Several models of the X-ray flux modulation observed in the low-mass
X-ray binaries (LMXBs), in particular the neutron star LMXBs, deal with
Keplerian and epicyclic frequencies of geodesic orbital motion. We
discuss non-geodesic corrections to the orbital and epicyclic
frequencies of charged test particles caused by presence of a neutron
star magnetic field. The magnetic field is considered to be generated by
an intrinsic static dipole magnetic moment of a neutron star represented
by the Schwarzschild geometry. We present fully general relativistic
formulae for the orbital and epicyclic frequencies, obtained using the
appropriate equations governing perturbations of the circular motion.
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)." The dipole magnetic field also violates equality of the
orbital and vertical epicyclic frequencies corresponding to the
spherical symmetry of the Schwarzschild geometry.
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In this Proceedings, the talks presented during workshops Proceedings of
RAGtime 8/9: Workshops on black holes and neutron stars, 15-19/19-21
September 2006/2007, Hradec nad Moravicí, Opava, Czech Republic
are collected.
Relativistic Astrophysics Group (RAG) at the Institute of Physics, the
Faculty of Philosophy and Science of the Silesian University in Opava,
started a series of Workshops on Black Holes and Neutron Stars called
RAGtime in 1999. The purpose of the workshops was to provide an
opportunity for the presentation and discussion of recent developments
in the field of relativistic astrophysics related to accretion processes
onto black holes and neutron stars, and to general physical phenomena
connected to the properties of black holes and their vicinity, and the
internal structure of neutron stars or quark stars, as they were
obtained by collaborating research groups at the Silesian University in
Opava, the Faculty of Mathematics and Physics of Charles University in
Prague, the International School for Advanced Studies in Trieste, the
Institute of Astrophysics at University of Oxford, the Department of
Astrophysics of Göteborg University, the Institute of Physics at
the University of Bergen, the Institute of Astronomy of the Polish
Academy of Science, and other remarkable institutes.
The RAGtime workshops are also vitally important for students of
theoretical physics and/or astrophysics at the Silesian University in
Opava, because they have a unique opportunity to be regularly in direct
contact with the most recent results of relativistic astrophysics and
they also have a possibility to discuss problems with leading
astrophysicists of worldwide reputation like Marek Abramowicz, John
Miller, Jeff McClintock, Ron Remillard, Włodzimierz
Kluźniak, Shoji Kato, Luciano Rezzolla, Vladimír Karas,
Petr Hadrava and others.
We would like to thank all the authors for careful preparation of their
contributions. We are also indebted to the Ministry of Education of the
Czech Republic for providing financial support in the framework of the
Grant MSM 4781305903, and all other sponsors for their contributions to
the successful course of the last RAGtime meetings.
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We have developed a realistic, fully general relativistic computer code
to simulate optical projection in a strong, spherically symmetric
gravitational field. The standard theoretical analysis of optical
projection for an observer in the vicinity of a Schwarzschild black hole
is extended to black hole spacetimes with a repulsive cosmological
constant, i.e, Schwarzschild-de Sitterspacetimes. Influence of the
cosmological constant is investigated for static observers and observers
radially free-falling from the static radius. Simulations include
effects of the gravitational lensing, multiple images, Doppler and
gravitational frequency shift, as well as the intensity amplification.
The code generates images of the sky for the static observer and a movie
simulations of the changing sky for the radially free-falling observer.
Techniques of parallel programming are applied to get a high performance
and a fast run of the BHC simulation code.
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In a series of papers it was discussed,on the basis of phenomenological
arguments, whether the high frequency quasiperiodic oscillations (kHz
QPOs)observed in the neutron-star and black-hole X-ray sources originate
in the same physical mechanism. Recently it was suggested that a general
trend seen in neutron star kHz QPOs instead excludes such a uniform
origin. Using the example of the atoll source 4U 1636-53 we illustrate
that this is not neccesarily true.
Read More
We have developed a realistic, fully general relativistic computer code
to simulate optical projection in a strong, spherically symmetric
gravitational field. The standard theoretical analysis of optical
projection for an observer in the vicinity of a Schwarzschild black hole
is extended to black hole spacetimes with a repulsive cosmological
constant, i.e, Schwarzschild-de Sitterspacetimes. Influence of the
cosmological constant is investigated for static observers and observers
radially free-falling from the static radius. Simulations include
effects of the gravitational lensing, multiple images, Doppler and
gravitational frequency shift, as well as the intensity amplification.
The code generates images of the sky for the static observer and a movie
simulations of the changing sky for the radially free-falling observer.
Techniques of parallel programming are applied to get a high performance
and a fast run of the BHC simulation code.
Read More
In a series of papers it was discussed,on the basis of phenomenological
arguments, whether the high frequency quasiperiodic oscillations (kHz
QPOs)observed in the neutron-star and black-hole X-ray sources originate
in the same physical mechanism. Recently it was suggested that a general
trend seen in neutron star kHz QPOs instead excludes such a uniform
origin. Using the example of the atoll source 4U 1636-53 we illustrate
that this is not neccesarily true.
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Assuming a resonant origin of the twin peak 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 kilohertz 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. We investigate this concept for a specific neutron star source. Each neutron star model is characterized by the equation of state (EOS), rotation frequency Ω and central energy density rho_{c}. These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. Particular kinds of resonances (KR) between the oscillations with epicyclic frequencies, or the frequencies derived from them, can take place at special positions assigned ambiguously to the spacetime structure. The pairs of resonant eigenfrequencies relevant to those positions are therefore fully given by KR, rho_{c}, Ω, EOS and can be compared to the observationally determined pairs of eigenfrequencies in order to eliminate the unsatisfactory sets (KR, rho_{c}, Ω, 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 most 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_{c}, Ω, EOS) into the 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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Several models have been outlined to explain the (upper and lower) kilohertz quasi-periodic oscillations (QPOs) detected in many accreting neutron star X-ray binaries. When facing the theory to observation, rather limited attention has been payed to the mutual relations between the (correlated) QPO amplitudes and quality factors till now. In this paper we report on recent results on these relations. For six neutron star atoll sources (namely 4U 1728-34, 4U 1608-52, 4U 1636-53, 4U 0614+09, 4U 1820-30 and 4U 1735-44) spanning wide range of frequencies we investigate whether the relationship between the rms amplitudes and quality factors of the observed kHz QPO modes ν _{L}, ν _{U} display features that could have a significant meaning in terms of the proposed QPO models. We find for all the six sources that after the twin kHz QPOs pass a point (or the narrow interval) where their ratio R equals 1.5 the lower/upper oscillation becomes stronger/weaker than other one with increasing QPO frequency. Existence of a similar effect close to R = 1.33 or R = 1.25 is also indicated. Moreover, for increasing QPO frequency, shortly after passing 3/2 ratio, the difference between QPO amplitudes as well as lower QPO quality factor reaches its maxima on a narrow frequency interval where lower QPO is much stronger than the upper one. This interval lies between frequencies corresponding to 3/2 and 4/3 (or 5/4) frequency ratio. This finding implies restrictions to the orbital QPO models (both hot spot- and disc oscillations- like) and also to QPO modulation mechanism. In a wider context, our results may indicate the existence of an energy overflow between the upper and lower QPO mode when their ratio is close to ratio of small integral numbers.
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We further investigate the issue of clustering of kHz QPO frequency ratios in neutron star low mass X-ray binaries. In this note we report on the recent analysis of occurrences and properties of kHz QPOs in the source 4U 1636-53. Assuming that kHz QPOs occur in pairs whose frequencies are linearly correlated, we find a prominent frequency (or a narrow frequency region) that separates upper and lower QPO observations. The two QPO modes are then simultaneously detected mainly in the vicinity of this transition points. We show that this can be understood in terms of correlations of QPO properties with frequency, such as quality factor and rms amplitude. We find that rms amplitudes and quality factors of both QPOs nearly equal at the transition point. In addition, the QPO frequencies are nearly commensurable there. We investigate also five other atoll sources obtaining similar results.
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The kHz quasiperiodic oscillations (QPOs) observed in low-mass X-ray neutron star binaries are most likely connected to the orbital motion in the accretion disc and show datapoint clustering of frequency ratio between the upper and lower QPOs in small natural numbers. It is shown for the atoll source 4U 1636-53 that using the Hartle-Thorne metric to describe the neutron star spacetime, the data clustered around the frequency ratios 3/2 and 5/4 could be fitted by three models (Relativistic Precession, Vertical Precession and Total Precession) involving the hot spot orbital motion with Keplerian, radial epicyclic and vertical epicyclic frequencies. We demonstrate that with taking into account the hotspots interaction with the neutron star magnetic field the discussed three models can provide good fits implying reasonable values of the neutron star mass and angular momentum. Therefore the hypothesis of more instances of one orbital resonance has the potential to explain the kHz QPO nature in the source 4U 1636-53.
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