Issue |
A&A
Volume 463, Number 3, March I 2007
|
|
---|---|---|
Page(s) | 807 - 816 | |
Section | Astrophysical processes | |
DOI | https://doi.org/10.1051/0004-6361:20066270 | |
Published online | 19 December 2006 |
Humpy LNRF-velocity profiles in accretion discs orbiting almost extreme Kerr black holes
A possible relation to quasi-periodic oscillations
Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, 74601 Opava, Czech Republic e-mail: zdenek.stuchlik@fpf.slu.cz
Received:
18
August
2006
Accepted:
29
November
2006
Context.Change of sign of the LNRF-velocity gradient has been found for
accretion discs orbiting rapidly rotating Kerr black holes with spin
for Keplerian discs and
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 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
is compared to the radial
and vertical
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 and
(with
) are located in vicinity of the “humpy” radius rh
where efficient triggering of oscillations with frequencies ~
could be expected.
Asymptotically (for
) 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
.
In the case of thick discs, the situation is more complex due to
dependence on distribution of the specific angular momentum
determining the disc properties. For
tori and
the frequency ratios of the humpy frequency and the orbital
and epicyclic frequencies are again nearly constant and independent of
both a and
being for the radial epicyclic frequency
close to 4.
In the limiting case of very slender tori (
) the epicyclic resonance radius
for all the
relevant interval of
.
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.
Key words: black hole physics / accretion, accretion disks / relativity
© ESO, 2007
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