Power-Law Spectra as a Result of Comptonization of the Soft Radiation in a Plasma Clou

Recent studies have shown that strong correlations are observed between the low frequencies (1-10 Hz) of quasi-periodic 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 transitions between these states. The observations indicate that the X-ray spectra of such state (phases) show the presence of a power-law component and are sometimes related to simultaneous radio emission, indicating 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 the power-law flux component. We argue for the existence of a bounded compact coronal region that is a natural consequence of the adjustment of the 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) a hard state, in which the TL is optically thin and very hot (kT k 50 keV), producing photon upscattering via thermal Comptonization (the photon spectrum index I?-1.7 for this state is dictated by gravitational energy release and Compton cooling in an optically thin shock near the adjustment radius), and (2) a soft state that is optically thick and relatively cold (kT S 5 k e y the index for this state, r -2.8, is determined by soft-photon upscattering and photon trapping in a converging flow into the BH). In the TL model for the corona, the QPO frequency Vhigh is related to the gravitational (close to Keplerian) frequency VK at the outer (adjustmcnt) radius and zqOw is related to the TL's normal mode (magnetoacoustic) oscillation frequency v m . 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.

We analyze the exact general relativistic integrodi †erential equation of radiative transfer describing the interaction of low-energy photons with a Maxwellian distribution of hot electrons in the gravitational Ðeld of a Schwarzschild black hole. We prove that, owing to Comptonization, an initial arbitrary spectrum of low-energy photons unavoidably results in spectra characterized by an extended power-law feature. We examine the spectral index by using both analytical and numerical methods for a variety of physical parameters as such the plasma temperature and the mass accretion rate. The presence of the event horizon as well as the behavior of the null geodesics in its vicinity largely determine the dependence of the spectral index on the Ñow parameters. We come to the conclusion that the bulk motion of a converging Ñow is more efficient in upscattering photons than thermal Comptonization, provided that the electron temperature in the Ñow is of order of a few kiloÈelectron volts or less. In this case, the spectrum observed at inÐnity consists of a soft component, which is produced by those input photons that escape after a few scatterings without any signiÐcant energy change, and a hard component (described by a power law), which is produced by the photons that underwent signiÐcant upscattering. The luminosity of the power-law component is relatively small compared to that of the soft component. For accretion into a black hole, the spectral energy index of the power law is always higher than 1 for plasma temperatures of order of a few kiloÈelectron volts. This result suggests that the bulk motion Comptonization might be responsible for the power-law spectra seen in the black hole X-ray sources.