Radiative Spectra from Disk Corona and Inner Hot Flow in Black-Hole X-Ray Binaries

Abstract

Abstract To understand the origin of hard X-ray emissions from black-hole X-ray binaries during their low/hard states, we calculate the X-ray spectra of black-hole accretion flow for the following three configurations of hot and cool media: (a) an inner hot-flow and a cool outer disk (inner hot-flow model), (b) a cool disk sandwiched by disk coronae (disk-corona model), and (c) a combination of those two (hybrid model). The basic features we require for successful models are (i) significant hard X-ray emission whose luminosity exceeds that of soft X-rays, (ii) high hard X-ray luminosities in the range of (0.4–30) $\times$ 10$^{37}$erg s$^{-1}$, and (iii) the existence of two power-law components in the hard X-ray band with photon indices of $\Gamma_{\rm s} \sim$ 2 $\gt \Gamma_{\rm h}$, where $\Gamma_{\rm s}$ and $\Gamma_{\rm h}$ are the photon indices of the softer ($\lt$ 10 keV) and harder ($\gt$10 keV) power-law components, respectively. The contributions by non-thermal electrons or time-dependent evolution are not considered. We find that Models (a) and (b) can be ruled out, since the spectra are always dominated by the soft component, and since only one power-law component, at most, can be reproduced. Only Model (c) can account for sufficiently strong hard X-ray emissions, as well as the existence of the two power-law components, for a large ratio of the accretion rate in the corona to that in the thin disk. The outer-disk corona (where the Compton $y$-parameter is smaller, $y \lt$ 1) produces the softer power-law component with a photon index of $\Gamma_{\rm s} \sim$ 2, whereas the inner hot-flow (where $y \gtrsim$ 1) generates the harder component with $\Gamma_{\rm h} \lt $ 2. This model can also account for the observed relationship between the photon index and the reflection fraction.