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 , the inner radii of radiation pressure dominated accretion discs are expected to i ) become effectively optically thin and ii ) produce significant luminosities .
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 \sqrt { 7 / 3 } \simeq 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 or lower luminosities .
Future X-ray telescopes could detect additional HFQPOs from 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 \sim 0.4 - 0.7 .