Bounds on neutron-star moments of inertia and the evidence for general relativistic frame dragging

Recent x-ray variability observations of accreting neutron stars may provide the first evidence for frame dragging effects around spinning relativistic objects. Motivated by this possibility and its implications for neutron-star structural properties, we calculate new optimal bounds on the masses, radii, and moments of inertia of slowly rotating neutron stars that show kilohertz quasi-periodic oscillations (QPOs). These bounds are derived under minimal assumptions about the properties of matter at high densities and therefore are largely independent of the unknown equation of state. We further derive a semi-analytical upper bound on the neutron-star moment of inertia without making any assumptions about the equation of state of matter at any density. We use this upper bound to show that the maximum possible nodal precession frequency of an inclined circular orbit around a slowly spinning neutron star is ${\nu }_{\mathrm{NP}}\simeq 45.2({\nu }_{\mathrm{s}}/300\mathrm{}\hspace{0.5em}\mathrm{Hz})$ Hz, where ${\nu }_{\mathrm{s}}$ is the spin frequency of the neutron star. We conclude that the nodal-precession interpretation of low-frequency QPOs in accreting neutron stars is inconsistent with the beat-frequency interpretation of the kHz QPOs or the identification of the highest-frequency QPO with that of a circular Keplerian orbit in the accretion disk.