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;