1998ApJ...509..793M

Quasi-periodic X-ray brightness oscillations (QPOs) with frequencies ≳1 kHz have now been discovered in more than a dozen neutron stars in low-mass X-ray binary systems using the Rossi X-Ray Timing Explorer. There is strong evidence that the frequencies of some kilohertz oscillations are the orbital frequencies of accreting gas in nearly circular orbits around these stars. Some stars that produce kilohertz QPOs may have spin frequencies ≳400 Hz. For spin rates this high, first-order analytic treatments of the effects of the star's rotation on its structure and the spacetime are inaccurate. Here we use the results of a large number of fully relativistic, self-consistent numerical calculations of the stellar structure of rapidly rotating neutron stars and their interior and exterior spacetimes to investigate the constraints on the properties of such stars that can be derived if stable circular orbits of various frequencies are observed. We have computed the equatorial radius of the star, the radius of the innermost stable circular orbit, and the frequency of the highest frequency stable circular orbit as functions of the stellar spin rate for spin rates up to the maximum possible and for several illustrative equations of state. Our calculations show that the upper bounds on the stiffness of neutron star matter implied by a given orbital frequency are typically significantly stricter for stars with spin frequencies ≳400 Hz than for slowly rotating stars.