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 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 & Astrophysic

DISTINGUISHING BETWEEN SPOT AND TORUS MODELS OF HIGH-FREQUENCY QUASIPERIODIC OSCILLATIONS

In the context of high-frequency quasi-periodic oscillation (HF QPOs) we further explore the appearance of an observable signal generated by hot spots moving along quasi-elliptic trajectories close to the innermost stable circular orbit in the Schwarzschild spacetime. The aim of our investigation is to reveal whether observable characteristics of the Fourier power-spectral density can help us to distinguish between the two competing models, namely, the idea of bright spots orbiting on the surface of an accretion torus versus the scenario of intrinsic oscillations of the torus itself. We take the capabilities of the present observatories (represented by the Rossi X-ray Timing Explorer, RXTE) into account, and we also consider the proposed future instruments (represented here by the Large Observatory for X-ray Timing, LOFT)

Epicyclic oscillations of non-slender fluid tori around Kerr black holes

Considering epicyclic oscillations of pressure-supported perfect fluid tori orbiting Kerr black holes we examine non-geodesic (pressure) effects on the epicyclic modes properties. Using a perturbation method we derive fully general relativistic formulas for eigenfunctions and eigenfrequencies of the radial and vertical epicyclic modes of a slightly non-slender, constant specific angular momentum torus up to second-order accuracy with respect to the torus thickness. The behaviour of the axisymmetric and lowest-order ($m=\pm 1$) non-axisymmetric epicyclic modes is investigated. For an arbitrary black hole spin we find that, in comparison with the (axisymmetric) epicyclic frequencies of free test particles, non-slender tori receive negative pressure corrections and exhibit thus lower frequencies. Our findings are in qualitative agreement with the results of a recent pseudo-Newtonian study of analogous problem defined within the Paczy{\'n}ski-Wiita potential. Implications of our results on the high-frequency QPO models dealing with epicyclic oscillations are addressed.Comment: 24 pages, 8 figure

Off-equatorial orbits in strong gravitational fields near compact objects

Near a black hole or an ultracompact star, motion of particles is governed by strong gravitational field. Electrically charged particles feel also electromagnetic force arising due to currents inside the star or plasma circling around. We study a possibility that the interplay between gravitational and electromagnetic action may allow for stable, energetically bound off-equatorial motion of charged particles. This would represent well-known generalized Stormer's 'halo' orbits, which have been discussed in connection with the motion of dust grains in planetary magnetospheres. We demonstrate that such orbits exist and can be astrophysically relevant when a compact star or a black hole is endowed with a dipole-type magnetic field. In the case of Kerr-Newman solution, numerical analysis shows that the mutually connected gravitational and electromagnetic fields do not allow existence of stable halo orbits above the outer horizon of black holes. Such orbits are either hidden under the inner black-hole horizon, or they require the presence of a naked singularity.Comment: 16 pages, 7 figures, accepted in Class. Quantum Grav. (2008

Studie QUALICOPC – porovnání rozvoje primární péče v 31 evropských zemích.

The QUALICOPC (Quality and Costs of Primary Care in Europe) study was initiated in 2010. The aim of this study is to evaluate quality, costs and equity of primary care in 31 European countries. The researchers of this study are trying to determine what the benefits of primary care are and what effect the strength of a primary care system has on the performance of health care systems. The study is funded by the European Commission under the so-called “Seventh Framework Programme” and is coordinated by NIVEL, The Netherlands Institute for Health Services Research. In this article the background and design of the QUALICOPC study is described. The data collection is being carried out at three levels: the health care system, the GP practice and the level of the patient. Information at the practice- and patient level is being collected through surveys among GPs and their patients. In each country the aim is to garner the response of 220 GPs from a representative sample and to address 2200 patients. The study in the Czech Republic is coordinated by The Institute of General Practice, the First Faculty of Medicine of Charles University in co-operation with the Czech Medical Association of Jan Evangelista Purkyne. (aut. ref.

Twin peak high-frequency quasi-periodic oscillations as a spectral imprint of dual oscillation modes of accretion tori

Context. High-frequency (millisecond) quasi-periodic oscillations (HF QPOs) are observed in the X-ray power-density spectra of several microquasars and low-mass X-ray binaries. Two distinct QPO peaks, so-called twin peak QPOs, are often detected simultaneously exhibiting their frequency ratio close or equal to 3:2. A widely discussed class of proposed QPOs models is based on oscillations of accretion toroidal structures orbiting in the close vicinity of black holes or neutron stars. Aims. Following the analytic theory and previous studies of observable spectral signatures, we aim to model the twin peak QPOs as a spectral imprint of specific dual oscillation regime defined by a combination of the lowest radial and vertical oscillation mode of slender tori. We consider the model of an optically thick slender accretion torus with constant specific angular momentum. We examined power spectra and fluorescent Kα iron line profiles for two different simulation setups with the mode frequency relations corresponding to the epicyclic resonance HF QPOs model and modified relativistic precession QPOs model. Methods. We used relativistic ray-tracing implemented in the parallel simulation code LSDplus. In the background of the Kerr spacetime geometry, we analyzed the influence of the distant observer inclination and the spin of the central compact object. Relativistic optical projection of the oscillating slender torus is illustrated by images in false colours related to the frequency shift. Results. We show that performed simulations yield power spectra with the pair of dominant peaks that correspond to the frequencies of radial and vertical oscillation modes and with the peak frequency ratio equal to the proper value 3:2 on a wide range of inclinations and spin values. We also discuss exceptional cases of a very low and very high inclination, as well as unstable high spin relativistic precession-like configurations that predict a constant frequency ratio equal to 1:2. We demonstrate a significant dependency of broadened Kα iron line profiles on the inclination of the distant observer. Conclusions. This study presents a further step towards the proper model of oscillating accretion tori producing HF QPOs. More realistic future simulations should be based on incorporating the resonant coupling of oscillation modes, the influence of torus opacity, and the pressure effects on the mode frequencies and the torus shape

Constraining models of twin-peak quasi-periodic oscillations with realistic neutron star equations of state

Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray power-density spectra of several accreting low-mass neutron star (NS) binaries. In our previous work we have considered several QPO models. We have identified and explored mass–angular-momentum relations implied by individual QPO models for the atoll source 4U 1636-53. In this paper we extend our study and confront QPO models with various NS equations of state (EoS). We start with simplified calculations assuming Kerr background geometry and then present results of detailed calculations considering the influence of NS quadrupole moment (related to rotationally induced NS oblateness) assuming Hartle–Thorne spacetimes. We show that the application of concrete EoS together with a particular QPO model yields a specific mass–angular-momentum relation. However, we demonstrate that the degeneracy in mass and angular momentum can be removed when the NS spin frequency inferred from the X-ray burst observations is considered. We inspect a large set of EoS and discuss their compatibility with the considered QPO models. We conclude that when the NS spin frequency in 4U 1636-53 is close to 580 Hz, we can exclude 51 of the 90 considered combinations of EoS and QPO models. We also discuss additional restrictions that may exclude even more combinations. Namely, 13 EOS are compatible with the observed twin-peak QPOs and the relativistic precession model. However, when considering the low-frequency QPOs and Lense–Thirring precession, only 5 EOS are compatible with the model