Mass estimate of the XTE J1650-500 black hole from the Extended Orbital Resonance Model for high-frequency QPOs

Abstract

XTE J1650-500 is a Galactic black-hole binary system for which at least one high-frequency QPO at 250Hz was reported. Moreover there are indications that the system harbours a near-extreme Kerr black-hole with the spin near 0.998 and mass M<7.3M_sun. Recently it was discovered that the orbital 3-velocity of Keplerian (geodesical) discs orbiting Kerr black holes with the spin a>0.9953, being analyzed in the locally non-rotating frames, reveals a hump near the marginally stable orbit. Further it was suggested that the hump could excite the epicyclic motion of particles near the ISCO with frequencies typical for high-frequency QPOs. 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. For the Kerr black hole with the spin a=0.9982 the "humpy frequency" and the radial epicyclic frequency are in ratio 1:3. Identifying the radial epicyclic frequency with the observed 250Hz QPO, we get the mass of the black hole in XTE J1650-500 near 5.1M_sun.