The spin distribution of millisecond X-ray pulsars

The spin frequency distribution of accreting millisecond X-ray pulsars cuts off sharply above 730 Hz, well below the breakup spin rate for most neutron star equations of state. I review several different ideas for explaining this cutoff. There is currently considerable interest in the idea that gravitational radiation from rapidly rotating pulsars might act to limit spin up by accretion, possibly allowing eventual direct detection with gravitational wave intereferometers. I describe how long-term X-ray timing of fast accreting millisecond pulsars like the 599 Hz source IGR J00291+5934 can test the gravitational wave model for the spin frequency limit.