Discovery of photon index saturation in the black hole binaries

We present a study of the correlations between spectral, timing properties and mass accretion rate observed in X-rays from the eight Galactic Black Hole (BH) binaries during the transition between hard and soft states. We analyze all transition episodes from X-ray sources observed with Rossi X-ray Timing Explorer (RXTE). We show that broad-band energy spectra of Galactic sources during all these spectral states can be adequately presented by Bulk Motion Comptonization (BMC) model. We also present observable correlations between the index and the normalization of the disk "seed" component. The use of "seed" disk normalization, which is presumably proportional to mass accretion rate in the disk, is crucial to establish the index saturation effect during the transition to the soft state. We discovered the photon index saturation of the hard spectral components at values of 2.1-3. We present a physical model which explains the index-seed photon normalization correlations. We argue that the index saturation effect of the hard component (BMC1) is due to the soft photon Comptonization in the converging inflow close to BH. We apply our scaling technique to determine BH masses and distances for Cygnus X-1, GX 339-4, 4U 1543-47, XTE J1550-564, XTE J1650-500, H 1743-322 and XTE J1859-226. Good agreement of our results for sources with known values of BH masses and distance provides an independent verification for our scaling technique.