**Publication date:** Jan 2006

**Abstract:**

Change of sign of the velocity gradient (mesured with respect to locally

non-rotating frames) has been found for accretion discs orbiting rapidly

rotating Kerr black holes with spin a > 0.9953 for Keplerian discs

[1] and a > 0.99979 for marginally stable thick discs [2]. Such

„humpy“ orbital velocity profiles occur close to but above the

marginally stable circular geodesic of the black hole spacetimes. The

maximal positive rate of change of the orbital velocity in terms of the

proper radial distance introduces a locally defined critical frequency

characterizing any processes in the disc capable to excite possible

oscillations connected with the velocity hump. Comparing the „humpy

frequency“ related to distant observers with the epicyclic frequencies

we show that in Keplerian discs orbiting extremely rapid Kerr holes (1 –

a < 10-4 ) the ratio of the epicyclic frequencies and the humpy

frequency is nearly constant, i.e., almost independent of a, being ̃ 3 :

2 for the radial epicyclic frequency and ̃ 11 : 2 for the vertical

epicyclic frequency. For black holes with a ̃ 0.996, i.e., when the

resonant phenomena with ratio 3 : 1 between the vertical and radial

epicyclic oscillations occur near the radius of the critical humpy

frequency, the ratio of the radial epicyclic and the humpy frequency is

̃ 12 : 1, which is close to the ratio between high- and low- frequency

QPO in X-ray systems. For a > 0.996 the resonant orbit r4:1 (with the

ratio 4 : 1 between the vertical and radial epicyclic oscillations)

occurs in the region of the hump. Applying the model on the nearly

extreme black hole candidate GRS 1915+105, we conclude that for black

hole parameters M = 14.8M☉ and a = 0.9998 the observed high-frequency

QPOs could be related to the hump-induced oscillations in thin accretion

disc, as the first two QPOs, 41 Hz and 67 Hz, can be identified with the

„humpy frequency“ and the radial epicyclic frequency (at the same

orbit). The other observed QPO-frequencies, 113 Hz and 166 Hz, can be

explained as the combinational ones of the „humpy“ and epicyclic

frequencies.

**Authors:**

Stuchlik, Zdenek; Slany, P.; Török, G.;