Zdenek Stuchlik (SU Opava, Czech Republic)

Multi-resonance orbital model of high-frequency quasiperiodic oscillations: possible high precision
determination of black hole and neutron star spin

Using known frequencies of the 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 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. The LOFT project enables a large improvement in
the precision of the timing measurements that can have some important consequences. We discuss the
possibility of higher precision of the black hole dimensionless spin measurements in the framework of 
multi-resonance models of QPOs inspired by observations of more than two resonant frequencies in some
sources. 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. We focus on the special case of duplex
frequencies, when the top, bottom, or mixed frequency is common for the two different radii where the
resonances occur giving triple frequency sets. For each type of both the direct and simple combinational
resonances, the set of triple frequency ratios and the related spin are given. The resonances are considered
up to n=5 as the excitation of higher order resonances is improbable. When two (or more) versions of
resonance could occur at the same radius, the probability of resonant phenomena is strongest because of
possible cooperative effects between the resonances. The method of triple frequency sets could be used
also for the neutron star systems, if eigenfrequencies of their QPOs are determined at some properly defined
resonant points. In the case of doubled twin peak QPOs excited at two different radii with common top,
bottom, or mixed frequency, the black hole dimensionless spin a is given by the triple frequency ratio set
only. The spin is determined precisely, but not uniquely, as the same frequency set could correspond to more
than one concrete spin a. The black hole mass is given by the frequency magnitudes.