Spectral Index and Quasi-Periodic Oscillation Frequency Correlation in Black Hole (BH) Sources: Observational Evidence of Two Phases and Phase Transition in BHs
Lev Titarchuk
Naval Research Laboratory / George Mason University
lev.titarchuk@nrl.navy.mil
Additional authors: Ralph Fiorito
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 (>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. the X-ray emission from BHC's. 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 ~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~ 10 keV and less); the index for this state, ~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 \nu_{high} is related to the gravitational (close to Keplerian) frequency \nu_{K} at the outer (adjustment) radius and \nu_{low} is related to the TL's normal mode (magnetoacoustic) oscillation frequency \nu_{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.
