes: sheetl ike and fountain-like, with the former being a spontaneous transition and t he latter requiring external pressure supports. Unfortunately, it is shown that both types of rapid acceleration fail to satisfy either the energy and momentum conservation or the MHD flux-freezing condition. Nevertheless, we have pinned down the only situation where a stationary, ideal-MHD low-sigm a wind may exist. It requires almost the entire wind acceleration to occur in the immediate neighborhood of the light cylinder. Moreover, it also dema nds drastic modifications to the conventional picture of the pulsar dipole magnetosphere, in that the outer magnetosphere must be dominated by the tor oidal fields and that the pulsar wind is carried by only a small fraction o f the magnetospheric field lines emerging from the star.