Perfect fluid tori with a uniform distribution of the specific angular momentum, ell(r, θ) = const, orbiting the Kerr de Sitter black holes or naked singularities are studied. It is well known that the structure of equipotential surfaces of such marginally stable tori reflects the basic properties of any tori with a general distribution of the specific angular momentum. Closed equipotential surfaces corresponding to stationary thick discs are allowed only in the spacetimes admitting stable circular geodesics. The last closed surface crosses itself in the cusp(s) enabling the outflow of matter from the torus due to the violation of hydrostatic equilibrium. The inner cusp enables an accretion onto the central object. The influence of the repulsive cosmological constant, Λ > 0, on the equipotential surfaces lies in the existence of the outer cusp (with a stabilizing effect on the thick discs) and in the strong collimation of open equipotential surfaces along the rotational axis. Both the effects take place near a so-called static radius where the gravitational attraction is just balanced by the cosmic repulsion. The outer cusp enables excretion, i.e., the outflow of matter from the torus into the outer space. The plus-family discs (which are always co-rotating in the black-hole backgrounds but can be counter-rotating, even with negative energy of the fluid elements, in some naked-singularity backgrounds) are thicker and more extended than the minus-family ones (which are always counter-rotating in all backgrounds). For co-rotating discs in the naked-singularity spacetimes, the potential well between the centre of the disc and its edges at the cusps is usually much higher than in the black-hole spacetimes. If the parameters of naked-singularity spacetimes are very close to the parameters of extreme black-hole spacetimes, the family of possible disc-like configurations includes members with two isolated discs where the inner one is always a counter-rotating accretion disc.
Read More
Relativistic Keplerian orbital frequency (νK) and related
epicyclic frequencies (radial νr, vertical
νθ) play an important role in the physics of
accretion discs orbiting Kerr black holes - quasiperiodic oscillations
observed in microquasars can be explained by associated resonant or
trapping effects. Because of growing theoretical evidence of the
possible existence of naked singularities, we discuss the behaviour of
the fundamenal orbital frequencies for Keplerian motion in the field of
Kerr naked singularities, primarily in order to find phenomena that
could observationally distinguish a hypothetical naked singularity from
black holes. Some astrophysically important consequences are sketched,
namely the existence of strong resonant frequency for all Kerr naked
singularities, with radial and vertical epicyclic frequencies equal and
given by the relation ω_sr = a-2√{a^2-1} (a^2+1
)-1.
Read More
Relativistic Keplerian orbital frequency (νK) and related epicyclic frequencies (radial νr, vertical νθ) play an important role in the physics of accretion discs orbiting Kerr black holes - quasiperiodic oscillations observed in microquasars can be explained by associated resonant or trapping effects. Because of growing theoretical evidence of the possible existence of naked singularities, we discuss the behaviour of the fundamenal orbital frequencies for Keplerian motion in the field of Kerr naked singularities, primarily in order to find phenomena that could observationally distinguish a hypothetical naked singularity from black holes. Some astrophysically important consequences are sketched, namely the existence of strong resonant frequency for all Kerr naked singularities, with radial and vertical epicyclic frequencies equal and given by the relation ω_sr = a-2√{a^2-1} (a^2+1 )-1.
Read More
In all microquasars with double peak high frequency QPOs, the ratio of
the frequencies is 3:2, which supports the suggestion that a non-linear
resonance between two modes of oscillation in the accretion disk plays a
role in exciting the observed modulations of the X-ray flux. We discuss
evidence in favor of this interpretation and relate the black hole spin
to the frequencies expected for various types of resonances that may
occur in nearly Keplerian disks in strong gravity. For those
microquasars where the mass of the central X-ray source is known, the
black hole spin can be deduced from a comparison of the observed and
expected frequencies.
Read More
In all microquasars with double peak high frequency QPOs, the ratio of the frequencies is 3:2, which supports the suggestion that a non-linear resonance between two modes of oscillation in the accretion disk plays a role in exciting the observed modulations of the X-ray flux. We discuss evidence in favor of this interpretation and relate the black hole spin to the frequencies expected for various types of resonances that may occur in nearly Keplerian disks in strong gravity. For those microquasars where the mass of the central X-ray source is known, the black hole spin can be deduced from a comparison of the observed and expected frequencies.
Read More
Newtonian theory predicts that the velocity V of free test particles on
circular orbits around a spherical gravity center is a decreasing
function of the orbital radius r, dV/dr<0. Only very recently,
Aschenbach [B. Aschenbach, Astronomy and Astrophysics, 425, 1075 (2004)]
has shown that, unexpectedly, the same is not true for particles
orbiting black holes: for Kerr black holes with the spin parameter
a>0.9953, the velocity has a positive radial gradient for geodesic,
stable, circular orbits in a small radial range close to the black-hole
horizon. We show here that the Aschenbach effect occurs also for
nongeodesic circular orbits with constant specific angular momentum
ℓ=ℓ0=const. In Newtonian theory it is
V=ℓ0/R, with R being the cylindrical radius. The
equivelocity surfaces coincide with the R=const surfaces which, of
course, are just coaxial cylinders. It was previously known that in the
black-hole case this simple topology changes because one of the
“cylinders” self-crosses. The results indicate that the
Aschenbach effect is connected to a second topology change that for the
ℓ=const tori occurs only for very highly spinning black holes,
a>0.99979.
Read More
Newtonian theory predicts that the velocity V of free test particles on circular orbits around a spherical gravity center is a decreasing function of the orbital radius r, dV/dr<0. Only very recently, Aschenbach [B. Aschenbach, Astronomy and Astrophysics, 425, 1075 (2004)] has shown that, unexpectedly, the same is not true for particles orbiting black holes: for Kerr black holes with the spin parameter a>0.9953, the velocity has a positive radial gradient for geodesic, stable, circular orbits in a small radial range close to the black-hole horizon. We show here that the Aschenbach effect occurs also for nongeodesic circular orbits with constant specific angular momentum ℓ=ℓ0=const. In Newtonian theory it is V=ℓ0/R, with R being the cylindrical radius. The equivelocity surfaces coincide with the R=const surfaces which, of course, are just coaxial cylinders. It was previously known that in the black-hole case this simple topology changes because one of the “cylinders” self-crosses. The results indicate that the Aschenbach effect is connected to a second topology change that for the ℓ=const tori occurs only for very highly spinning black holes, a>0.99979.
Read More
Surprisingly, the relict cosmological constant has a crucial influence on properties of accretion discs orbiting black holes in quasars and active galactic nuclei. We show it by considering basic properties of both the geometrically thin and thick accretion discs in the Kerr-de Sitter black hole (naked-singularity) spacetimes. Both thin and thick discs must have an outer edge allowing outflow of matter into the outer space, located nearby the so-called static radius, where the gravitational attraction of a black hole is balanced by the cosmological repulsion. Jets produced by thick discs can be significantly collimated after crossing the static radius. Extension of discs in quasars is comparable with extension of the associated galaxies, indicating a possibility that the relict cosmological constant puts an upper limit on extension of galaxies.
Read More
Extremely compact objects (9GM/4c^2<R<3GM/c^2) contain trapped
null geodesics that cannot escape the objects. Certain part of neutrinos
produced in their interior will therefore be trapped, thus influencing
neutrino luminosity of the objects and consequently their thermal
evolution. The existence of trapped neutrinos also indicates
possibility of ``two-temperature'' cooling regime of extremely compact
objects. It is shown that the trapping of neutrinos can be relevant
even for moderately extremely compact stars.
Read More
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.
Read More
