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We propose a new model of the steep power law state of luminous black holeX-ray binaries. The model uses the fact that at high luminosities, the innerradii of radiation pressure dominated accretion discs are expected to i) becomeeffectively optically thin and ii) produce significant luminosities. The gastemperature therefore rises sharply inwards, producing local saturated Comptonspectra with rapidly increasing peak energy. These spectra sum together to forma steep power law tail to the spectrum. A given photon energy on this tailcorresponds to a narrow range in radius, so that local vertical oscillations ofthe disc naturally produce high quality high-frequency quasi-periodicoscillations (HFQPOs) in the hard X-ray band. The two lowest order modes have arobust frequency ratio of ~1.53. This model explains the appearance of steeppower law spectra and HFQPOs at high luminosity, the 3:2 HFQPO frequencyratios, and their association with the power law spectral component. We predictan increase in QPO quality factor when the power spectrum is restricted to anarrower photon energy band, and an increase in HFQPO frequency at higher X-rayenergies or lower luminosities. Future X-ray telescopes could detect additionalHFQPOs from higher order modes. We demonstrate how this model could be used tomeasure black hole spin from HFQPOs, and qualitatively estimate the spin of GROJ1655-40 as a/M ~ 0.4 - 0.7.

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