Multi-resonance orbital model of HF QPOs

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.