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Numerical general relativistic radiative magnetohydrodynamic simulations of accretion disks around a stellar mass black hole with a luminosity above 0.5 of the Eddington value reveal their stratified, elevated vertical structure. We refer to these thermally stable numerical solutions as puffy disks. Above a dense and geometrically thin core of dimensionless thickness $h/r \sim 0.1$, crudely resembling a classic thin accretion disk, a puffed-up, geometrically thick layer of lower density and $h/r \sim 1.0$ is formed. We discuss the observational properties of puffy disks, in particular the geometrical obscuration of the inner disk by the elevated puffy region at higher observing inclinations, and collimation of the radiation along the accretion disk spin axis, which may explain the apparent super-Eddington luminosity of some X-ray objects. We also present synthetic spectra of puffy disks, and show that they are qualitatively similar to those of a Comptonized thin disk. We demonstrate that the existing xspec spectral fitting models provide good fits to synthetic observations of puffy disks, but cannot correctly recover the input black hole spin. The puffy region remains optically thick to scattering; in its spectral properties the puffy disk roughly resembles that of a warm corona sandwiching the disk core. We suggest that puffy disks may correspond to X-ray binary systems of luminosities above 0.3 of the Eddington luminosity in the intermediate spectral states.

The Resonant Switch (RS) model of twin high-frequency quasi-periodic oscillations (HF QPOs) observed in neutron star binary systems, based on switch of the twin oscillations at a resonant point, has been applied to the atoll source 4U 1636-53 under assumption that the neutron star exterior can be approximated by the Kerr geometry. Strong restrictions of the neutron star parameters M (mass) and a (spin) arise due to fitting the frequency pairs admitted by the RS model to the observed data in the regions related to the resonant points. The most precise variants of the RS model are those combining the relativistic precession frequency relations with their modifications. Here, the neutron star mass and spin estimates given by the RS model are confronted with a variety of equations of state (EoS) governing structure of neutron stars in the framework of the Hartle-Thorne theory of rotating neutron stars applied for the observationally given rotation frequency f_rot~580 Hz (or alternatively f_rot~290 Hz) of the neutron star at 4U 1636-53. It is shown that only two variants of the RS model based on the Kerr approximation are compatible with two EoS applied in the Hartle-Thorne theory for f_rot~580 Hz, while no variant of the RS model is compatible for f_rot~290 Hz. The two compatible variants of the RS model are those giving the best fits of the observational data. However, a self-consistency test by fitting the observational data to the RS model with oscillation frequencies governed by the Hartle-Thorne geometry described by three spacetime parameters M, a and (quadrupole moment) q related by the two available EoS puts strong restrictions. The test admits only one variant of the RS model of twin HF QPOs for the Hartle-Thorne theory with the Gandolfi et al. (2010) EoS predicting the parameters of the neutron star $M \sim 2.10 \mathrm{M}_{\odot}$, $a \sim 0.208$, and $q/a^2 \sim 1.77$., Comment: 28 pages, 6 figures, accepted for publication in Acta Astronomica

We have previously applied several models of high-frequency quasi-periodic oscillations (HF QPOs) to estimate the spin of the central Kerr black hole in the three Galactic microquasars, GRS 1915+105, GRO J1655-40, and XTE J1550-564. Here we explore the alternative possibility that the central compact body is a super-spinning object (or a naked singularity) with the external space-time described by Kerr geometry with a dimensionless spin parameter a = cJ/GM2 > 1.We calculate the relevant spin intervals for a subset of HF QPO models considered in the previous study. Our analysis indicates that for all but one of the considered models there exists at least one interval of a > 1 that is compatible with constraints given by the ranges of the central compact object mass independently estimated for the three sources. For most of the models, the inferred values of a are several times higher than the extreme Kerr black hole value a = 1. These values may be too high since the spin of superspinars is often assumed to rapidly decrease due to accretion when a >> 1. In this context, we conclude that only the epicyclic and the Keplerian resonance model provides estimates that are compatible with the expectation of just a small deviation from a = 1., Comment: 6 pages, 4 figures, accepted by A&A

Twin peak quasi-periodic oscillations (QPOs) appear in the X-ray power-density spectra of several accreting low-mass neutron star (NS) binaries. Observations of the peculiar Z-source Circinus X-1 display unusually low QPO frequencies. Using these observations, we have previously considered the relativistic precession (RP) twin peak QPO model to estimate the mass of central NS in Circinus X-1. We have shown that such an estimate results in a specific mass-angular-momentum (M-j) relation rather than a single preferred combination of M and j. Here we confront our previous results with another binary, the atoll source 4U 1636-53 that displays the twin peak QPOs at very high frequencies, and extend the consideration to various twin peak QPO models. In analogy to the RP model, we find that these imply their own specific M-j relations. We explore these relations for both sources and note differences in the chi-square behavior that represent a dichotomy between high- and low-frequency sources. Based on the RP model, we demonstrate that this dichotomy is related to a strong variability of the model predictive power across the frequency plane. This variability naturally comes from the radial dependence of characteristic frequencies of orbital motion. As a consequence, the restrictions on the models resulting from observations of low-frequency sources are weaker than those in the case of high-frequency sources. Finally we also discuss the need for a correction to the RP model and consider the removing of M-j degeneracies, based on the twin peak QPO-independent angular momentum estimates., Comment: 16 pages, 7 figures

The multi-resonance orbital model of high-frequency quasi-periodic oscillations (HF QPOs) enables precise determination of the black hole dimensionless spin a if observed set of oscillations demonstrates three (or more) commensurable frequencies. The black hole spin is related to the frequency ratio only, while its mass M is related to the frequency magnitude. The model is applied to the triple frequency set of HF QPOs observed in Sgr A* source with frequency ratio 3:2:1. Acceptable versions of the multi-resonance model are determined by the restrictions on the Sgr A* supermassive black hole mass. Among the best candidates the version of strong resonances related to the black hole "magic" spin a=0.983 belongs. However, the version demonstrating the best agreement with the mass restrictions predicts spin a=0.980., Comment: 19 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1305.3552

Using known frequencies of the twin-peak high-frequency quasiperiodic oscillations (HF QPOs) and known mass of the central black hole, the black-hole dimensionless spin can be determined by assuming a concrete version of the resonance model. However, a wide range of observationally limited values of the black hole mass implies low precision of the spin estimates. We discuss the possibility of higher precision of the black hole spin measurements in the framework of a multi-resonance model inspired by observations of more than two HF QPOs in the black hole systems, which are expected to occur at two (or more) different radii of the accretion disc. For the black hole systems we focus on the special case of duplex frequencies, when the top, bottom, or mixed frequency is common at two different radii where the resonances occur giving triple frequency sets. The sets of triple frequency ratios and the related spin are given. The strong resonance model for "magic" values of the black hole spin means that two (or more) versions of resonance could occur at the same radius, allowing cooperative effects between the resonances. For neutron star systems we introduce a resonant switch model that assumes switching of oscillatory modes at resonant points. In the case of doubled twin-peak HF QPOs excited at two different radii with common top, bottom, or mixed frequency, the black hole spin is given by the triple frequency ratio set. The spin is determined precisely, but not uniquely, because the same frequency set could correspond to more than one concrete spin. The black hole mass is given by the magnitude of the observed frequencies. The resonant switch model puts relevant limits on the mass and spin of neutron stars, and we expect a strong increase in the fitting procedure precision when different twin oscillatory modes are applied to data in the vicinity of different resonant points., Comment: 43 pages, 10 figures

Resonant Switch (RS) model of twin peak high-frequency quasi-periodic oscillations (HF QPOs) assumes switch of twin oscillations at a resonant point where frequencies of the upper and lower oscillations become commensurable and the twin oscillations change from one pair of the oscillating modes (corresponding to a specific model of HF QPOs) to some other pair due to non-linear resonant phenomena. The RS model is used to determine range of allowed values of spin and mass of the neutron star located at the atoll source 4U 1636-53 where two resonant points are observed at frequency ratios $nu_{U}$ : $nu_{L}$ = 3:2, 5:4. We consider the standard specific models of the twin oscillations based on the orbital and epicyclic geodetical frequencies. The resonant points are determined by the energy switch effect exhibited by the vanishing of the amplitude difference of the upper and lower oscillations. The predicted ranges of the neutron star parameters are strongly dependent on the twin modes applied in the RS model. We demonstrate that for some of the oscillatory modes used in the RS model the predicted parameters of the neutron star are unacceptable. Among acceptable RS models the most promising are those combining the Relativistic Precession and the Total Precession frequency relations or their modifications., Comment: 20 pages, 10 figures

We study non-geodesic corrections to the quasicircular motion of charged test particles in the field of magnetized slowly rotating neutron stars. The gravitational field is approximated by the Lense-Thirring geometry, the magnetic field is of the standard dipole character. Using a fully-relativistic approach we determine influence of the electromagnetic interaction (both attractive and repulsive) on the quasicircular motion. We focus on the behaviour of the orbital and epicyclic frequencies of the motion. Components of the four-velocity of the orbiting charged test particles are obtained by numerical solution of equations of motion, the epicyclic frequencies are obtained by using the standard perturbative method. The role of the combined effect of the neutron star magnetic field and its rotation in the character of the orbital and epicyclic frequencies is discussed., Comment: 2 pages, to be published in Proceedings of IAUS 290 "Feeding Compact Objects: Accretion on All Scales", C. M. Zhang, T. Belloni, M. Mendez and S. N. Zhang (eds.)

The black hole mass and spin estimates assuming various specific models of the 3:2 high frequency quasi-periodic oscillations (HF QPOs) have been carried out in Torok et al. (2005, 2011). Here we briefly summarize some current points. Spectral fitting of the spin a=cJ/GM^2 in the microquasar GRS 1915+105 reveals that this system can contain a near extreme rotating black hole (e.g., McClintock et al. 2011). Confirming the high value of the spin would have significant consequences for the theory of the HF QPOs. The estimate of a>0.9 is almost inconsistent with the relativistic precession (RP), tidal disruption (TD), and the warped disc (WD) model. The epicyclic resonance (Ep) and discoseismic models assuming the c- and g- modes are instead favoured. However, consideration of all three microquasars that display the 3:2 HF QPOs leads to a serious puzzle because the differences in the individual spins, such as a=0.9 compared to a=0.7, represent a generic problem almost for any unified orbital 3:2 QPO model., Comment: 2 pages, to be published in Proceedings of IAUS 290 "Feeding Compact Objects: Accretion on All Scales", C. M. Zhang, T. Belloni, M. Mendez and S. N. Zhang (eds.)

We present a Resonant Switch (RS) model of twin peak high-frequency quasi-periodic oscillations (HF QPOs), assuming switch of twin oscillations at a resonant point, where frequencies of the upper and lower oscillations $\nu_U$ and $\nu_L$ become to be commensurable and the twin oscillations change from one pair of the oscillating modes (corresponding to a specific model of HF QPOs) to some other pair due to non-linear resonant phenomena. The RS model enables to determine range of allowed values of spin $a$ and mass $M$ of the neutron star located at the atoll source 4U 1636-53 where two resonant points are observed at frequency ratios $\nu_U:\nu_L$ = 3:2, 5:4., Comment: 2 pages, to be published in Proceedings of IAUS 290 "Feeding Compact Objects: Accretion on All Scales", C. M. Zhang, T. Belloni, M. Mendez and S. N. Zhang (eds.)

We consider twin-peak quasi-periodic oscillations observed in the accreting low-mass neutron star binaries and explore restrictions to central compact object properties that are implied by various QPO models. For each model and each source, the consideration results in a specific relation between the compact object mass $M$ and the angular-momentum $j$ rather than in their single preferred combination. Moreover, restrictions on the models resulting from observations of the low-frequency sources are weaker than those in the case of the high-frequency sources., Comment: 2 pages, to be published in Proceedings of IAUS 290 "Feeding Compact Objects: Accretion on All Scales", C. M. Zhang, T. Belloni, M. Mendez and S. N. Zhang (eds.)

Using known frequencies of the twin peak high-frequency quasiperiodic oscillations (HF QPOs) and known mass M of the central black hole, the black-hole dimensionless spin a can be determined assuming a concrete version of the resonance model. However, large range of observationally limited values of the black hole mass implies a low precision of the spin estimates. We discuss the possibility of higher precision of the black hole spin measurements in the framework of multi-resonance model inspired by observations of more than two HF QPOs in some black hole sources. We determine the spin and mass dependence of the twin peak frequencies with a general rational ratio n:m assuming a non-linear resonance of oscillations with the epicyclic and Keplerian frequencies or their combinations. In the multi-resonant model, the twin peak resonances are combined properly to give the observed frequency set. We focus on the special case of duplex frequencies, when the top, bottom, or mixed frequency is common at two different radii where the resonances occur giving triple frequency sets., Comment: 2 pages, to be published in Proceedings of IAUS 290 "Feeding Compact Objects: Accretion on All Scales", C. M. Zhang, T. Belloni, M. Mendez and S. N. Zhang (eds.)

Spectral fitting of the spin a in the microquasar GRS 1915+105 estimate values higher than a=0.98. However, there are certain doubts about this (nearly) extremal number. Confirming a high value of a>0.9 would have significant concequences for the theory of high-frequency quasiperiodic oscillations (HF QPOs). Here we discuss its possible implications assuming several commonly used orbital models of 3:2 HF QPOs. We show that the estimate of a>0.9 is almost inconsistent with two hot-spot (relativistic precession and tidal disruption) models and the warped disc resonance model. In contrast, we demonstrate that the epicyclic resonance and discoseismic models assuming the c- and g- modes are favoured. We extend our discussion to another two microquasars that display the 3:2 HF QPOs. The frequencies of these QPOs scale roughly inversely to the microquasar masses, and the differences in the individual spins, such as a=0.9 compared to a=0.7, represent a generic problem for most of the discussed geodesic 3:2 QPO models. To explain the observations of all the three microquasars by one unique mechanism, the models would have to accommodate very large non-geodesic corrections., Comment: 7 pages, 3 figures, 2 tables; v2: corrections in the introduction, language corrections (Astronomy & Astrophysics proof-readed version)

Exchange of dominance between twin kHz quasi-periodic oscillations (QPOs) observed in some low-mass-X-ray-binaries (LMXB) suggests the possibility of a resonance between two oscillatory modes. We study the behaviour of the effective gravitational potential around specific resonant radii, and estimate the role of the higher-order terms governing the non-linear, anharmonic forcing. We discuss the impact it has on the mode amplitude in the linear and non--linear regimes. We also discuss a related possibility of lowering of the neutron star mass estimates from the highest observed QPO frequencies., Comment: research note, 5 pages, 6 figures, accepted for publication in Astronomy and Astrophysics

Boutloukos et al. (2006) discovered twin-peak quasi-periodic oscillations (QPOs) in 11 observations of the peculiar Z-source Circinus X-1. Among several other conjunctions the authors briefly discussed the related estimate of the compact object mass following from the geodesic relativistic precession model for kHz QPOs. Neglecting the neutron star rotation they reported the inferred mass M_0 = 2.2 +/- 0.3 M_\sun. We present a more detailed analysis of the estimate which involves the frame-dragging effects associated with rotating spacetimes. For a free mass we find acceptable fits of the model to data for (any) small dimensionless compact object angular momentum j=cJ/GM^2. Moreover, quality of the fit tends to increase very gently with rising j. Good fits are reached when M ~ M_0[1+0.55(j+j^2)]. It is therefore impossible to estimate the mass without the independent knowledge of the angular momentum and vice versa. Considering j up to 0.3 the range of the feasible values of mass extends up to 3M_\sun. We suggest that similar increase of estimated mass due to rotational effects can be relevant for several other sources., Comment: 10 pages, 9 figures (in colour)

The high-frequency quasi-periodic oscillations (HF QPOs) that appear in the X-ray fluxes of low-mass X-ray binaries remain an unexplained phenomenon. Among other ideas, it has been suggested that a non-linear resonance between two oscillation modes in an accretion disc orbiting either a black hole or a neutron star plays a role in exciting the observed modulation. Several possible resonances have been discussed. A particular model assumes resonances in which the disc-oscillation modes have the eigenfrequencies equal to the radial and vertical epicyclic frequencies of geodesic orbital motion. This model has been discussed for black hole microquasar sources as well as for a group of neutron star sources. Assuming several neutron (strange) star equations of state and Hartle-Thorne geometry of rotating stars, we briefly compare the frequencies expected from the model to those observed. Our comparison implies that the inferred neutron star radius "RNS" is larger than the related radius of the marginally stable circular orbit "rms" for nuclear matter equations of state and spin frequencies up to 800Hz. For the same range of spin and a strange star (MIT) equation of state, the inferrred radius RNS is roughly equal to rms. The Paczynski modulation mechanism considered within the model requires that RNS < rms. However, we find this condition to be fulfilled only for the strange matter equation of state, masses below one solar mass, and spin frequencies above 800Hz. This result most likely falsifies the postulation of the neutron star 3:2 resonant eigenfrequencies being equal to the frequencies of geodesic radial and vertical epicyclic modes. We suggest that the 3:2 epicyclic modes could stay among the possible choices only if a fairly non-geodesic accretion flow is assumed, or if a different modulation mechanism operates., Comment: 7 pages, 4 figures (in colour), accepted for publication in Astronomy & Astrophysics

The width (W), root mean squared amplitude (Rs) of lower and upper kHz quasi-periodic oscillations (QPOs) from accreting neutron stars vary with frequency. Similarly, the QPO frequency varies with the source count rate (S). Hence, the significance of a QPO, scaling as S x Rs^2/W^(1/2) will also depend on frequency. In addition, the significance also scales up with the square root of the integration time of the Fourier power density spectrum (T). Consequently, depending on the way data are considered, kHz QPOs may be detected only over a limited range of their frequency spans or detected predominantly at some frequencies, leading potentially to biases in the observed distributions of frequencies or frequency ratios. Although subject of much controversy, an observed clustering of QPO frequency ratios around 3/2 in Sco X-1, also seen in other sources, has been previously used as an argument supporting resonance based models of neutron star QPOs. In this paper, we measure how the statistical significance of both kHz QPOs vary with frequency for three prototype neutron star kHz QPO sources, namely 4U1636-536, 4U0614+091 and Sco X-1. As the significance of QPO detection depends on frequency, we show that in sensitivity-limited observations (as in the case of the RXTE/PCA), a simultaneous detection of both the lower and upper kHz QPOs can only be achieved over limited frequency ranges. As a result, even a uniform distribution of QPO frequencies will lead to peaks (in particular around 3/2) in the histogram of frequency ratios. This implies that the observed clustering of ratios does not provide any evidence for intrinsically preferred frequency ratios, thus weakening the case for a resonance mechanism at the origin of neutron star kHz QPOs., Comment: Accepted for publication in MNRAS, 9 pages, 9 figures

AIMS: For six neutron-star atoll sources (4U 1608-52, 4U 1636-53, 4U 0614+09, 4U 1728-34, 4U 1820-30 and 4U 1735-44) we investigate the relationship between the observed fractional rms amplitudes of the twin kHz QPOs. We discuss whether this displays features that could have a physical meaning in terms of the proposed QPO models. METHOD: We consider the difference in rms amplitude between the upper and lower kHz QPOs, as a function of the frequency ratio R. We compare two data sets. Set I is a collection taken from published data. Set II has rms amplitude values obtained by automatic fitting of continuous segments of RXTE-PCA observations. RESULTS: For each of the six sources, we find that there is a point in the R domain around which the amplitudes of the two twin kHz QPOs are the same. We find such a point located inside a narrow interval R=1.5 +-3%. Further investigation is needed in the case of two sources to explore this finding, since we have not determined this point in Set II. There is evidence of a similar point close to R = 1.33 or R = 1.25 in the four sources. We suggest that some of these points may correspond to the documented clustering of the twin kHz QPO frequency ratios. CONCLUSIONS: For the sources studied, the rms amplitudes of the two kHz peaks become equal when the frequencies of the oscillations pass through a certain ratio R, which is roughly the same for each of the sources. In terms of the orbital QPO models, with some assumptions concerning the QPO modulation, this finding implies the existence of a specific orbit at a common value of the dimensionless radius, at which the oscillations corresponding to the two peaks come into balance. In a more general context, the amplitude difference behaviour suggests the possible existence of an energy interchange between the upper and lower QPO modes., Comment: 5 pages, 2 figures, proofreaded version

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 or the vertical epicyclic frequency, and the radial epicyclic frequency, or some combinations of these frequencies. Generally, different resonances could arise at different radii of an accretion disc. However, we have shown that for special values of dimensionless black hole spin 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 black hole spin are determined for triple frequency ratio sets \nu_{K} : \nu_{\theta} : \nu_{r} = 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 \nu_{K} : \nu_{\theta} : \nu_{r} = 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 very close to 3:2:1 imply the black hole mass in the interval 4.3 x 10^6 M_sun < M < 5.4 x 10^6 M_sun, in agreement with estimates given by other, independent, observations., Comment: 17 pages, 4 figures, accepted for publication in Acta Astronomica

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-Nordstrom 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., Comment: 26 pages, 6 figures

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., Comment: 6 pages, 4 figures, Acta Astronomica (accepted revised version)

A long discussion has been devoted to the issue of clustering of the kHz 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 4U 1636-53. Quality factors and rms amplitudes of both the QPOs nearly equal to 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 approximative 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., Comment: 7 pages, 2 figures, Acta Astronomica; accepted revised version

Assuming a resonant origin of the 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 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. In several specific models, the two modes are related to physically plausible combinations of Keplerian, vertical and radial frequencies of geodesic orbital motion. We investigate this concept for a specific neutron star source, a fixed pair of modes and various neutron star equations of state. Each neutron star model is characterized by the equation of state (EOS), rotation frequency ($\Omega$) and central energy density ($\rho_\mathrm c$). These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. When the parameters of neutron star model are fixed, the two considered modes imply a frequency-frequency relation which can be compared to the observation in order to eliminate the unsatisfactory sets (KR,$\rho_\mathrm c, \Omega$, 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 best 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,$\rho_\mathrm c, \Omega$, EOS) into chromosome we use the Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies., Comment: 9 pages, 1 figure

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*., Comment: 18 pages, 6 figures

The results we presented were biased because of the typing error in the code transcription of the equation (A.12). We will replace by the corrected version soon. The brief of the corrected results can be found at http://www.physics.cz/research/doc/posters/1181038112_0.pdf, Comment: 7 pages, 3 figures, submitted to A&A

Trapping of neutrinos in extremely compact stars containing trapped null geodesics is studied. We calculated the ratio of produced to trapped neutrinos in the simplest model of uniform density stars. This gives the upper limit on trapping coefficients in real objects., Comment: 3 pages, 2 figures, to appear in "Proceedings of the 11th Marcel Grossmann Meeting on General Relativity", eds H. Kleinert, R. T. Jantzen, R. Ruffini

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. Aschenbach (2004) has identified the maximal rate of change of the orbital velocity within the "humpy" profile with a locally defined critical frequency of disc oscillations, but it has been done in a coordinate-dependent form. We define the critical "humpy" frequency H in general relativistic, coordinate independent form, and relate the frequency defined in the LNRF to distant observers. At radius of its definition, so-called "humpy" radius r_h, the "humpy" frequency H is compared to the radial (R) and vertical (V) epicyclic frequencies and the orbital frequency of the disc. For Keplerian thin discs, we show that the epicyclic resonance radii r_31 and r_41 (with V:R = 3:1 or 4:1) are located in vicinity of r_h where efficient triggering of oscillations with frequencies ~ H could be expected. Asymptotically (for 1-a < 10^(-4)) the ratio of the epicyclic and Keplerian frequencies and the humpy frequency is nearly constant, i.e., almost independent of spin, being for the radial epicyclic frequency R:H ~ 3:2. For thick discs the situation is more complex due to dependence on distribution of the specific angular momentum l determining the disc properties. For l = const tori and 1-a < 10^(-6) the frequency ratios of the humpy frequency and the orbital and epicyclic frequencies are again nearly constant and independent of both a and l, being for the radial epicyclic frequency R:H close to 4. In the limiting case of very slender tori (l ~ l_ms) the epicyclic resonance radius r_41 ~ r_h for spin 1-a < 2x10^(-4)., Comment: 11 pages,10 figures, 1 table. Accepted for publication in Astronomy and Astrophysics

In the Galactic microquasars with double peak kHz quasi-periodic oscillations (QPOs), the ratio of the two frequencies is 3:2. This supports the suggestion that double peak kHz QPOs are due to a non-linear resonance between two modes of accretion disk oscillations. For the microquasars with known mass, we briefly compare the black hole spin estimates based on the orbital resonance model with the recently reported spin predictions obtained by fitting the spectral continua. Results of these two approaches are not in good agreement. We stress that if the spectral fit estimates are accurate and can be taken as referential (which is still questionable), the disagreement between the predicted and referential values would represent a rather generic problem for any relativistic QPO model, as no spin influence would appear in the observed 1/M scaling of the QPO frequencies. The epicyclic frequencies relevant in these models are often considered to be equal to those of a test particle motion. However modifications of the frequencies due to the disc pressure or other non-geodesic effects may play an important role, and the inaccuracy introduced in the spin estimates by the test particle approximation could be crucial., Comment: 3 pages, proceedings of the IAU XXVIth General Assembly

We show that in the equatorial plane of marginally stable thick discs (with uniformly distributed specific angular momentum the orbital velocity relative to the locally non-rotating frames (LNRF) has a positive radial gradient in the vicinity of black holes with spin a>0.99979. The change of sign of the velocity gradient occurs just above the center of the thick toroidal discs, in the region where stable circular geodesics of the Kerr spacetime are allowed. The global character of the phenomenon is given in terms of topology changes of the von Zeipel surfaces (equivalent to the equivelocity surfaces in the tori with constant specific angular momentum distribution). Toroidal von Zeipel surfaces exist around the circle corresponding to the minimum of the equatorial LNRF velocity profile, indicating a possibility of development of some vertical instabilities in those parts of marginally stable tori with positive gradient of the LNRF velocity. Eventual oscillatory frequencies connected with the phenomenon are given in a coordinate-independent form., Comment: Updated version of the Section talk at Albert Einstein Century International Conference at Palais de l'Unesco, Paris, France, 18-23 July, 2005; to appear in the Proceedings; AIP style files included; 8 pages

Kilohertz Quasi-Periodic Oscillations (QPOs) have been detected in many accreting X-ray binaries. It has been suggested that the highest QPO frequencies observed in the modulation of the X-ray flux reflect a non-linear resonance between two modes of accreting disk oscillation. This hypothesis implies certain very general predictions, several of which have been borne out by observations. Some of these follow from properties of non-linear oscillators, while the others are specific to oscillations of fluid in strong gravity. A 3:2 resonant ratio of frequencies can be clearly recognized in the black-hole as well as in the neutron-star QPO data., Comment: 8 pages, 8 figures, to appear in Proceedings of the Albert Einstein Century International Conference

In all four microquasars which show double peak kHz QPOs, the ratio of the two frequencies is 3:2. This strongly supports the suggestion that twin peak kHz QPOs are due to a resonance between some modes of accretion disk oscillations. Here, we stress that fits to observations of the hypothetical resonances between vertical and radial epicyclic frequencies (particularly of the parametric resonance) give an accurate estimate of the spin for the three microquasars with known mass. Measurement of double peak QPOs frequencies in the Galaxy centre seems also to be consistent with the 3:2 ratio established by previous observations in microquasars, however the Sgr A* data are rather difficult for the same exact analysis. If confirmed, the 3:2 ratio of double peak QPOs in Sgr A* would be of a fundamental importance for the black hole accretion theory and the precise measurement could help to solve the question of QPOs nature., Comment: 5 pages, 5 figures, 3 tables

Relativistic Keplerian orbital frequency and related epicyclic frequencies play an important role in physics of accretion discs orbiting Kerr black holes and can by resonant or trapping effects explain quasiperiodic oscillations observed in microquasars. Because of growing theoretical evidence on possible existence of naked singularities, we discuss behaviour of the fundamenal orbital frequencies for Keplerian motion in the field of Kerr naked singularities, primarily in order to find phenomena that could observationally distinguish a hypothetical naked singularity from black holes. Some astrophysically important consequences are sketched, namely the existence of strong resonant frequency for all Kerr naked singularities, with radial and vertical epicyclic frequencies being equal at well defined radius., Comment: 15 pages, 12 figures

Many Galactic black hole and neutron star sources in low X-ray mass binaries show QPOs (quasi periodic oscillations) in their observed X-ray fluxes, i.e. peaks in the Fourier variability power spectra. Pairs of twin peaks are observed, and in black-hole systems their frequencies (upp), (down) are in rational ratios. For example, in all four microquasars with twin peaks observed, (upp):(down) = 3:2. The rational ratios have been postulated in a model that explained twin peak QPOs as a non-linear resonance between modes of accretion disk oscillations. For those microquasars where the mass of the X-ray source is known, we determine the black-hole spin, following from the observed QPO frequencies within various models of resonance., Comment: 8 pages, 16 figures