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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Relation between the lower and upper frequency mode of twin peak quasiperiodic oscilations observed in 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 a twin QPO excitation being uniform across the inner edge of an accretion disc, 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 also find 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 disc-oscillation QPO models as well.
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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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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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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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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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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 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
