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;