**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;