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The Enhanced X-ray Timing and Polarimetry (eXTP) mission is a space mission to be launched in the late 2020s that is currently in development led by China in international collaboration with European partners. Here we provide a progress report on the Czech contribution to the eXTP science. We report on our simulation results performed in Opava (Institute of Physics of the Silesian University in Opava) and Prague (Astronomical Institute of the Czech Academy of Sciences), where the advanced timing capabilities of the satellite have been assessed for bright X-ray binaries that contain an accreting neutron star (NS) and exhibit the quasi-periodic oscillations. Measurements of X-ray variability originating in oscillations of fluid in the innermost parts of the accretion region determined by general relativity, such as the radial or Lense-Thirring precession, can serve for sensitive tests enabling us to distinguish between the signatures of different viable dense matter equations of state. We have developed formulae describing non-geodesic oscillations of accreted fluid and their simplified practical forms that allow for an expeditious application of the universal relations determining the NS properties. These relations, along with our software tools for studying the propagation of light in strong gravity and neutron star models, can be used for precise modeling of the X-ray variability while focusing on properties of the intended Large Area Detector (LAD). We update the status of our program and set up an electronic repository that will provide simulation results and gradual updates as the mission specifications progress toward their final formulation., Comment: 16 pages, 6 figures, proceedings of IBWS conference, eds. Martin Jelinek and Marianna Dafcikova, 22-26 May 2023 (Karlovy Vary, Czech Republic), ISSN: 1336-0337

Estimations of black hole spin in the three Galactic microquasars GRS 1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts. Among others, a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations (HF QPOs). Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid motion. Here we assume accretion flow described by the model of a pressure-supported torus and carry out related corrections to the mass-spin estimates. We find that for dimensionless black hole spin a<0.9, the resonant eigenfrequencies are very close to those calculated for the geodesic motion. Their values slightly grow with increasing torus thickness. These findings agree well with results of a previous study carried out in the pseudo-Newtonian approximation. The situation becomes different for a>0.9, in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases. We conclude that the assumed non-geodesic effects shift the lower limit of the spin, implied for the three microquasars by the epicyclic model and independently measured masses, from a~0.7 to a~0.6. Their consideration furthermore confirms compatibility of the model with the rapid spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies. Individual sources with a moderate spin (a<0.9) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (a~1). This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments, such as the proposed Large Observatory for X-ray Timing (LOFT)., Comment: 6 pages, 4 figures, accepted by Astronomy & Astrophysics

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)., Comment: 6 pages, 5 figures; based on a talk given at 10th IBWS workshop, some of findings presented in Bakala et al. (2014, MNRAS, eprint arXiv:1401.4468) are discussed in a broader context; to appear in Proceedings of the 10th INTEGRAL/BART Workshop in Karlovy Vary (Czech Republic, 22-25 April 2013), Acta Polytechnica, 2014

High frequency quasi-periodic oscillations (HF QPOs) appear in the X-ray variability of several accreting low-mass binaries. In a series of works it was suggested that these QPOs may have connection to inhomogeneities orbiting close to an inner edge of the accretion disc. In this paper we explore the appearance of an observable signal generated by small radiating circular hot spots moving along quasi-elliptic trajectories close to the innermost stable circular orbit in the Schwarzschild spacetime. Our consideration takes into account the capabilities of observatories that have been operating in the past two decades represented by the Rossi X-ray Timing Explorer (RXTE) and the proposed future instruments represented by the Large Observatory for X-ray Timing (LOFT). For these purposes we choose such model parameters that lead to lightcurves comparable to those observed in Galactic black hole sources, in particular the microquasar GRS 1915+105. We find that when a weak signal corresponding to the hot-spot Keplerian frequency is around the limits of the RXTE detectability, the LOFT observations can clearly reveal its first and second harmonics. Moreover, in some specific situations the radial epicyclic frequency of the spot can be detected as well. Finally, we also compare the signal produced by the spots to the signal produced by axisymmetric epicyclic disc-oscillation modes and discuss the key differences that could be identified via the proposed future technology. We conclude that the ability to recognize the harmonic content of the signal can help to distinguish between the different proposed physical models., Comment: 8 pages, 7 figures, accepted by MNRAS

Context. One of the often discussed models for X-ray binaries high-frequency quasi-periodic oscillations is the oscillating torus model that 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 to constrain this model by studying the observed power spectra of quasi-periodic oscillations., Comment: 7 pages, 2 figures, accepted by A&A

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 figures