**Publication date:** Dec 2007

**Abstract:**

Using known frequencies of the accretion disc twin peak quasiperiodic

oscillations (QPOs) and the known mass of the central black hole, the

black hole dimensionless spin a can be determined, assuming a concrete

version of the orbital resonance model. However, because of large range

of observationally limited values of the black hole mass, its spin can

be estimated with a low precision only. Higher precision of the black

hole spin measurement is possible in the framework of multi-resonance

model of QPOs inspired by complex high-frequency QPO patterns observed

in some black hole and neutron star systems. In the simple orbital

resonance models we determine the spin and mass dependence of the twin

peak frequencies for non-linear resonances of oscillations with the

epicyclic and Keplerian frequencies or their combinations in the case of

a general rational frequency ratio n : m, n > m. In the

multi-resonant model, the twin peak resonances are combined properly to

give the observed frequency set. The multi-resonant model is proposed in

three distinct versions. In the first one, related probably to the

neutron star binary systems, more instances of one resonance occur at

more specific radii. In the second case, more resonances are sharing one

specific radius, allowing for "cooperative" resonant phenomena in the

field of black holes with a specific value of spin. In the third

("ugly") case, more resonances occur at more specific radii; we restrict

our attention to the case of two such resonant radii. For special values

of the spin, only triple-set of frequencies is observed because of

coincidence of some frequencies, allowing determination of the spin from

the triple frequency ratio set. The spin is determined precisely, but

not uniquely as the same frequency set could be relevant for more than

one concrete spin and combination of resonant oscillations.

**Authors:**

Stuchlík, Zdeněk; Kotrlová, Andrea; Török, Gabriel;