Publication date: Dec 2007
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 hole mass, 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 multi-resonant 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 for more than
one concrete spin and combination of resonant oscillations.
Authors:
Stuchlík, Zdeněk; Kotrlová, Andrea; Török, Gabriel;