A long discussion has been devoted to the issue of clustering of the kHz quasi periodic oscillation (QPO) frequency ratios in the neutron star sources. While the distribution of ratios inferred from an occurrence of a single QPO seems to be consistent with a random walk, the distribution based on simultaneous detections of both peaks indicates a preference of ratios of small integers. Based on the public RXTE data we further investigate this issue for the source 4U1636-53. Quality factors and rms amplitudes of both the QPOs nearly equal at the points where the frequencies are commensurable, and where the twin QPO detections cluster. We discuss a connection of the clustering with the varying properties of the two QPO modes. Assuming approximate relations for the observed correlations of the QPO properties, we attempt to reproduce the frequency and ratio distributions using a simple model of a random-walk evolution along the observed frequency-frequency correlation. We obtain results which are in qualitative agreement with the observed distributions.
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A long discussion has been devoted to the issue of clustering of the kHz
quasi periodic oscillation (QPO) frequency ratios in the neutron star
sources. While the distribution of ratios inferred from an occurrence of
a single QPO seems to be consistent with a random walk, the distribution
based on simultaneous detections of both peaks indicates a preference of
ratios of small integers. Based on the public RXTE data we further
investigate this issue for the source 4U1636-53. Quality factors and rms
amplitudes of both the QPOs nearly equal at the points where the
frequencies are commensurable, and where the twin QPO detections
cluster. We discuss a connection of the clustering with the varying
properties of the two QPO modes. Assuming approximate relations for the
observed correlations of the QPO properties, we attempt to reproduce the
frequency and ratio distributions using a simple model of a random-walk
evolution along the observed frequency-frequency correlation. We obtain
results which are in qualitative agreement with the observed
distributions.
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The equations of state (EoS) of relativistic asymmetric nuclear matter are obtainable from assumed form of the interaction Lagrangian. They are one of important inputs to describe the neutron stars. The structure of the neutron stars, i.e. the density of matter and the pressure as functions of radial distance starting from their values at the center of a star, is straightforwardly dependent on EoS. Similarly, a limitation on the total mass of the neutron star can be obtained therefrom. Thus, EoS and the underlying nucleon interactions can be tested also by the means of astronomical observations.
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Near a black hole or an ultracompact star, the motion of particles is governed by a strong gravitational field. Electrically charged particles also feel the electromagnetic force arising due to currents inside the star or plasma circling around. We study the possibility that the interplay between gravitational and electromagnetic actions may allow for the stable, energetically bound off-equatorial motion of charged particles. This would represent the well-known generalized Störmer's 'halo orbits', which have been discussed in connection with the motion of dust grains in planetary magnetospheres. We demonstrate that such orbits exist and can be astrophysically relevant when a compact star or a black hole is endowed with a dipole-type magnetic field. In the case of the Kerr Newman solution, numerical analysis shows that the mutually connected gravitational and electromagnetic fields do not allow the existence of stable halo orbits above the outer horizon of black holes. Such orbits are either hidden under the inner black-hole horizon, or they require the presence of a naked singularity.
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The equations of state (EoS) of relativistic asymmetric nuclear matter
are obtainable from assumed form of the interaction Lagrangian. They are
one of important inputs to describe the neutron stars. The structure of
the neutron stars, i.e. the density of matter and the pressure as
functions of radial distance starting from their values at the center of
a star, is straightforwardly dependent on EoS. Similarly, a limitation
on the total mass of the neutron star can be obtained therefrom. Thus,
EoS and the underlying nucleon interactions can be tested also by the
means of astronomical observations.
Read More
Near a black hole or an ultracompact star, the motion of particles is
governed by a strong gravitational field. Electrically charged particles
also feel the electromagnetic force arising due to currents inside the
star or plasma circling around. We study the possibility that the
interplay between gravitational and electromagnetic actions may allow
for the stable, energetically bound off-equatorial motion of charged
particles. This would represent the well-known generalized
Störmer's 'halo orbits', which have been discussed in connection
with the motion of dust grains in planetary magnetospheres. We
demonstrate that such orbits exist and can be astrophysically relevant
when a compact star or a black hole is endowed with a dipole-type
magnetic field. In the case of the Kerr Newman solution, numerical
analysis shows that the mutually connected gravitational and
electromagnetic fields do not allow the existence of stable halo orbits
above the outer horizon of black holes. Such orbits are either hidden
under the inner black-hole horizon, or they require the presence of a
naked singularity.
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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--Nordström 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-Nordström 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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