Spectral Index as a Function of Mass Accretion Rate in Black Hole Sources. Monte-Carlo Simulations and an Analytical Description

Abstract

In this Paper, we present theoretical arguments that the observationally established index saturation effect vs mass accretion rate is a signature of the bulk (converging) flow onto the black hole. We demonstrate that the index saturation value depends on the plasma temperature of converging flow. We self-consistently 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- mdot 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 mdot increases, BH sources evolve to high and very soft states (HSS and VSS, respectively), in which the strong blackbody-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-law tail in the resulting VSS spectrum can be very low, which is why, to date {\it RXTE} observations of the VSS X-ray spectrum has been characterized by the presence of the strong BB-like component only. We also predict specific patterns for high-energy efold (cutoff) energy (E_{fold}) evolution with mdot for thermal and dynamical (bulk) Comptonization cases. For the former case, E_{fold} monotonically decreases with mdot, in the latter case, the E_{fold}-decrease is followed by its increase at high values of mdot. The observational evolution of E_{fold} vs mdot can be one more test for the presence of a converging flow effect in the formation of the resulting spectra in the close vicinity of BHs.