We apply a genetic algorithm method for selection of neutron star models relating them to the resonant models of the twin peak quasiperiodic oscillations observed in the X-ray neutron star binary systems. 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. 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 ρc . 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,ρc , Ω, EOS and can be compared to the observationally determined pairs of eigenfrequencies in order to eliminate the unsatisfactory sets (KR,ρc , 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,ρ, Ω, EOS) into chromosome we used Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies.
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Using known frequencies of the accretion disc twin peak quasiperiodic oscillations (QPOs) and the known mass of the central black hole, the black hole dimensionless spin a can be determined, assuming a concrete version of the orbital resonance model. However, because of large range of observationally limited values of the black holemass, its spin can be estimated with a low precision only. Higher precision of the black hole spin measurement is possible in the framework of multi-resonance model of QPOs inspired by complex high-frequency QPO patterns observed in some black hole and neutron star systems. In the simple orbital resonance models we determine the spin and mass dependence of the twin peak frequencies for non-linear resonances of oscillations with the epicyclic and Keplerian frequencies or their combinations in the case of a general rational frequency ratio n : m, n ∼ m. In the multi-resonant model, the twin peak resonances are combined properly to give the observed frequency set. The multiresonant model is proposed in three distinct versions. In the first one, related probably to the neutron star binary systems, more instances of one resonance occur at more specific radii. In the second case, more resonances are sharing one specific radius, allowing for "cooperative" resonant phenomena in the field of black holes with a specific value of spin. In the third ("ugly") case, more resonances occur at more specific radii; we restrict our attention to the case of two such resonant radii. For special values of the spin, only triple-set of frequencies is observed because of coincidence of some frequencies, allowing determination of the spin from the triple frequency ratio set. The spin is determined precisely, but not uniquely as the same frequency set could be relevant formore than one concrete spin and combination of resonant oscillations.
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Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test particle motion is constructed and compared with its general-relativistic counterpart given by the Schwarzschild-de Sitter geometry. The results indicate that such an approach could be useful in applications of developed Newtonian theories of accretion disks in astrophysically interesting situations in large galactic structures for the Schwarzschild-de Sitter space-times with the cosmological parameter y = Λ M2/3 ≤ 10-6.
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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.
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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 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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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 the framework of the brany cosmology, the influence of the bulk spacetime on the black holes in the brane can be described by the so called tidal charge, which has a character similar to the charge parameter in the standard black-hole solutions, but can be both positive and negative. We discuss the influence of the tidal charge on the test particle and photon motion in the spherically symmetric spacetimes with a nonzero cosmological constant using the analysis realised in the case of Reissner-Nordström-(anti-)de Sitter spacetimes. We concentrate on the properties of circular geodesics as they play an important role in determining the brane properties of both thin and thick accretion discs. Some implications of the tidal charge influence are outlined.
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Being inspired by existence of non-equatorial circular (halo) stable orbits of charged particles in composite of gravitational, dipole magnetic and co-rotational electric fields near some planets, we find possible existence of these orbits in strong gravitational fields described by the Kerr-Newman geometry. By using the general relativistic inertial forces formalism combined with the effective potential approach, we show that the stable halo orbits do exist there. But it seems that they are out of the astrophysical importance, being hidden under the inner black-hole horizon, or appearing in the naked singularity spacetimes.
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