Multi-resonance orbital model of high-frequency quasi-periodic oscillations: possible high-precision determination of black hole and neutron star spin. (arXiv:1305.3552v1 [astro-ph.HE])

Multi-resonance orbital model of high-frequency quasi-periodic oscillations: possible high-precision determination of black hole and neutron star spin. (arXiv:1305.3552v1 [astro-ph.HE]):
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 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. We discuss the
possibility of higher precision of the black hole spin 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. 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. The sets of triple frequency ratios and the related spin
are given. 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. 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 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. 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.