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Multi-Resonance Orbital Model Applied to High-Frequency Quasi-Periodic Oscillations Observed in Sgr A*

Kotrlová A., Stuchlík Z., Török G.

Acta Astronomica

2013

Vol. 63, No. 2

275--292

The multi-resonance orbital model of high-frequency quasi-periodic oscillations (HF QPOs) enables precise determination of the black hole dimensionless spin a if observed set of oscillations demonstrates three (or more) commensurable frequencies. The black hole spin a is related to the frequency ratio only, while its mass M is related to the frequency magnitude. The model is applied to the triple frequency set of HF QPOs observed in Sgr A* source with frequency ratio 3:2:1. Acceptable versions of the multi-resonance model are determined by the restrictions on the Sgr A* supermassive black hole mass. The version of strong resonances related to the black hole "magic" spin a=0.983 is acceptable but the version demonstrating the best agreement with the mass restrictions predicts spin a=0.980.

Black Holes Admitting Strong Resonant Phenomena

Stuchlík Z., Kotrlová A., Török G.

Acta Astronomica

2008

Vol. 58, No. 4

441--461

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 Mʘ< M < 5.4×106 Mʘ, in agreement with estimates given by other, independent, observations.