  Strong, coherent, quasi-periodic brightness oscillations (QPOs) with
frequencies ranging from about 300 Hz to 1200 Hz have been discovered with the
Rossi X-ray Timing Explorer in the X-ray emission from some fifteen neutron
stars in low-mass binary systems. Two simultaneous kilohertz QPOs differing in
frequency by 250 to 350 Hertz have been detected in twelve of the fifteen
sources. Here we propose a model for these QPOs. In this model the X-ray source
is a neutron star with a surface magnetic field of 10^7 to 10^10 G and a spin
frequency of a few hundred Hertz, accreting gas via a Keplerian disk. The
frequency of the higher-frequency QPO in a kilohertz QPO pair is the Keplerian
frequency at a radius near the sonic point at the inner edge of the Keplerian
flow whereas the frequency of the lower-frequency QPO is approximately the
difference between the Keplerian frequency at a radius near the sonic point and
the stellar spin frequency. This model explains naturally many properties of
the kilohertz QPOs, including their frequencies, amplitudes, and coherence. We
show that if the frequency of the higher-frequency QPO in a pair is an orbital
frequency, as in the sonic-point model, the frequencies of these QPOs place
interesting upper bounds on the masses and radii of the neutron stars in the
kilohertz QPO sources and provide new constraints on the equation of state of
matter at high densities. Further observations of these QPOs may provide
compelling evidence for the existence of a marginally stable orbit, confirming
a key prediction of general relativity in the strong-field regime.
