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;