In order to test the role of large-scale magnetic fields in
quasi-periodic oscillation phenomena observed in microquasars, we study
the oscillatory motion of charged particles in the vicinity of a
Schwarzschild black hole immersed into an external asymptotically
uniform magnetic field. We determine the fundamental frequencies of
small harmonic oscillations of charged test particles around stable
circular orbits in the equatorial plane of a magnetized black hole, and
discuss the radial profiles of frequencies of the radial and latitudinal
harmonic oscillations in dependence on the mass of the black hole and
the strength of the magnetic field. We demonstrate that assuming
relevance of resonant phenomena of the radial and latitudinal
oscillations of charged particles at their frequency ratio 3 :2, the
oscillatory frequencies of charged particles can be well related to the
frequencies of the twin high-frequency quasi-periodic oscillations
observed in the microquasars GRS 1915+105, XTE 1550-564 and GRO
1655-40.
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We apply the relativistic precession (RP) model with its variants and the resonance epicyclic model with its variants, based on the frequencies of the geodesic epicyclic motion in the field of a Kerr black hole, to put limits on the mass of the black hole in the ultraluminous X-ray source M82 X-1 demonstrating twin high-frequency quasi-periodic oscillations (HF QPOs) with the frequency ratio near 3:2. The mass limits implied by the geodesic HF QPO models are compared to those obtained due to the model of string loop oscillations around a stable equilibrium position. Assuming the whole range of the black hole dimensionless spin, 0 < a < 1, the restrictions on the black hole mass related to the twin HF QPOs are widely extended and strongly model dependent; nevertheless, they give the lower limit M_{M82 X-1} > 130 M_{⊙} confirming existence of an intermediate black hole in the M82 X-1 source. The upper limit given by one of the variants of the geodesic twin HF QPO models goes up to M_{M82 X-1}<1500 M_{⊙}. The range 37-210 mHz of the low-frequency QPOs observed in the M82 X-1 source introduces additional restrictive limits on the black hole mass, if we model the low-frequency QPOs by nodal precession of the epicyclic motion. The nodal precession model restrictions combined with those implied by the geodesic models of the twin HF QPOs give allowed ranges of the M82 X-1 black hole parameters, namely 140 M_{⊙}Read More
We present results of our study of charged-fluid toroidal structures surrounding a non-rotating black hole surrounded by a dipole and large-scale, asymptotically uniform magnetic fields. In continuation of our former study of electrically charged matter in approximation of zero conductivity, we demonstrate the existence of orbiting structures in the equatorial plane, levitating above it and those hovering near the symmetry axis. We constrain the range of black-hole, magnetic fields and matter parameters that allow stable configurations of the fluid structures and derive the geometrical shape of equi-pressure surfaces, characterizing the temperature and other astrophysical characteristic profiles. Our simplified analytical study suggests that these regions of stability may be relevant for trapping electrically charged particles and dust grains in some areas of the black hole magnetosphere, being thus important in some astrophysical situations.
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We study physical processes around a rotating black hole in pure Gauss-Bonnet (GB) gravity. In pure GB gravity, the gravitational potential has a slower fall-off as compared to the corresponding Einstein potential in the same dimension. It is therefore expected that the energetics of a pure GB black hole would be weaker, and our analysis bears out that the efficiency of energy extraction by the Penroseprocess is increased to 25.8 % and the particle acceleration is increased to 55.28 %; the optical shadow of the black hole is decreased. These are in principle distinguishing observable features of a pure GB black hole.
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In order to test the role of large-scale magnetic fields in quasi-periodic oscillation phenomena observed in microquasars, we study the oscillatory motion of charged particles in the vicinity of a Schwarzschild black hole immersed into an external asymptotically uniform magnetic field. We determine the fundamental frequencies of small harmonic oscillations of charged test particles around stable circular orbits in the equatorial plane of a magnetized black hole, and discuss the radial profiles of frequencies of the radial and latitudinal harmonic oscillations in dependence on the mass of the black hole and the strength of the magnetic field. We demonstrate that assuming relevance of resonant phenomena of the radial and latitudinal oscillations of charged particles at their frequency ratio $3;:2$ 3 : 2 , the oscillatory frequencies of charged particles can be well related to the frequencies of the twin high-frequency quasi-periodic oscillations observed in the microquasars GRS 1915+105, XTE 1550-564 and GRO 1655-40.
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We study deflection of light rays and gravitational lensing in the
regular Bardeen no-horizon spacetimes. Flatness of these spacetimes in
the central region implies existence of interesting optical effects
related to photons crossing the gravitational field of the no-horizon
spacetimes with low impact parameters. These effects occur due to
existence of a critical impact parameter giving maximal deflection of
light rays in the Bardeen no-horizon spacetimes. We give the critical
impact parameter in dependence on the specific charge of the spacetimes,
and discuss "ghost" direct and indirect images of Keplerian discs,
generated by photons with low impact parameters. The ghost direct images
can occur only for large inclination angles of distant observers, while
ghost indirect images can occur also for small inclination angles. We
determine the range of the frequency shift of photons generating the
ghost images and determine distribution of the frequency shift across
these images. We compare them to those of the standard direct images of
the Keplerian discs. The difference of the ranges of the frequency shift
on the ghost and direct images could serve as a quantitative measure of
the Bardeen no-horizon spacetimes. The regions of the Keplerian discs
giving the ghost images are determined in dependence on the specific
charge of the no-horizon spacetimes. For comparison we construct direct
and indirect (ordinary and ghost) images of Keplerian discs around
Reissner-Nördström naked singularities demonstrating a clear
qualitative difference to the ghost direct images in the regular Bardeen
no-horizon spacetimes. The optical effects related to the low impact
parameter photons thus give clear signature of the regular Bardeen
no-horizon spacetimes, as no similar phenomena could occur in the black
hole or naked singularity spacetimes. Similar direct ghost images have
to occur in any regular no-horizon spacetimes having nearly flat central
region.
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The Resonant Switch (RS) model of twin high-frequency quasi-periodic
oscillations (HF QPOs) observed in neutron star binary systems, based on
switch of the twin oscillations at a resonant point, has been applied to
the atoll source 4U 1636-53 under assumption that the neutron star
exterior can be approximated by the Kerr geometry. Strong restrictions
of the neutron star parameters M (mass) and a (spin) arise due to
fitting the frequency pairs admitted by the RS model to the observed
data in the regions related to the resonant points. The most precise
variants of the RS model are those combining the relativistic precession
frequency relations with their modifications. Here, the neutron star
mass and spin estimates given by the RS model are confronted with a
variety of equations of state (EoS) governing structure of neutron stars
in the framework of the Hartle-Thorne theory of rotating neutron stars
applied for the observationally given rotation frequency
frot≍580 Hz (or alternatively frot≍290
Hz) of the neutron star in 4U 1636-53. It is shown that only two
variants of the RS model based on the Kerr approximation are compatible
with two EoS applied in the Hartle-Thorne theory for
frot≍580 Hz, while no variant of the RS model is
compatible for frot≍290 Hz. The two compatible variants
of the RS model are those giving the best fits of the observational
data. However, a self-consistency test by fitting the observational data
to the RS model with oscillation frequencies governed by the
Hartle-Thorne geometry described by three spacetime parameters M,a and
(quadrupole moment) q related by the two available EoS puts strong
restrictions. The test admits only one variant of the RS model of twin
HF QPOs for the Hartle-Thorne theory with the EoS predicting the
parameters of the neutron star M≍2.10 M⊙,
a≍0.208, and q/a2≍1.77.
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Estimations of black hole spin in the three Galactic microquasars GRS
1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on
spectral and timing X-ray measurements and various theoretical concepts.
Among others, a non-linear resonance between axisymmetric epicyclic
oscillation modes of an accretion disc around a Kerr black hole has been
considered as a model for the observed high-frequency quasi-periodic
oscillations (HF QPOs). Estimates of spin predicted by this model have
been derived based on the geodesic approximation of the accreted fluid
motion. Here we assume accretion flow described by the model of a
pressure-supported torus and carry out related corrections to the
mass-spin estimates. We find that for dimensionless black hole spin a
≡ cJ/GM2 ≲ 0.9, the resonant eigenfrequencies are
very close to those calculated for the geodesic motion. Their values
slightly grow with increasing torus thickness. These findings agree well
with results of a previous study carried out in the pseudo-Newtonian
approximation. The situation becomes different for a ≳ 0.9, in
which case the resonant eigenfrequencies rapidly decrease as the torus
thickness increases. We conclude that the assumed non-geodesic effects
shift the lower limit of the spin, implied for the three microquasars by
the epicyclic model and independently measured masses, from a ~ 0.7 to a
~ 0.6. Their consideration furthermore confirms compatibility of the
model with the rapid spin of GRS 1915+105 and provides highly testable
predictions of the QPO frequencies. Individual sources with a moderate
spin (a ≲ 0.9) should exhibit a smaller spread of the measured 3:2
QPO frequencies than sources with a near-extreme spin (a ~ 1). This
should be further examined using the large amount of high-resolution
data expected to become available with the next generation of X-ray
instruments, such as the proposed Large Observatory for X-ray Timing
(LOFT).
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We study deflection of light rays and gravitational lensing in the regular Bardeen no-horizon spacetimes. Flatness of these spacetimes in the central region implies existence of interesting optical effects related to photons crossing the gravitational field of the no-horizon spacetimes with low impact parameters. These effects occur due to existence of a critical impact parameter giving maximal deflection of light rays in the Bardeen no-horizon spacetimes. We give the critical impact parameter in dependence on the specific charge of the spacetimes, and discuss "ghost" direct and indirect images of Keplerian discs, generated by photons with low impact parameters. The ghost direct images can occur only for large inclination angles of distant observers, while ghost indirect images can occur also for small inclination angles. We determine the range of the frequency shift of photons generating the ghost images and determine distribution of the frequency shift across these images. We compare them to those of the standard direct images of the Keplerian discs. The difference of the ranges of the frequency shift on the ghost and direct images could serve as a quantitative measure of the Bardeen no-horizon spacetimes. The regions of the Keplerian discs giving the ghost images are determined in dependence on the specific charge of the no-horizon spacetimes. For comparison we construct direct and indirect (ordinary and ghost) images of Keplerian discs around Reissner-Nördström naked singularities demonstrating a clear qualitative difference to the ghost direct images in the regular Bardeen no-horizon spacetimes. The optical effects related to the low impact parameter photons thus give clear signature of the regular Bardeen no-horizon spacetimes, as no similar phenomena could occur in the black hole or naked singularity spacetimes. Similar direct ghost images have to occur in any regular no-horizon spacetimes having nearly flat central region.
Read More
The Resonant Switch (RS) model of twin high-frequency quasi-periodic
oscillations (HF QPOs) observed in neutron star binary systems, based on
switch of the twin oscillations at a resonant point, has been applied to
the atoll source 4U 1636-53 under assumption that the neutron star
exterior can be approximated by the Kerr geometry. Strong restrictions
of the neutron star parameters M (mass) and a (spin) arise due to
fitting the frequency pairs admitted by the RS model to the observed
data in the regions related to the resonant points. The most precise
variants of the RS model are those combining the relativistic precession
frequency relations with their modifications. Here, the neutron star
mass and spin estimates given by the RS model are confronted with a
variety of equations of state (EoS) governing structure of neutron stars
in the framework of the Hartle-Thorne theory of rotating neutron stars
applied for the observationally given rotation frequency
frot≍580 Hz (or alternatively frot≍290 Hz) of the
neutron star in 4U 1636-53. It is shown that only two variants of the RS
model based on the Kerr approximation are compatible with two EoS
applied in the Hartle-Thorne theory for frot≍580 Hz, while no
variant of the RS model is compatible for frot≍290 Hz. The
two compatible variants of the RS model are those giving the best fits
of the observational data. However, a self-consistency test by fitting
the observational data to the RS model with oscillation frequencies
governed by the Hartle-Thorne geometry described by three spacetime
parameters M,a and (quadrupole moment) q related by the two available
EoS puts strong restrictions. The test admits only one variant of the RS
model of twin HF QPOs for the Hartle-Thorne theory with the EoS
predicting the parameters of the neutron star M≍2.10 M☉,
a≍0.208, and q/a2≍1.77.
Read More
