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    Humpy LNRF-velocity profiles in accretion discs orbiting almost extreme Kerr black holes. A possible relation to quasi-periodic oscillations

    Zdeněk Stuchlík · Březen 01, 2007 · Fyzika · 0 comments
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    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.;

    https://ui.adsabs.harvard.edu/abs/2007A&A…463..807S

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