Spectral Properties of Accretion Disks Around Galactic and Extragalactic Black Holes

Abstract

We study the spectral properties of a very general class of accretion disks which can be decomposed into three distinct components apart from a shock at $r=r_s$: (1) An optically thick Keplerian disk on the equatorial plane ($r>r_s$), (2) A sub-Keplerian optically thin halo above and below this Keplerian disk $r>r_s$ and (3) A hot, optically slim, $τ\sim 1$ postshock region $r<r_s\sim 5-10 r_g$ where $r_g$ is the Schwarzschild radius. The postshock region intercepts soft photons from the Keplerian component and reradiates them as hard X-rays and $γ$ rays after Comptonization. We solve two-temperature equations in the postshock region with Coulomb energy exchange between protons and electrons, and incorporating radiative processes such as bremsstrahlung and Comptonization. We also present the exact prescription to compute the reflection of the hard X-rays from the cool disk. We produce radiated spectra from both the disk components as functions of the accretion rates and compare them with the spectra of galactic and extragalactic black hole candidates. We find that the transition from hard state to soft state is smoothly initiated by a single parameter, namely, the mass accretion rate of the disk. In the soft state, when the postshock region is very optically thick and cooled down, bulk motion of the converging flow determines the spectral index to be about $1.5$ in agreement with observations.