**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 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. Results: The mass of the Kerr

black hole in XTE J1650-500 binary system is estimated to be around 5.1

Msun.

**Authors:**

Slaný, P.; Stuchlík, Z.;