Publication date: Apr 2013
Abstract:
Context. Using known frequencies of the twin-peak high-frequency
quasiperiodic oscillations (HF QPOs) and known mass of the central black
hole, the black-hole dimensionless spin a can be determined by assuming
a concrete version of the resonance model. However, a wide range of
observationally limited values of the black hole mass implies low
precision of the spin estimates. Aims: We discuss the possibility
of higher precision for the black hole spin a measurements in the
framework of a multi-resonance model inspired by observations of more
than two HF QPOs in the black hole systems, which are expected to occur
at two (or more) different radii of the accretion disc. This framework
is also applied in a modified form to the neutron star systems.
Methods: 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. For
the black hole systems 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.
Results: The sets of triple frequency ratios and the related spin
a are given. The resonances are considered up to n = 5 since excitation
of higher order resonances is improbable. The strong resonance model for
"magic" values of the black hole spin means that two (or more) versions
of resonance could occur at the same radius, allowing cooperative
effects between the resonances. For neutron star systems we introduce a
resonant switch model that assumes switching of oscillatory modes at
resonant points. Conclusions: In the case of doubled twin-peak HF
QPOs excited at two different radii with common top, bottom, or mixed
frequency, the black hole spin a is given by the triple frequency ratio
set. The spin is determined precisely, but not uniquely, because the
same frequency set could correspond to more than one concrete spin a.
The black hole mass is given by the magnitude of the observed
frequencies. The resonant switch model puts relevant limits on the mass
and spin of neutron stars, and we expect a strong increase in the
fitting procedure precision when different twin oscillatory modes are
applied to data in the vicinity of different resonant points. We expect
the multi-resonance model to be applicable to data from the planned LOFT
or similar X-ray satellite observatory.
Appendices are available in electronic form at http://www.aanda.org
Authors:
Stuchlík, Z.; Kotrlová, A.; Török, G.;