**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;