**Publication date:** Jan 2008

**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 holemass, 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 multiresonant 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 formore than one concrete

spin and combination of resonant oscillations.

**Authors:**

Stuchlik, Zdenek; Kotrlova, Andrea; Török, Gabriel;