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: firstname.lastname@example.org
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
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