  Observations made using the Rossi X-ray Timing Explorer have shown that
accreting weak-field neutron stars in low-mass X-ray binary systems (LMXBs)
produce three distinct types of millisecond X-ray oscillations that can be used
to determine the spin rates and estimate the magnetic fields of these stars.
These oscillations show that more than two dozen neutron stars in LMXBs have
spin rates and magnetic fields in the range that will make them radio-emitting
millisecond pulsars when accretion ceases, supporting the hypothesis that
neutron stars in LMXBs are the progenitors of the rotation-powered millisecond
pulsars. The spins of the 16 known accreting millisecond pulsars in LMXBs are
consistent with spin-up to accretion spin equilibrium for magnetic fields
ranging from 3 x 10^7 G to 3 x 10^8 G and time-averaged accretion rates ranging
from 3 x 10^{-3} MdotE to MdotE, provided these stars have been accreting long
enough. The P-Pdot distribution of rotation-powered millisecond pulsars
indicates that their initial spins are set by spin-up to spin equilibrium at
accretion rates ranging from 10^{-3} MdotE to MdotE or that they never reached
accretion spin equilibrium.
