Determination of black hole mass in Cygnus X-1 by scaling of spectral index-QPO frequency correlation

It is well established that timing and spectral properties of Galactic black hole (BH) X-ray binaries (XRB) are strongly correlated. In particular, it has been shown that low-frequency quasi-periodic oscillation (QPO) log v(low) - photon index Gamma correlation curves have a specific pattern. In a number of sources the shape of the index-low-frequency QPO correlations are self-similar with a position offset in the log v(low)-Gamma plane. Titarchuk & Fiorito presented strong theoretical and observational arguments that the QPO frequency values in this log v(low)-Gamma correlation should be inversely proportional to M-BH. A simple translation of the correlation for a given source along the frequency axis leads to the observed correlation for another source. As a result of this translation one can obtain a scaling factor that is simply a BH mass ratio for these particular sources. This property of the correlations offers a fundamentally new method for BH mass determination in XRBs. Here we use the observed QPOYindex correlations observed in three BH sources: GRO J1655 - 40, GRS 1915 + 105, and Cyg X-1. The BH mass of 6.3 +/- 0.5 M-circle dot in GRO J1655 - 40 is obtained using optical observations. RXTE observations during the recent 2005 outburst yielded sufficient data to establish the correlation pattern during both the rise and decay of the event. We use GRO J1655 - 40 as a standard reference source to measure the BH mass in Cyg X-1. We also revisit the GRS 1915+105 data as a further test of our scaling method. We infer the value of BH mass of 15.6 +/- 1.5M(circle dot) in this source, which is consistent with the previous BH mass estimate in GRS 1915 of 13.3 +/- 4 M-circle dot. We obtain the BH mass in Cyg X-1 in the range of 8.7 +/- 0.8 M-circle dot.