Lense-Thirring Precession and Quasi-periodic Oscillations in X-Ray Binaries

It has recently been suggested that gravitomagnetic precession of the inner part of the accretion disk, possibly driven by radiation torques, may be responsible for some of the quasi-periodic X-ray brightness oscillations (QPOs) and other spectral features with frequencies between 20 and 300 Hz observed in the power spectra of some low-mass binary systems containing accreting neutron stars and black hole candidates. We have explored the free and driven normal modes of geometrically thin disks in the presence of gravitomagnetic and radiation warping torques. We have found a family of low-frequency gravitomagnetic (LFGM) modes with precession frequencies that range from the lowest frequency allowed by the size of the disk up to a certain critical frequency ω_crit, which is ~1 Hz for a compact object of solar mass. The lowest frequency (lowest order) LFGM modes are similar to the previously known radiation warping modes, extend over much of the disk, and have damping rates ≳10 times their precession frequencies. The highest frequency LFGM modes are tightly wound spiral corrugations of the disk that extend to ~10 times its inner radius and have damping rates ≳10³ times their precession frequencies. A radiation warping torque can cause a few of the lowest frequency LFGM modes to grow with time, but even a strong radiation warping torque has essentially no effect on the LFGM modes with frequencies ≳10^-4 Hz. We have also discovered a second family of high-frequency gravitomagnetic (HFGM) modes with precession frequencies that range from ω_crit up to slightly less than the gravitomagnetic precession frequency ω_gm,i of a particle at the inner edge of the disk, which is 30 Hz if the disk extends inward to the innermost stable circular orbit around a 2 M_☉ compact object with dimensionless angular momentum cJ/GM² = 0.2. The lowest frequency HFGM modes are very strongly damped and have warp functions and precession frequencies very similar to those of the highest frequency LFGM modes. In contrast, the highest frequency (lowest order) HFGM modes are very localized spiral corrugations of the inner disk and are weakly damped, with Q-values of ~2-50. We discuss the implications of our results for the observability of Lense-Thirring precession in X-ray binaries.