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    Marginally stable thick discs with gradient inversion of orbital velocity measured in locally non-rotating frames. A mechanism for excitation of oscillations in accretion discs?

    Zdeněk Stuchlík · Prosinec 01, 2004 · Fyzika · 0 comments
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    Publication date: Dec 2004

    Abstract:
    Aschenbach [Aschenbach, B. (2004). Measuring mass and angular momentum
    of black holes with high-frequency quasi-periodic oscillations.
    Astronomy and Astrophysics, 425:1075-1082] has shown that in Kerr black-
    hole spacetimes with rotation parameter a>0.9953, the Keplerian
    orbital velocity measured in locally non-rotating frames (LNRF) has a
    positive radial gradient in a small region in the vicinity of the event
    horizon and proposed that excitation of oscillations in Keplerian thin
    discs can be related to this fact. Similarly, we show that in the
    equatorial plane of marginally stable thick discs (with uniformly
    distributed specific angular momentum ℓ(r,θ)=const) the orbital velocity
    relative to the LNRF has a positive radial gradient in the vicinity of
    black holes with a>0.99979. The change of sign of the velocity
    gradient occurs just above the centre of the thick toroidal discs, in
    the region where stable circular geodesics of the Kerr spacetime are
    allowed. Therefore, the same mechanism as in the Keplerian discs could
    trigger oscillations in thick discs, but the rotational parameter of the
    Kerr spacetime must be much closer to the extreme-hole state with a=1.
    The global character of the phenomenon is given in terms of topology
    changes of the von Zeipel surfaces (equivalent to equivelocity surfaces
    in the tori with ℓ (r,θ)=const). Toroidal von Zeipel surfaces exist
    around the circle corresponding to the minimum of the equatorial LNRF
    velocity profile, indicating a possibility of development of some
    vertical instabilities in those parts of marginally stable tori with
    positive gradient of the LNRF velocity.

    Authors:
    Stuchlík, Zdeněk; Slaný, Petr; Török, Gabriel;

    https://ui.adsabs.harvard.edu/abs/2004ragt.meet..239S

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