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.;