Spectral index as a function of mass accretion rate in black hole sources: Monte carlo simulations and an analytical description

Abstract

We present herein a theoretical study of correlations between spectral indexes of X-ray emergent spectra and mass accretion rate (ṁ) in black hole (BH) sources, which provide a definitive signature for BHs. It has been firmly established, using the Rossi X-ray Timing Explorer (RXTE) in numerous BH observations during hard-soft state spectral evolution, that the photon index of X-ray spectra increases when ṁ increases and, moreover, the index saturates at high values of ṁ. In this paper, we present theoretical arguments that the observationally established index saturation effect versus mass accretion rate is a signature of the bulk (converging) flow onto the BH. Also, we demonstrate that the index saturation value depends on the plasma temperature of converging flow. We selfconsistently calculate the Compton cloud (CC) plasma temperature as a function of mass accretion rate using the energy balance between energy dissipation and Compton cooling. We explain the observable phenomenon, index-ṁ correlations using a Monte Carlo simulation of radiative processes in the innermost part (CC) of a BH source and we account for the Comptonization processes in the presence of thermal and bulk motions, as basic types of plasma motion.We show that, when ṁ increases, BH sources evolve to high and very soft states (HSS and VSS, respectively), in which the strong blackbody(BB)-like and steep power-law components are formed in the resulting X-ray spectrum. The simultaneous detections of these two components strongly depends on sensitivity of high-energy instruments, given that the relative contribution of the hard power-lawtail in the resultingVSS spectrum can be very low, which is why, to date RXTE observations of the VSS X-ray spectrum have been characterized by the presence of the strong BB-like component only.We also predict specific patterns for high-energy e-fold (cutoff) energy (E fold) evolution with ṁ for thermal and dynamical (bulk) Comptonization cases. For the former case, Efold monotonically decreases with ṁ, in the latter case, the Efold decrease is followed by its increase at high values of ṁ. The observational evolution of Efold versus ṁ can be another test for the presence of a converging flow effect in the formation of the resulting spectra in the close vicinity of BHs. © 2011 The American Astronomical Society. All rights reserved.