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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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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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 neutral particle motion around rotating regular black hole that was derived from the Ayón-Beato-García (ABG) black hole solution by the Newman-Janis algorithm in the preceding paper (Toshmatov et al., Phys. Rev. D, 89:104017, 2014) has been studied. The dependencies of the ISCO (innermost stable circular orbits along geodesics) and unstable orbits on the value of the electric charge of the rotating regular black hole have been shown. Energy extraction from the rotating regular black hole through various processes has been examined. We have found expression of the center of mass energy for the colliding neutral particles coming from infinity, based on the BSW (Baňados-Silk-West) mechanism. The electric charge Q of rotating regular black hole decreases the potential of the gravitational field as compared to the Kerr black hole and the particles demonstrate less bound energy at the circular geodesics. This causes an increase of efficiency of the energy extraction through BSW process in the presence of the electric charge Q from rotating regular black hole. Furthermore, we have studied the particle emission due to the BSW effect assuming that two neutral particles collide near the horizon of the rotating regular extremal black hole and produce another two particles. We have shown that efficiency of the energy extraction is less than the value 146.6 % being valid for the Kerr black hole. It has been also demonstrated that the efficiency of the energy extraction from the rotating regular black hole via the Penrose process decreases with the increase of the electric charge Q and is smaller in comparison to 20.7 % which is the value for the extreme Kerr black hole with the specific angular momentum a= M.
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The neutral particle motion around rotating regular black hole that was
derived from the Ayón-Beato-García (ABG) black hole
solution by the Newman-Janis algorithm in the preceding paper (Toshmatov
et al., Phys. Rev. D, 89:104017, 2014) has been studied. The
dependencies of the ISCO (innermost stable circular orbits along
geodesics) and unstable orbits on the value of the electric charge of
the rotating regular black hole have been shown. Energy extraction from
the rotating regular black hole through various processes has been
examined. We have found expression of the center of mass energy for the
colliding neutral particles coming from infinity, based on the BSW
(Baňados-Silk-West) mechanism. The electric charge Q of rotating
regular black hole decreases the potential of the gravitational field as
compared to the Kerr black hole and the particles demonstrate less bound
energy at the circular geodesics. This causes an increase of efficiency
of the energy extraction through BSW process in the presence of the
electric charge Q from rotating regular black hole. Furthermore, we have
studied the particle emission due to the BSW effect assuming that two
neutral particles collide near the horizon of the rotating regular
extremal black hole and produce another two particles. We have shown
that efficiency of the energy extraction is less than the value 146.6 %
being valid for the Kerr black hole. It has been also demonstrated that
the efficiency of the energy extraction from the rotating regular black
hole via the Penrose process decreases with the increase of the electric
charge Q and is smaller in comparison to 20.7 % which is the value for
the extreme Kerr black hole with the specific angular momentum a= M.
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We study scalar, electromagnetic, and gravitational test fields in the Hayward, Bardeen, and Ayón-Beato-García regular black hole spacetimes and demonstrate that the test fields are stable in all of these spacetimes. Using the sixth order WKB approximation of the linear "axial" perturbative scheme, we determine dependence of the quasinormal mode (QNM) frequencies on the characteristic parameters of the test fields and the spacetime charge parameters of the regular black holes. We give also the grey body factors, namely, the transmission and reflection coefficients of scattered scalar, electromagnetic, and gravitational waves. We show that the damping of the quasinormal modes in regular black hole spacetimes is suppressed compared to the case of Schwarzschild black holes, and increasing the charge parameter of the regular black holes increases reflection and decreases the transmission factor of the incident waves for each of the test fields.
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We study scalar, electromagnetic, and gravitational test fields in the
Hayward, Bardeen, and Ayón-Beato-García regular black hole
spacetimes and demonstrate that the test fields are stable in all of
these spacetimes. Using the sixth order WKB approximation of the linear
"axial" perturbative scheme, we determine dependence of the quasinormal
mode (QNM) frequencies on the characteristic parameters of the test
fields and the spacetime charge parameters of the regular black holes.
We give also the grey body factors, namely, the transmission and
reflection coefficients of scattered scalar, electromagnetic, and
gravitational waves. We show that the damping of the quasinormal modes
in regular black hole spacetimes is suppressed compared to the case of
Schwarzschild black holes, and increasing the charge parameter of the
regular black holes increases reflection and decreases the transmission
factor of the incident waves for each of the test fields.
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The model of current-carrying string loop oscillations is tested to explain the special set of frequencies related to the high-frequency quasiperiodic oscillations (HF QPOs) observed recently in the low-mass X-ray binary XTE J1701-407 containing a neutron star. The external geometry of the neutron star is approximated by the Kerr geometry, introducing errors not exceeding 10 % for slowly rotating massive neutron stars. The frequencies of the radial and vertical string loop oscillations are then governed by the mass and dimensionless spin of the neutron star, and by the dimensionless parameter describing combined effects of the string loop tension and its angular momentum. It is explicitly demonstrated that the string-loop oscillation model can explain the observed kHz frequencies for the neutron star parameters restricted to the intervals and . However, the stringy parameter cannot be the same for all the three HF QPO observations in the XTE J1701-407 source; the limits on the acceptable values of are given in dependence on the spacetime parameters and.
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The model of current-carrying string loop oscillations is tested to
explain the special set of frequencies related to the high-frequency
quasiperiodic oscillations (HF QPOs) observed recently in the low-mass
X-ray binary XTE J1701-407 containing a neutron star. The external
geometry of the neutron star is approximated by the Kerr geometry,
introducing errors not exceeding 10 % for slowly rotating massive
neutron stars. The frequencies of the radial and vertical string loop
oscillations are then governed by the mass and dimensionless spin of the
neutron star, and by the dimensionless parameter describing combined
effects of the string loop tension and its angular momentum. It is
explicitly demonstrated that the string-loop oscillation model can
explain the observed kHz frequencies for the neutron star parameters
restricted to the intervals and . However, the stringy parameter cannot
be the same for all the three HF QPO observations in the XTE J1701-407
source; the limits on the acceptable values of are given in dependence
on the spacetime parameters and.
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Using the pseudo-Newtonian (PN) potential, we estimate the influence of the repulsive cosmological constant Ʌ ~ 1.3×10-56 cm-2 implied by recent cosmological tests onto the motion of both Small and Large Magellanic Clouds (SMC and LMC) in the gravitational field of the Milky Way. The role of the cosmological constant is most conspicuous when binding mass is estimated for the satellite galaxies. We have found a strong influence of cosmic repulsion on the total binding mass for both galaxies. We have found that in some cases, the effect of the cosmic repulsion can be even comparable to the effects of the dynamical friction and the Andromeda galaxy.
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