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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 accretion-powered millisecond X-ray pulsars known among more than 80 LMXBs containing neutron stars, but there are another 11 nuclear powered millisecond pulsars which reveal their spin only during brief, thermonuclear X-ray bursts. In addition, 2 of the accretion-powered pulsars also exhibit X-ray burst oscillations, and their unusual properties, along with the absence of persistent pulsations in most LMXBs, suggest that the magnetic fields in many LMXBs may be hidden by accreted material. Interestingly, the nuclear-powered pulsars offer a statistically unbiased probe of the spin distribution of recycled pulsars and show that this distribution cuts off sharply above 730 Hz, well below the breakup spin rate for most neutron star equations of state. This indicates that some mechanism acts to halt or balance spin-up due to accretion and that submillisecond pulsars must be very rare (and are possibly nonexistent). It is unclear what provides the necessary angular momentum sink, although gravitational radiation is an attractive possibility.
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
Radiation of X-ray bursts and of accretion shocks in weakly magnetized neutron stars in low-mass X-ray binaries is produced in plane-parallel atmospheres dominated by electron scattering. We first discuss polarization produced by single (non-magnetic