Publication date: Dec 2008
Context: XTE J1650-500 is a Galactic black-hole binary system for which
at least one high-frequency QPO at 250 Hz has been reported. Moreover
there are indications that the system harbours a near-extreme Kerr black
hole with a spin aast ≃ 0.998 and mass M_BH ≲ 7.3
Msun. Recently it was discovered that the orbital 3-velocity
of test-particle (geodesical) discs orbiting Kerr black holes with a
spin aast > 0.9953, analyzed in the locally non-rotating
frames, reveals a hump near the marginally stable orbit. It was
suggested that the hump could excite the epicyclic motion of particles
near the ISCO with frequencies typical for high-frequency QPOs. The
characteristic frequency of the hump-induced oscillations was defined as
the maximal positive rate of change of the LNRF-related orbital velocity
with the proper radial distance. If the characteristic “humpy frequency”
and the radial epicyclic frequency are commensurable, strong resonant
phenomena are expected.
Aims: We apply the idea of hump-induced
oscillations in accretion discs around near-extreme Kerr black holes to
estimate the black-hole mass in the XTE J1650-500 binary system.
Methods: For the Kerr black hole with spin aast ≃ 0.9982
the characteristic “humpy frequency” and the radial epicyclic frequency
are in the ratio 1:3 at the orbit where the positive rate of change of
the LNRF-related orbital velocity with the proper radial distance is
maximal. Identifying the radial epicyclic frequency with the observed
250 Hz QPO, we arrive at the mass of the black hole. In this method the
ratio of frequencies determines the spin (and vice versa), and the
values of the frequencies determine the black-hole mass.
The mass of the Kerr black hole in XTE J1650-500 binary system is
estimated to be around 5.1 Msun.
Slaný, P.; Stuchlík, Z.;