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 states, steep power-law (soft) states and in transition between these states. The observations indicate that the X-ray spectrum of such state (phases) show the presence of a power-law component and are sometimes related to simultaneous radio emission indicated the probable presence of a jet. Strong QPOs (less than 20% rms) are present in the power density spectrum in the spectral range where the power-law component is dominant ( i.e. 60-90% ). This evidence contradicts the dominant long standing interpretation of QPOs as a signature of the thermal accretion disk. We present the data from the literature and our own data to illustrate the dominance of power-law index-QPO frequency correlations. 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 approx. greater than 50 keV) producing photon upscattering via thermal Componization; the photon spectrum index Gamma appprox.1.5 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 (approx. less than 5 keV); the index for this state, Gamma approx. 2.8 is determined by soft-photon upscattering and photon trapping in converging flow into BH. In the TL model for corona the QPO frequency vnu(sub high) is related to the gravitational (close to Keplerian) frequency nu(sub K) at the outer (adjustment) radius and nu(sub low) is related to the TL s normal mode (magnetoacoustic) oscillation frequency nu(sub MA). The observed correlations between index and low and high QPO frequencies are readily explained in terms of this model. We also suggest a new method for evaluation of the BH mass using the index-frequency correlation.