Mass and Spin Estimates OT Two Near-Extreme Kerr Black Hole Candidates GRS 1915+105 and XTE J1650-500 from the Extended Orbital Resonance Model for High-Frequency Qpos
Humpy profile of the LNRF-related orbital velocity was found for accretion discs orbiting rapidly rotating Kerr black holes with a spin a > 0.9953 (Keplerian discs) and a > 0.99979 (marginally stable thick discs). Maximal positive rate of change of the orbital velocity in terms of the proper radial distance is used to define a local frequency characterising possible physical processes in the disc connected with the velocity hump. Comparing the "humpy frequency" related to distant observers with epicyclic frequencies of perturbed orbital motion, it was shown that in Keplerian discs orbiting near-extreme Kerr black holes (a > 0.998) the the ratio of radial epicyclic frequency and humpy frequency (both evaluated at the same radius) is in terms of small integers asymptotically going to the ratio 3:2 for a → 1. The Extended Orbital Resonance Model with non-linear hump-induced oscillations was applied to two X-ray variable sources GRS 1915+105 and XTE J1650-500. In the case of GRS 1915+105, the model is able to address the whole set of reported QPOs, giving the mass and spin of the central black hole: a = 0.9998; M = 14:8M⊙. For XTE J1650-500, similar ideas give values a = 0.9982; M = 5:1M⊙.