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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 interferometers. 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.
Accreting Millisecond X-Ray Pulsars (AMXPs) are astrophysical laboratories without parallel in the study of extreme physics. In this chapter we review the past fifteen years of discoveries in the field. We summarize the observations of the fifteen kn
Nuclear-powered X-ray millisecond pulsars are the third type of millisecond pulsars, which are powered by thermonuclear fusion processes. The corresponding brightness oscillations, known as burst oscillations, are observed during some thermonuclear X
Neutron Stars are among the most exotic objects in the Universe. A neutron star, with a mass of 1.4-2 Solar masses within a radius of about 10-15 km, is the most compact stable configuration of matter in which degeneracy pressure can still balance gr
I present an overview of our current observational knowledge of the six known accretion-driven millisecond X-ray pulsars. A prominent place in this review is given to SAX J1808.4-3658; it was the first such system discovered and currently four outbur
Despite considerable evidence verifying that millisecond pulsars are spun up through sustained accretion in low-mass X-ray binaries (LMXBs), it has proven surprisingly difficult to actually detect millisecond X-ray pulsars in LMXBs. There are only 5