Three high-mass X-ray binaries have been discovered recently exhibiting enormous spin-up rates. Conventional accretion theory predicts extremely high-surface dipolar magnetic fields that we believe are unphysical. Instead, we propose quite the opposite scenario; some of these pulsars exhibit weak magnetic fields, so much so that their magnetospheres are crushed by the weight of inflowing matter. The enormous spin-up rate is achieved before inflowing matter reaches the pulsar's surface as the penetrating inner disc transfers its excess angular momentum to the receding magnetosphere, which, in turn, applies a powerful spin-up torque to the pulsar. This mechanism also works in reverse; it spins a pulsar down when the magnetosphere expands beyond corotation and finds itself rotating faster than the accretion disc, which then exerts a powerful retarding torque to the magnetic field and to the pulsar itself. The above scenaria cannot be accommodated within the context of neutron-star accretion processes occurring near spin equilibrium, thus they constitute a step towards a new theory of extreme (far from equilibrium) accretion phenomena.
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