Pavel Bakala

ON MASS CONSTRAINTS IMPLIED BY THE RELATIVISTIC PRECESSION MODEL OF TWIN-PEAK QUASI-PERIODIC OSCILLATIONS IN CIRCINUS X-1

Boutloukos et al. 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 ☉. 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 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 3 M ☉. We suggest that similar increase of estimated mass due to rotational effects can be relevant for several other sources.

On magnetic-field-induced non-geodesic corrections to relativistic orbital and epicyclic frequencies

We discuss non-geodesic corrections to orbital and epicyclic frequencies of charged test particles orbiting a non-rotating neutron star with a dipole magnetic field. Using a fully relativistic approach we consider the influence of both the magnetic attraction and repulsion on the orbital and epicyclic motion. The magnetic repulsion introduces a rather complex and unusual behaviour of the circular orbital motion that is well defined down to the radius where the vertical epicyclic frequency loses its meaning. We demonstrate that for the intensity of the magnetic interaction appropriately restricted, the stable circular orbits extend down to the magnetic innermost stable circular orbit (MISCO) that is located well under the geodetic innermost stable circular orbit (GISCO) and even can reach the region under the photon circular orbit. The lowest stable circular orbit at rMISCOmin  = 2.73M, associated with the highest possible orbital frequency , corresponds to the critical value of the particle-specific charge and the neutron star magnetic dipole moment product . For the magnetic attraction acting above the GISCO, the situation is much more simple and we demonstrate that the most significant correction arises for the radial epicyclic frequency and consequently for the location of the MISCO when the strong magnetic attraction pushes its location far behind the location of GISCO. We show that the Lorentz force also naturally violates the equality of the orbital and vertical epicyclic frequencies implied by the spherical symmetry of the background Schwarzschild geometry giving rise to the new effect of nodal precession of the orbital motion plane. Finally, we apply the magnetic attraction corrections on the relativistic precession model of the twin-peak high-frequency quasiperiodic oscillations observed in the galactic low mass x-ray binaries, showing possible high relevance of the modified radial epicyclic frequency.

MASS-ANGULAR-MOMENTUM RELATIONS IMPLIED BY MODELS OF TWIN PEAK QUASI-PERIODIC OSCILLATIONS

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.

Extreme gravitational lensing in vicinity of Schwarzschild-de Sitter black holes

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.

Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model

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 800 Hz. For the same range of spin and a strange star (MIT) equation of

On magnetic-field-induced corrections to the orbital and epicyclic frequencies: paper II. Slowly rotating magnetized neutron stars

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, and the magnetic field is of the standard dipole character. Using a fully relativistic approach, we determine the 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 the numerical solution of equations of motion, and 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. It is demonstrated that even in the Lense–Thirring spacetime, particles being static relative to distant observers can exist due to the combined gravo-electromagnetic interaction.

Towards modeling quasi-periodic oscillations of microquasars with oscillating slender tori

Context. One of the often discussed models for high-frequency quasi-periodic oscillations of X-ray binaries is the oscillating torus model, which considers oscillation modes of slender accretion tori. Aims. Here, we aim at developing this model by considering the observable signature of an optically thick slender accretion torus subject to simple periodic deformations. Methods. We compute light curves and power spectra of a slender accretion torus subject to simple periodic deformations: vertical or radial translation, rotation, expansion, and shear. Results. We show that different types of deformations lead to very different Fourier power spectra and therefore could be observationally distinguished. Conclusions. This work is a first step in a longer term study of the observable characteristics of the oscillating torus model. It gives promising perspectives on the possibility of constraining this model by studying the observed power spectra of quasi-periodic oscillations.

A remark about possible unity of the neutron star and black hole high frequency QPOs

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.

Twin peak quasi-periodic oscillations as signature of oscillating cusp torus

Serious theoretical effort has been devoted to explain the observed frequencies of twin-peak quasi-periodic oscillations (HF QPOs) observed in low-mass X-ray neutron star binaries. Here we propose a new model of HF QPOs. Within its framework we consider an oscillating torus with cusp that changes location

Spectral signature of oscillating slender tori surrounding Kerr black holes

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