Publication date: Mar 2007
Abstract:
Context: Change of sign of the LNRF-velocity gradient has been found for
accretion discs orbiting rapidly rotating Kerr black holes with spin
a>0.9953 for Keplerian discs and a>0.99979 for marginally stable
thick discs. Such a „humpy“ LNRF-velocity profiles occur just above the
marginally stable circular geodesic of the black hole spacetimes.
Aims: Aschenbach (2004) has identified the maximal rate of change of
the orbital velocity within the „humpy“ profile with a locally defined
critical frequency of disc oscillations, but it has been done in a
coordinate-dependent form that should be corrected.
Methods: We
define the critical „humpy“ frequency νh in general
relativistic, coordinate independent form, and relate the frequency
defined in the LNRF to the distant observers. At radius of its
definition, the resulting „humpy“ frequency νh is compared to
the radial νr and vertical νv epicyclic
frequencies and the orbital frequency of the discs. We focus our
attention to Keplerian thin discs and perfect-fluid slender tori where
the approximation of oscillations with epicyclic frequencies is
acceptable.
Results: In the case of Keplerian discs, we show that
the epicyclic resonance radii r3{:1} and r4{:1}
(with ν_v{:}ν_r=3{:}1, 4{:}1) are located in vicinity of the „humpy“
radius rh where efficient triggering of oscillations with
frequencies νh could be expected. Asymptotically (for
1-a<10-4) the ratio of the epicyclic and Keplerian
frequencies and the humpy frequency is nearly constant, i.e., almost
independent of a, being for the radial epicyclic frequency
ν_r{:}νh ̃ 3{:}2. In the case of thick discs, the situation
is more complex due to dependence on distribution of the specific
angular momentum ℓ determining the disc properties. For ℓ=const. tori
and 1-a<10-6 the frequency ratios of the humpy frequency
and the orbital and epicyclic frequencies are again nearly constant and
independent of both a and ℓ being for the radial epicyclic frequency
ν_r{:}νh close to 4. In the limiting case of very slender
tori (ℓ̃ℓms) the epicyclic resonance radius
r4{:1}̃ rh for all the relevant interval of
1-a<2× 10-4.
Conclusions: .The hypothetical „humpy“
oscillations could be related to the QPO resonant phenomena between the
epicyclic oscillations in both the thin discs and marginally stable tori
giving interesting predictions that have to be compared with QPO
observations in nearly extreme Kerr black hole candidate systems.
Generally, more than two observable oscillations are predicted.
Authors:
Stuchlík, Z.; Slaný, P.; Török, G.;