The Converging Inflow Spectrum Is an Intrinsic Signature for a Black Hole: Monte Carlo Simulations of Comptonization on Free-falling Electrons

An accreting black hole is, by definition, characterized by the drain. Namely, matter falls into a black hole much the same way as water disappears down a drain: matter goes in and nothing comes out. As this can only happen in a black hole, it provides a way to see ``a black hole,'' a unique observational signature of black holes. The accretion proceeds almost in a free-fall manner close to the black hole horizon, where the strong gravitational field dominates the pressure forces. In this paper we calculate (by using Monte Carlo simulations) the specific features of X-ray spectra formed as a result of upscattering of the soft (disk) photons in the converging inflow (CI) within about 3 Schwarzschild radii of the black hole. The full relativistic treatment has been implemented to reproduce these spectra. We show that spectra in the soft state of black hole systems (BHS) can be described as the sum of a thermal (disk) component and the convolution of some fraction of this component with the CI upscattering spread (Green's) function. The latter boosted photon component is seen as an extended power law at energies much higher than the characteristic energy of the soft photons. We demonstrate the stability of the power spectral index (α=1.8+/-0.1) over a wide range of the plasma temperature, 0-10 keV, and mass accretion rates (higher than 2 in Eddington units). We also demonstrate that the sharp high-energy cutoff occurs at energies of 200-400 keV, which are related to the average energy of electrons m_ec² impinging on the event horizon. The spectrum is practically identical to the standard thermal Comptonization spectrum (Hua & Titarchuk) when the CI plasma temperature is getting of order of 50 keV (the typical ones for the hard state of BHS). In this case one can see the effect of the bulk motion only at high energies, where there is an excess in the CI spectrum with respect to the pure thermal one. Furthermore, we demonstrate that the change of spectral shapes from the soft X-ray state to the hard X-ray state is clearly to be related to the temperature of the bulk flow. We derive a generic formula for the temperature of the emitting region (CI) that depends on the ratio of the energy release in this very region and in the disk. Using this formula, we demonstrate that the temperature of the emission region in the hard state of the BHS is approximately 2 times higher than the ones of neutron star systems (NSS) in the hard state, which is confirmed by recent RXTE and Beppo-SAX observations of the hard state of NSS. The effect of the bulk Comptonization compared with the thermal one is getting stronger when the plasma temperature drops below 10 keV. These Monte Carlo simulated CI spectra are an inevitable stamp of the BHS where the strong gravitational field dominates the pressure forces.