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. Name ly, matter falls into a black hole much the same way as water disappears do wn a drain: matter goes in and nothing comes out. As this can only happen i n a black hole, it provides a way to see "a black hole," a unique observati onal signature of black holes. The accretion proceeds almost in a free-fall manner close to the black hole horizon, where the strong gravitational fie ld dominates the pressure forces. In this paper we calculate (by using Mont e Carlo simulations) the specific features of X-ray spectra formed as a res ult of upscattering of the soft (disk) photons in the converging inflow (CI ) within about 3 Schwarzschild radii of the black hole. The full relativist ic 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 t he sum of a thermal (disk) component and the convolution of some fraction o f this component with the CI upscattering spread (Green's) function. The la tter boosted photon component is seen as an extended power law at energies much higher than the characteristic energy of the soft photons. We demonstr ate the stability of the power spectral index (alpha = 1.8 +/- 0.1) over a wide range of the plasma temperature, 0-10 keV, and mass accretion rates (h igher than 2 in Eddington units). We also demonstrate that the sharp high-e nergy cutoff occurs at energies of 200-400 keV, which are related to the av erage energy of electrons m(e)c(2) impinging on the event horizon. The spec trum is practically identical to the standard thermal Comptonization spectr um (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 s ee the effect of the bulk motion only at high energies, where there is an e xcess 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 stat e to the hard X-ray slate is clearly to be related to the temperature of th e bulk flow. We derive a generic formula for the temperature of the emittin g 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 tempera ture 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 therm al 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 w here the strong gravitational field dominates the pressure forces.