Low-frequency quasi-periodic oscillations spectra and Lense-Thirring precession

We show that the low-frequency quasi-periodic oscillations (QPOs) seen in the power-density spectra of black hole binaries (and neutron stars) can be explained by the Lense-Thirring precession. This has been proposed many times in the past, and simple, single-radius models can qualitatively match the observed increase in QPO frequency by decreasing a characteristic radius, as predicted by the truncated disc models. However, this also predicts that the frequency is strongly dependent on spin, and gives a maximum frequency at the last stable orbit which is generally much higher than the remarkably constant maximum frequency at similar to 10 Hz observed in all black hole binaries. The key aspect of our model, which makes it match these observations, is the precession of a radially extended region of the hot inner flow. The outer radius is set by the truncation radius of the disc as above, but the inner radius lies well outside of the last stable orbit at the point where numerical simulations show that the density drops off sharply for a misaligned flow. Physically motivated analytic estimates for this inner radius show that it increases with a(*), decreasing the expected frequency in a way which almost completely cancels the expected increase with spin, and ties the maximum predicted frequency to around 10 Hz for all a(*). This is the first QPO model which explains both frequencies and spectrum in the context of a well-established geometry for the accretion flow.