Determination of Black Hole Masses in Galactic Black Hole Binaries using Scaling of Spectral and Variability Characteristics

Abstract

We present a study of correlations between X-ray spectral and timing properties observed from a number of Galactic Black Hole (BH) binaries during hard-soft state spectral evolution. We analyze 17 transition episodes from 8 BH sources observed with RXTE. Our scaling technique for BH mass determination uses a correlation between spectral index and quasi-periodic oscillation (QPO) frequency. In addition, we use a correlation between index and the normalization of the disk "seed" component to cross-check the BH mass determination and estimate the distance to the source. While the index-QPO correlations for two given sources contain information on the ratio of the BH masses in those sources, the index-normalization correlations depend on the ratio of the BH masses and the distance square ratio. In fact, the index-normalization correlation also discloses the index-mass accretion rate saturation effect given that the normalization of disk "seed" photon supply is proportional to the disk mass accretion rate. We present arguments that this observationally established index saturation effect is a signature of the bulk motion (converging) flow onto black hole which was early predicted by the dynamical Comptonization theory. We use GRO J1655-40 as a primary reference source for which the BH mass, distance and inclination angle are evaluated by dynamical measurements with unprecedented precision among other Galactic BH sources. We apply our scaling technique to determine BH masses and distances forCygnus 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.