Relation between the lower and upper frequency mode of the twin peak
quasi-periodic oscillations observed in the neutron star X-ray binaries
is qualitatively well fitted by the frequency relation following from
the relativistic precession model. Assuming this model with no preferred
radius and the probability of an observable twin QPO excitation being
uniform across the inner edge of an accretion disk we compare the
expected and observed twin peak QPO distribution in the case of atoll
source 4U 1636-53. We find these two distributions highly incompatible.
We argue that the observed distribution roughly corresponds to the
expected one if an additional consideration of preferred resonant orbits
is included. We notice that our findings are relevant for some
disk-oscillation QPO models as well.
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A recently published study on long term evolution of the frequencies of
the kilohertz quasi-periodic oscillations (QPOs) in the atoll source 4U
1636-53 concluded that there is no preferred frequency ratio in a
distribution of twin QPOs that was inferred from the distribution of a
single frequency alone. However, we find that the distribution of the
ratio of actually observed pairs of kHz QPO frequencies is peaked close
to the 3/2 value, and possibly also close to the 5/4 ratio. To resolve
the apparent contradiction between the two studies, we examine in detail
the frequency distributions of the lower kHz QPO and the upper kHz QPO
detected in our data set. We demonstrate that for each of the two kHz
QPOs (the lower or the upper), the frequency distribution in all
detections of a QPO differs from the distribution of frequency of the
same QPO in the subset of observations where both the kHz QPOs are
detected. We conclude that detections of individual QPOs alone should
not be used for calculation of the distribution of the frequency ratios.
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Interior solutions of Einstein's equations with a non-zero cosmological
constant are given for static and spherically symmetric configurations
of uniform density. The metric tensor and pressure are determined for
both positive and negative values of the cosmological constant. Limits
on the outer radius of the interior solutions are established. It is
shown that, contrary to the cases of the limits on the interior
Schwarzschild and Reissner--Nordstr"om solutions with a zero
cosmological constant, these limits do not fully coincide with the
conditions of embeddability of the optical reference geometry associated
with the exterior (vacuum) Schwarzschild--de Sitter spacetime.
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Properties of the Reissner-Nordstr"om black-hole and naked-singularity
spacetimes with a nonzero cosmological constant are represented by their
geodetical structure and embedding diagrams of the central planes of
both the ordinary geometry and associated optical reference geometry.
Motion of test particles and photons is described in terms of an
appropriate `effective potential.' Circular geodesics are discussed and
photon escape cones are determined. In all asymptotically anti-dS
black-hole spacetimes and some asymptotically dS black-hole spacetimes a
region containing stable circular geodesics exists, which allows
accretion processes in the disk regime. The inner region is limited from
below by particles with zero angular momentum that are located in stable
equilibrium positions. The inertial and gravitational forces related to
the optical reference geometry are introduced and specified for the
circular motion. It is shown how the properties of the centrifugal force
are closely related to the properties of the optical reference geometry
embedding diagrams.
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Change of sign of the LNRF-velocity gradient has been found for accretion discs orbiting rapidly rotating Kerr black holes with spin a > 0.9953 for Keplerian discs and a > 0.99979 for marginally stable thick discs. Such a "humpy" LNRF-velocity profiles occur just above the marginally stable circular geodesic and could be related to oscillations of accretion discs. The frequency of such "hump"-induced oscillations can be identified with the maximal rate of change of the orbital velocity within the "humpy" profile. Therefore, we introduce an extended orbital resonance model (EXORM) of quasiperiodic oscillations (QPOs) assuming non-linear resonant phenomena between oscillations with the orbital epicyclic frequencies and the humpy frequency defined in a fully general relativistic way. The EXORM is developed for both Keplerian discs and perfect-fluid tori where the approximation of oscillations with epicyclic frequencies is acceptable. Clearly, the EXORM could be applied to the near-extreme Kerr black hole systems exhibiting relatively complex QPO frequency patterns. Assuming a Keplerian disc, it can be shown that in the framework of the EXORM, all the QPOs observed in the microquasar GRS 1915+105 could be explained, while it is not possible in the case of QPOs observed in the Galactic Centre source Sgr A*.
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Assuming a resonant origin of the quasiperiodic oscillations observed in the X-ray neutron star binary systems, we apply a genetic algorithm method for selection of neutron star models. It was suggested that pairs of kilo-Hertz peaks in the X-ray Fourier power density spectra of some neutron stars reflect a non-linear resonance between two modes of accretion disk oscillations. In several specific models, the two modes are related to physically plausible combinations of Keplerian, vertical and radial frequencies of geodesic orbital motion. We investigate this concept for a specific neutron star source, a fixed pair of modes and various neutron star equations of state. Each neutron star model is characterized by the equation of state (EOS), rotation frequency ($Omega$) and central energy density ($rho_mathrm c$). These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. When the parameters of neutron star model are fixed, the two considered modes imply a frequency-frequency relation which can be compared to the observation in order to eliminate the unsatisfactory sets (KR,$rho_mathrm c, Omega$, EOS). For the elimination we use the advanced genetic algorithm. Genetic algorithm comes out from the method of natural selection when subjects with the best adaptation to assigned conditions have best chances to survive. The chosen genetic algorithm with sexual reproduction contains one chromosome with restricted lifetime, uniform crossing and genes of type 3/3/5. For encryption of physical description (KR,$rho_mathrm c, Omega$, EOS) into chromosome we use the Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies.
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Change of sign of the LNRF-velocity gradient has been found for
accretion discs orbiting rapidly rotating Kerr black holes with spin a
> 0.9953 for Keplerian discs and a > 0.99979 for marginally stable
thick discs. Such a "humpy" LNRF-velocity profiles occur just above the
marginally stable circular geodesic and could be related to oscillations
of accretion discs. The frequency of such "hump"-induced oscillations
can be identified with the maximal rate of change of the orbital
velocity within the "humpy" profile. Therefore, we introduce an extended
orbital resonance model (EXORM) of quasiperiodic oscillations (QPOs)
assuming non-linear resonant phenomena between oscillations with the
orbital epicyclic frequencies and the humpy frequency defined in a fully
general relativistic way. The EXORM is developed for both Keplerian
discs and perfect-fluid tori where the approximation of oscillations
with epicyclic frequencies is acceptable. Clearly, the EXORM could be
applied to the near-extreme Kerr black hole systems exhibiting
relatively complex QPO frequency patterns. Assuming a Keplerian disc, it
can be shown that in the framework of the EXORM, all the QPOs observed
in the microquasar GRS 1915+105 could be explained, while it is not
possible in the case of QPOs observed in the Galactic Centre source Sgr
A*.
Read More
Assuming a resonant origin of the quasiperiodic oscillations observed in
the X-ray neutron star binary systems, we apply a genetic algorithm
method for selection of neutron star models. It was suggested that pairs
of kilo-Hertz peaks in the X-ray Fourier power density spectra of some
neutron stars reflect a non-linear resonance between two modes of
accretion disk oscillations. In several specific models, the two modes
are related to physically plausible combinations of Keplerian, vertical
and radial frequencies of geodesic orbital motion. We investigate this
concept for a specific neutron star source, a fixed pair of modes and
various neutron star equations of state. Each neutron star model is
characterized by the equation of state (EOS), rotation frequency
($Omega$) and central energy density ($rho_mathrm c$). These
determine the spacetime structure governing geodesic motion and position
dependent radial and vertical epicyclic oscillations related to the
stable circular geodesics. When the parameters of neutron star model are
fixed, the two considered modes imply a frequency-frequency relation
which can be compared to the observation in order to eliminate the
unsatisfactory sets (KR,$rho_mathrm c, Omega$, EOS). For the
elimination we use the advanced genetic algorithm. Genetic algorithm
comes out from the method of natural selection when subjects with the
best adaptation to assigned conditions have best chances to survive. The
chosen genetic algorithm with sexual reproduction contains one
chromosome with restricted lifetime, uniform crossing and genes of type
3/3/5. For encryption of physical description (KR,$rho_mathrm c,
Omega$, EOS) into chromosome we use the Gray code. As a fitness
function we use correspondence between the observed and calculated pairs
of eigenfrequencies.
Read More
We discuss the non-geodesic corrections to the formulae for orbital and
epicyclic frequencies given by the presence of a neutron star magnetic
field. In this paper we focus on the "Lorentzian" corrections arising if
specific charge of a test particle is considered. This corrections are
valid for a slightly charged accreting matter. We consider a magnetic
field generated by an intrinsic static dipole magnetic moment of a
slowly rotating neutron star on the background of the Schwarzschild
geometry.We calculate relevant orbital and epicyclic frequencies in a
fully general relativistic form using the equations governing
perturbations of the circular motion. The nongeodesic corrections are
rather high in the vicinity of the central compact object. The most
significant correction arises for the radial epicyclic frequency. The
zero point of the corrected radial epicyclic frequency defines radius of
the effective innermost stable circular orbit (EISCO). This correction
implies an influence of a test particle charge on the effective position
of the innermost marginally stable circular orbit (EISCO) and
constraints a restriction to the specific charge under an evidence for
the orbital motion close to the central compact object. A dipole
magnetic field influences the radial epicyclic frequency and the
position of EISCO. It also cancels the equality of orbital and vertical
epicyclic frequencies present in spherically symmetric Schwarzschild
geometry. However, these corrections become substantial only for a
specific charge values which implying shift of the innermost stable
circular orbit inconsistent with the present astrophysical view of
LMXBs. Hence, in the lowest approximation realitic for observed
neutron-star binary system with QPOs, the influence of the eventual
specific charge of the accreted matter should enter the orbital QPO
models in the form of a slightly lowered radial epicyclic frequency and
slightly shifted ISCO.
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We discuss the non-geodesic corrections to the formulae for orbital and epicyclic frequencies given by the presence of a neutron star magnetic field. In this paper we focus on the "Lorentzian" corrections arising if specific charge of a test particle is considered. This corrections are valid for a slightly charged accreting matter. We consider a magnetic field generated by an intrinsic static dipole magnetic moment of a slowly rotating neutron star on the background of the Schwarzschild geometry.We calculate relevant orbital and epicyclic frequencies in a fully general relativistic form using the equations governing perturbations of the circular motion. The nongeodesic corrections are rather high in the vicinity of the central compact object. The most significant correction arises for the radial epicyclic frequency. The zero point of the corrected radial epicyclic frequency defines radius of the effective innermost stable circular orbit (EISCO). This correction implies an influence of a test particle charge on the effective position of the innermost marginally stable circular orbit (EISCO) and constraints a restriction to the specific charge under an evidence for the orbital motion close to the central compact object. A dipole magnetic field influences the radial epicyclic frequency and the position of EISCO. It also cancels the equality of orbital and vertical epicyclic frequencies present in spherically symmetric Schwarzschild geometry. However, these corrections become substantial only for a specific charge values which implying shift of the innermost stable circular orbit inconsistent with the present astrophysical view of LMXBs. Hence, in the lowest approximation realitic for observed neutron-star binary system with QPOs, the influence of the eventual specific charge of the accreted matter should enter the orbital QPO models in the form of a slightly lowered radial epicyclic frequency and slightly shifted ISCO.
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