**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 νK or the vertical epicyclic frequency

νθ, and the radial epicyclic frequency

νr, 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

νK:νθ:νr=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

νK:νθ:νr=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

4.3×106 Msolar< M<

5.4×106 Msolar, in agreement with estimates

given by other, independent, observations.

**Authors:**

Stuchlík, Z.; Kotrlová, A.; G. Török;