Spectral Index and Quasi-Periodic Oscillation Frequency Correlation in   Black Hole (BH) Sources: Observational Evidence of Two Phases and Phase   Transition in BHs
  Recent studies have shown that strong correlations are observed between the low frequencies (1-10 Hz) of quasiperiodic oscillations (QPOs) and the spectral power law index of several Black Hole (BH) candidate sources, in low hard state, steep power-law (soft) state and in transition between these states. We provide a model, that identifies and explains the origin of the QPOs and how they are imprinted on the properties of power-law flux component. We argue the existence of a bounded compact coronal region which is a natural consequence of the adjustment of Keplerian disk flow to the innermost sub-Keplerian boundary conditions near the central object and that ultimately leads to the formation of a transition layer (TL) between the adjustment radius and the innermost boundary. The model predicts two phases or states dictated by the photon upscattering produced in the TL: (1) hard state, in which the TL is optically thin and very hot (kT ~ 50 keV) producing photon upscattering via thermal Componization; the photon spectrum index Gamma~1.7 for this state is dictated by gravitational energy release and Compton cooling in an optically thin shock near the adjustment radius; (2) a soft state which is optically thick and relatively cold (kT~5 keV); the index for this state, Gamma~2.8 is determined by soft-photon upscattering and photon trapping in converging flow into BH. 
Lev Titarchuk (GMU/NRL/GSFC) and Ralph Fiorito (UMD/GSFC)