Mass estimate of the XTE J1650-500 black hole from the extended orbital resonance model for high-frequency QPOs

    by Zdeněk Stuchlík· 01 prosince, 2008· in Fyzika· 0 comments
    Context: XTE J1650-500 is a Galactic black-hole binary system for which at least one high-frequency QPO at 250 Hz has been reported. Moreover there are indications that the system harbours a near-extreme Kerr black hole with a spin aast ≃ 0.998 and mass M_BH ≲ 7.3 Msun. Recently it was discovered that the orbital 3-velocity of test-particle (geodesical) discs orbiting Kerr black holes with a spin aast > 0.9953, analyzed in the locally non-rotating frames, reveals a hump near the marginally stable orbit. It was suggested that the hump could excite the epicyclic motion of particles near the ISCO with frequencies typical for high-frequency QPOs. The characteristic frequency of the hump-induced oscillations was defined as the maximal positive rate of change of the LNRF-related orbital velocity with the proper radial distance. If the characteristic “humpy frequency” and the radial epicyclic frequency are commensurable, strong resonant phenomena are expected.
    Aims: We apply the idea of hump-induced oscillations in accretion discs around near-extreme Kerr black holes to estimate the black-hole mass in the XTE J1650-500 binary system.
    Methods: For the Kerr black hole with spin aast ≃ 0.9982 the characteristic “humpy frequency” and the radial epicyclic frequency are in the ratio 1:3 at the orbit where the positive rate of change of the LNRF-related orbital velocity with the proper radial distance is maximal. Identifying the radial epicyclic frequency with the observed 250 Hz QPO, we arrive at the mass of the black hole. In this method the ratio of frequencies determines the spin (and vice versa), and the values of the frequencies determine the black-hole mass.
    Results: The mass of the Kerr black hole in XTE J1650-500 binary system is estimated to be around 5.1 Msun.
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    Black Holes Admitting Strong Resonant Phenomena

    by Zdeněk Stuchlík· 01 prosince, 2008· in Fyzika· 0 comments
    High-frequency twin peak quasiperiodic oscillations (QPOs) are observed in four microquasars, i.e., Galactic black hole binary systems, with frequency ratio very close to 3:2. In the microquasar GRS 1915+105 the structure of QPOs exhibits additional frequencies and more than two frequencies are observed in the Galaxy nuclei Sgr A* or in some extragalactic sources (NGC 4051, MCG-6-30-15 and NGC 5408 X-1). The observed QPOs can be explained by a variety of the orbital resonance model versions assuming resonance of oscillations with the Keplerian frequency νK or the vertical epicyclic frequency νθ, and the radial epicyclic frequency νr, or some combinations of these frequencies. Generally, different resonances could arise at different radii of an accretion disk. However, we have shown that for special values of dimensionless black hole spin a strong resonant phenomena could occur when different resonances can be excited at the same radius, as cooperative phenomena between the resonances may work in such situations. The special values of a are determined for triple frequency ratio sets νK:νθ:νr=s:t:u with s,t,u being small integers. The most promising example of such a special situation arises for black holes with extraordinary resonant spin a=0.983 at the radius r=2.395 M, where νK:νθ:νr=3:2:1. We also predict that when combinations of the orbital frequencies are allowed, QPOs with four frequency ratio set 4:3:2:1 could be observed in the field of black holes with a=0.866,0.882 and 0.962. Assuming the extraordinary resonant spin a=0.983 in Sgr A*, its QPOs with observed frequency ratio ≈3:2:1 imply the black hole mass in the interval 4.3×106 Msolar< M< 5.4×106 Msolar, in agreement with estimates given by other, independent, observations.
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    Mass estimate of the XTE J1650-500 black hole from the extended orbital resonance model for high-frequency QPOs

    by Zdeněk Stuchlík· 01 prosince, 2008· in Fyzika· 0 comments
    Context: XTE J1650-500 is a Galactic black-hole binary system for which at least one high-frequency QPO at 250 Hz has been reported. Moreover there are indications that the system harbours a near-extreme Kerr black hole with a spin aast ≃ 0.998 and mass M_BH ≲ 7.3 Msun. Recently it was discovered that the orbital 3-velocity of test-particle (geodesical) discs orbiting Kerr black holes with a spin aast > 0.9953, analyzed in the locally non-rotating frames, reveals a hump near the marginally stable orbit. It was suggested that the hump could excite the epicyclic motion of particles near the ISCO with frequencies typical for high-frequency QPOs. The characteristic frequency of the hump-induced oscillations was defined as the maximal positive rate of change of the LNRF-related orbital velocity with the proper radial distance. If the characteristic “humpy frequency” and the radial epicyclic frequency are commensurable, strong resonant phenomena are expected. Aims: We apply the idea of hump-induced oscillations in accretion discs around near-extreme Kerr black holes to estimate the black-hole mass in the XTE J1650-500 binary system. Methods: For the Kerr black hole with spin aast ≃ 0.9982 the characteristic “humpy frequency” and the radial epicyclic frequency are in the ratio 1:3 at the orbit where the positive rate of change of the LNRF-related orbital velocity with the proper radial distance is maximal. Identifying the radial epicyclic frequency with the observed 250 Hz QPO, we arrive at the mass of the black hole. In this method the ratio of frequencies determines the spin (and vice versa), and the values of the frequencies determine the black-hole mass. Results: The mass of the Kerr black hole in XTE J1650-500 binary system is estimated to be around 5.1 Msun.
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    Black Holes Admitting Strong Resonant Phenomena

    by Zdeněk Stuchlík· 01 prosince, 2008· in Fyzika· 0 comments
    High-frequency twin peak quasiperiodic oscillations (QPOs) are observed in four microquasars, i.e., Galactic black hole binary systems, with frequency ratio very close to 3:2. In the microquasar GRS 1915+105 the structure of QPOs exhibits additional frequencies and more than two frequencies are observed in the Galaxy nuclei Sgr A* or in some extragalactic sources (NGC 4051, MCG-6-30-15 and NGC 5408 X-1). The observed QPOs can be explained by a variety of the orbital resonance model versions assuming resonance of oscillations with the Keplerian frequency νK or the vertical epicyclic frequency νθ, and the radial epicyclic frequency νr, or some combinations of these frequencies. Generally, different resonances could arise at different radii of an accretion disk. However, we have shown that for special values of dimensionless black hole spin a strong resonant phenomena could occur when different resonances can be excited at the same radius, as cooperative phenomena between the resonances may work in such situations. The special values of a are determined for triple frequency ratio sets νK:νθ:νr=s:t:u with s,t,u being small integers. The most promising example of such a special situation arises for black holes with extraordinary resonant spin a=0.983 at the radius r=2.395 M, where νK:νθ:νr=3:2:1. We also predict that when combinations of the orbital frequencies are allowed, QPOs with four frequency ratio set 4:3:2:1 could be observed in the field of black holes with a=0.866,0.882 and 0.962. Assuming the extraordinary resonant spin a=0.983 in Sgr A*, its QPOs with observed frequency ratio ≍3:2:1 imply the black hole mass in the interval 4.3×106 Msolar< M< 5.4×106 Msolar, in agreement with estimates given by other, independent, observations.
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    QPO observations related to neutron star equations of state

    by Zdeněk Stuchlík· 27 listopadu, 2008· in Fyzika· 0 comments
    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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    Multi-resonance orbital models of QPOs

    by Zdeněk Stuchlík· 27 listopadu, 2008· in Fyzika· 0 comments
    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 for Schwarzschild-De Sitter Space-Times

    by Zdeněk Stuchlík· 27 listopadu, 2008· in Fyzika· 0 comments
    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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    Relativistic discs in black-hole spacetimes with cosmological constant

    by Zdeněk Stuchlík· 27 listopadu, 2008· in Fyzika· 0 comments

    Quasiperiodic oscillations in a strong gravitational field around neutron stars testing braneworld models

    by Zdeněk Stuchlík· 01 listopadu, 2008· in Fyzika· 0 comments
    The strong gravitational field of neutron stars in the brany universe could be described by spherically symmetric solutions with a metric in the exterior to the brany stars being of the Reissner Nordström type containing a brany tidal charge representing the tidal effect of the bulk spacetime onto the star structure. We investigate the role of the tidal charge in orbital models of high-frequency quasiperiodic oscillations (QPOs) observed in neutron star binary systems. We focus on the relativistic precession model. We give the radial profiles of frequencies of the Keplerian (vertical) and radial epicyclic oscillations. We show how the standard relativistic precession model modified by the tidal charge fits the observational data, giving estimates of the allowed values of the tidal charge and the brane tension based on the processes going in the vicinity of neutron stars. We compare the strong field regime restrictions with those given in the weak-field limit of solar system experiments.
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    Quasiperiodic oscillations in a strong gravitational field around neutron stars testing braneworld models

    by Zdeněk Stuchlík· 01 listopadu, 2008· in Fyzika· 0 comments
    The strong gravitational field of neutron stars in the brany universe could be described by spherically symmetric solutions with a metric in the exterior to the brany stars being of the Reissner Nordström type containing a brany tidal charge representing the tidal effect of the bulk spacetime onto the star structure. We investigate the role of the tidal charge in orbital models of high-frequency quasiperiodic oscillations (QPOs) observed in neutron star binary systems. We focus on the relativistic precession model. We give the radial profiles of frequencies of the Keplerian (vertical) and radial epicyclic oscillations. We show how the standard relativistic precession model modified by the tidal charge fits the observational data, giving estimates of the allowed values of the tidal charge and the brane tension based on the processes going in the vicinity of neutron stars. We compare the strong field regime restrictions with those given in the weak-field limit of solar system experiments.
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