**Publication date:** Dec 2008

**Abstract:**

High-frequency twin peak quasiperiodic oscillations (QPOs) are observed in four microquasars, i.e., Galactic black hole binary systems, with frequency ratio very close to 3:2. In the microquasar GRS 1915+105 the structure of QPOs exhibits additional frequencies and more than two frequencies are observed in the Galaxy nuclei Sgr A* or in some extragalactic sources (NGC 4051, MCG-6-30-15 and NGC 5408 X-1). The observed QPOs can be explained by a variety of the orbital resonance model versions assuming resonance of oscillations with the Keplerian frequency ν_{K} or the vertical epicyclic frequency ν_{θ}, and the radial epicyclic frequency ν_{r}, or some combinations of these frequencies. Generally, different resonances could arise at different radii of an accretion disk. However, we have shown that for special values of dimensionless black hole spin a strong resonant phenomena could occur when different resonances can be excited at the same radius, as cooperative phenomena between the resonances may work in such situations. The special values of a are determined for triple frequency ratio sets ν_{K}:ν_{θ}:ν_{r}=s:t:u with s,t,u being small integers. The most promising example of such a special situation arises for black holes with extraordinary resonant spin a=0.983 at the radius r=2.395 M, where ν_{K}:ν_{θ}:ν_{r}=3:2:1. We also predict that when combinations of the orbital frequencies are allowed, QPOs with four frequency ratio set 4:3:2:1 could be observed in the field of black holes with a=0.866,0.882 and 0.962. Assuming the extraordinary resonant spin a=0.983 in Sgr A*, its QPOs with observed frequency ratio ≈3:2:1 imply the black hole mass in the interval 4.3×10^{6} M_{solar}< M< 5.4×10^{6} M_{solar}, in agreement with estimates given by other, independent, observations.

**Authors:**

Stuchlík, Z.; Kotrlová, A.; G. Török;