Spectral Index and Quasi‐Periodic Oscillation Frequency Correlation in Black Hole Sources: Observational Evidence of Two Phases and Phase Transition in Black Holes

Abstract

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.

Quasi periodic oscillations in black hole binaries

“…-Instabilities: Titarchuk and Fiorito, 2004 proposed the so called transition layer model, where type-C QPOs are the result of viscous magneto-acoustic oscillations of a spherical bounded transition layer, formed by matter from the accretion disc adjusting to the sub-keplerian www.an-journal.org boundary conditions near the central compact object. Cabanac et al, 2010 proposed a model to explain simultaneously type-C QPOs and the associated broad band noise.…”

SPECTRAL AND TIMING PROPERTIES OF THE BLACK HOLE X-RAY BINARY H1743–322 IN THE LOW/HARD STATE STUDIED WITHSUZAKU

“…LF QPOs (below 10 Hz) were detected in many BHXBs during the low/hard and intermediate states, such as XTE J150−564 (e.g., Cui et al 1999;Sobczak et al 1999) and GX 339−4 (e.g., Miyamoto et al 1991;Motta et al 2011;Tamura et al 2012). Previous studies suggested that their frequencies are positively correlated with the photon index of the Comptonization below ≈10 Hz, at which the correlation saturates (Vignarca et al 2003;Titarchuk & Fiorito 2004;Titarchuk & Shaposhnikov 2005). Our results follow this ubiquitous correlation between the QPO frequency and the photon index; the photon index becomes lower by ≈0.03 in the ≈30% decrease of the QPO frequency.…”

A possible interpretation for the apparent differences in LFQPO types in microquasars

“…Up to now, theoretical models of LFQPO have focused on type C LFQPO and tended to tie its frequency to a magnetoacoustical frequency (e.g. Titarchuk & Fiorito 2004) or to the Keplerian frequency at some radius in the disk (e.g. Tagger & Pellat 1999).…”