A model of the steep power law spectra and high-frequency quasi-periodic oscillations in luminous black hole X-ray binaries

We propose a new model of the steep power law state of luminous black hole X-ray binaries. The model uses the fact that at high luminosities, radiation pressure dominated accretion discs become effectively optically thin. The gas temperature therefore rises sharply inwards, producing local saturated Compton spectra with rapidly increasing peak energy. These spectra sum together to form a steep power law tail to the spectrum. A given photon energy on this tail corresponds to a narrow range in radius, so that local vertical oscillations of the disc naturally produce high quality high-frequency quasi-periodic oscillations (HFQPOs) in the hard X-ray band. The two lowest order modes have a robust frequency ratio of √ 7/3 ≃ 1.53. This model explains the appearance of steep power law spectra and HFQPOs at high luminosity, the 3:2 HFQPO frequency ratios, and their association with the power law spectral component. We predict an increase in QPO quality factor when the power spectrum is restricted to a narrower photon energy band, and an increase in HFQPO frequency at higher X-ray energies (& 30 keV) or lower luminosities. Future X-ray telescopes could detect additional HFQPOs corresponding to higher order modes. We demonstrate how this model could be used to measure black hole spin from HFQPOs, and qualitatively estimate the spin of GRO J1655-40 as a/M ∼ 0.4 − 0.7.