**Publication date:** Jan 2012

**Abstract:**

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_{☉}.

**Authors:**

Slaný, Petr; Stuchlík, Zdeněk;