Accretion onto Fast X-Ray Pulsars

The recent emergence of a new class of accretion-powered, transient, millisecond X-ray pulsars presents some difficulties for the conventional picture of accretion onto rapidly rotating magnetized neutron stars and their spin behavior during outbursts. In particular, it is not clear that the standard paradigm can accommodate the wide range in M (i.e., >~ a factor of 50) over which these systems manage to accrete and the high rate of spin-down that the neutron stars exhibit in at least a number of cases. When the accretion rate drops sufficiently, the X-ray pulsar is said to become a ``fast rotator,'' and in the conventional view, this is accompanied by a transition from accretion to ``propellering,'' in which accretion ceases and the matter is ejected from the system. On the theoretical side, we note that this scenario for the onset of propellering cannot be entirely correct because it is not energetically self-consistent. We show that, instead, the transition is likely to take place through disks that combine accretion with spin-down and terminate at the corotation radius. We demonstrate the existence of such disk solutions by modifying the Shakura-Sunyaev equations with a simple magnetic torque prescription. The solutions are completely analytic and have the same dependence on M and α (the viscosity parameter) as the original Shakura-Sunyaev solutions, but the radial profiles can be considerably modified, depending on the degree of fastness. We apply these results to compute the torques expected during the outbursts of the transient millisecond pulsars and find that we can explain the large spin-down rates that are observed for quite plausible surface magnetic fields of ~10⁹ G.