**Publication date:** Feb 2013

**Abstract:**

Using known frequencies of the twin peak high-frequency quasiperiodic

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

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

version of the resonance model. However, large range of observationally

limited values of the black hole mass implies a low precision of the

spin estimates. We discuss the possibility of higher precision of the

black hole spin a measurements in the framework of multi-resonance model

inspired by observations of more than two HF QPOs in some black hole

sources. We determine the spin and mass dependence of the twin peak

frequencies with a general rational ratio n:m assuming a non-linear

resonance of oscillations with the epicyclic and Keplerian frequencies

or their combinations. In the multi-resonant model, the twin peak

resonances are combined properly to give the observed frequency set. We

focus on the special case of duplex frequencies, when the top, bottom,

or mixed frequency is common at two different radii where the resonances

occur giving triple frequency sets.

**Authors:**

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