**Publication date:** Dec 2008

**Abstract:**

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 a_{ast} ≃ 0.998 and mass M_BH ≲ 7.3

M_{sun}. Recently it was discovered that the orbital 3-velocity

of test-particle (geodesical) discs orbiting Kerr black holes with a

spin a_{ast} > 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 a_{ast} ≃ 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.

Results:

The mass of the Kerr black hole in XTE J1650-500 binary system is

estimated to be around 5.1 M_{sun}.

**Authors:**

Slaný, P.; Stuchlík, Z.;