Publication date: Apr 2007
Abstract:
Change of sign of the LNRF-velocity radial gradient has been found for
accretion discs orbiting a rapidly rotating Kerr black hole with spin a
> 0.9953 (Keplerian discs) and a > 0.99979 (marginally stable
thick discs). 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 shall 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 constant,
i.e., independent of spin, 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, there is ratio of the
radial epicyclic and the humpy frequency ˜1:12, i.e., the
critical frequency is close to the low-frequency QPOs related to the
high-frequency QPOs in such spacetimes. For a > 0.996 the resonant
orbit with the ratio 4:1 between the vertical and radial epicyclic
oscillations occurs in the region of the hump. In the case of thick
discs, the situation is more complex due to the dependence on the
distribution of the specific angular momentum L characterizing the disc
rotation. For L = const tori and (1-a) < 10-6 the
frequency ratios of the humpy frequency and the epicyclic frequencies
are again constant and independent of both the spin and the specific
angular momentum.
Authors:
Stuchlík, Zdeněk; Slaný, Petr; Török, Gabriel;