Determination of Black Hole Mass in Cygnus X‐1 by Scaling of Spectral Index–QPO Frequency Correlation

Abstract

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) frequency - photon index 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 QPO frequency-Gamma plane. Titarchuk & Fiorito presented strong theoretical and observational arguments that the QPO frequency values in this QPO frequency-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 which 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 QPO-index 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_Sun 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 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 +/- 1.5) M_Sun in this source which is consistent with the previous BH mass estimate in GRS 1915 of (13.3 +/- 4) M_Sun. We obtain the BH mass in Cyg X-1 in the range (8.7 +/- 0.8) M_Sun.