Sonic-Point Model of Kilohertz QPOs in LMXBs

Quasi-periodic brightness oscillations with frequencies in the range 500--1200 Hz have recently been discovered in seven low-mass X-ray binaries. These oscillations are very strong, with rms amplitudes ranging up to $\sim 20$%, and are remarkably coherent, with $\nu/\Delta\nu$ ratios as high as $\sim 200$. A pair of high-frequency QPOs has been detected in four of the seven sources. Here we propose a model for these kilohertz quasi-periodic oscillations in which the higher ($\sim 900 \dash 1200$ Hz) frequency is the Keplerian frequency $\nu_{Ks}$ at the sonic point at the inner edge of the Keplerian disk and the lower ($\sim 600 \dash 800$ Hz) frequency is the beat between $\nu_{Ks}$ and the $\sim 150 \dash 500$ Hz spin frequency $\nu_{\rm spin}$ of a weakly magnetic ($B_s \sim 10^7 \dash 10^9$ G) neutron star. If the magnetic field of the neutron star is too weak ($B_s \ll 10^7$ G) or the mass accretion rate is too low, this beat frequency may not be visible. This model is consistent with the magnetic fields, accretion 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, and explains naturally the observed frequencies of the kilohertz QPOs, their large amplitude and high coherence, and the steep increase of their amplitudes with photon energy. If the sonic-point origin of these QPOs is confirmed, measurements of kilohertz quasi-periodic oscillation frequencies in LMXBs will provide new bounds on the masses of neutron stars and new constraints on the equation of state of matter at high densities.