Sonic-point model of kilohertz quasi-periodic brightness oscillations in low-mass X-ray binaries

Quasi-periodic brightness oscillations (QPOs) with frequencies ranging from similar to 300 to similar to 1200 Hz have been discovered in the X-ray emi ssion from 14 neutron stars in low-mass binary systems and from another neu tron star in the direction of the Galactic center. These kilohertz QPOs are very strong, with rms relative amplitudes ranging up to similar to 15% of the total X-ray count rate, and are remarkably coherent, with frequency-to- FWHM ratios as large as similar to 200. Two simultaneous kilohertz QPOs dif fering in frequency by similar to 250-350 Hz have been detected in 12 of th e 15 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 similar to 10(7) -10(10) G and a spin frequency of a few hundred hertz, accreting gas via a Keplerian disk. Some of the accreting gas is channeled by the stellar magne tic held but some remains in a Keplerian disk flow that penetrates to withi n a few kilometers of the stellar surface. The frequency of the higher freq uency QPO in a kilohertz QPO pair is the Keplerian frequency at a radius ne ar the sonic point at the inner edge of the Keplerian flow, whereas the fre quency of the lower frequency QPO is the difference between the Keplerian f requency at a radius near the sonic point and the fundamental or first over tone of the stellar spin frequency. The difference between the frequencies of the pair of QPOs is therefore close to (but not necessarily equal to) th e stellar spin frequency. The amplitudes of the QPOs at the sonic-point Kep lerian frequency and at the beat frequency depend on the strength of the ne utron star's magnetic held and the accretion rate, and hence one or both of these QPOs may sometimes be undetectable. Oscillations at the stellar spin frequency and its overtones are expected to be weak but may sometimes be d etectable. This model is consistent with the magnetic field strengths, accr etion rates, and scattering optical depths inferred from previous modeling of the X-ray spectra and rapid X-ray variability of the atoll and Z sources . It explains naturally the frequencies of the kilohertz QPOs and the simil arity of these frequencies in sources with different accretion rates and ma gnetic fields. The model also explains the high coherence and large amplitu des of the kilohertz QPOs and the steep increase of QPO amplitude with phot on energy. The increase in QPO frequency with inferred accretion rate seen in many sources is also understandable in this model. We show that if the f requency 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 u pper bounds on the masses and radii of the neutron stars in the kilohertz Q PO sources and provide new constraints on the equation of state of matter a t 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.