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 noneq uatorial orbit precesses about the body's symmetry axis. In this paper we c ompute the precession frequencies of circular orbits around rapidly rotatin g neutron stars for a variety of masses and equations of state. The precess ion frequencies computed are expressed as numerical functions of the orbita l 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 quadrup ole effect, and relativistic corrections. The first post-Newtonian correcti on to the Newtonian quadrupole precession is derived in the limit of slow r otation. We show that the post-Newtonian precession formula is a good appro ximation to the exact precession close to the neutron star in the slow-rota tion limit (up to similar to 400 Hz in the present context). The results ar e applied to recent RXTE observations of neutron star low-mass X-ray binari es, which display kilohertz quasi-periodic oscillations and, within the fra mework of beat-frequency models, allow the measurement of both the neutron star spin frequency and the Keplerian frequency of the innermost ring of ma tter in the accretion disk around it. For a wide range of realistic equatio ns of state, we find that the predicted precession frequency of this ring i s close to one-half of the low-frequency (similar to 20-35 Hz) quasi-period ic oscillations seen in several Atoll sources.