**Publication date:** n/a 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.;