Relativistic precession around rotating neutron stars: Effects due to frame dragging and stellar oblateness

General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a nonequatorial orbit precesses about the body's symmetry axis. In this paper we compute the precession frequencies of circular orbits around rapidly rotating neutron stars for a variety of masses and equations of state. The precession frequencies computed are expressed as numerical functions of the orbital frequency observed at infinity. The post-Newtonian expansion of the exact precession formula is examined to identify the relative magnitudes of the precession caused by the Lense-Thirring effect, the usual Newtonian quadrupole effect, and relativistic corrections. The first post-Newtonian correction to the Newtonian quadrupole precession is derived in the limit of slow rotation. We show that the post-Newtonian precession formula is a good approximation to the exact precession close to the neutron star in the slow-rotation limit (up to similar to 400 Hz in the present context). The results are applied to recent RXTE observations of neutron star low-mass X-ray binaries, which display kilohertz quasi-periodic oscillations and, within the framework of beat-frequency models, allow the measurement of both the neutron star spin frequency and the Keplerian frequency of the innermost ring of matter in the accretion disk around it. For a wide range of realistic equations of state, we find that the predicted precession frequency of this ring is close to one-half of the low-frequency (similar to 20-35 Hz) quasi-periodic oscillations seen in several Atoll sources.