## Main research directions

- Study, modelling and visualisation of astrophysical processes in the vicinity of compact objects (black holes, neutron and strange stars), analysis of astrophysical data
- Modelling of the inner structure of compact objects and their equation of state
- Exploration of detailed influence of structure and induced spacetime of compact objects on their inner physical processes and processes in their vicinity
- Simulations of observed X-ray variability and spectra of accreting compact objects considering existing and future X-ray observatories
- Utilisation of advanced algorithms and hardware for parallel and accelerated computations and data processing

## Recent

During the past year we were mostly focusing on various aspects of physics of oscillations of accretion discs and modelling of the inner structure of neutron stars. We explored the behavior of epicyclic and other lowest-order oscillation modes for different geometrical thickness of the flow and compared the outputs to analytical results. Some of our finding has been promptly reported in a conference proceeding (Horak et al., 2017) and a joint research paper is now in preparation. In parallel we have explored a full parameter space determining the behavior of non-axisymmetric radial and vertical epicyclic modes. We have also carried out simulations of observational spectra and light curves resulting for models of oscillating tori based on the analytical formulae. Similar research direction concerning other accretion structures has been introduced in collaboration with prof. Luigi Stella (INAF, Rome). The outcomes have been presented at conferences and in a proceeding paper (Lancova et al., 2017).

We have completed our investigation of predictions of several X-ray variability models assuming objects alternative to black holes and neutron stars (Kotrlova et al. 2017, A&A, Stuchlik et al. 2017, AcA). In these studies we find miscellaneous possibilities for identification of the observed QPO phenomena with the physical processes around superspinnig objects having angular momentum only slightly higher than extremal Kerr black holes. We have extended our previous work on modelling the QPO phenomena in neutron star sources (Torok et al. 2018, MNRAS). We have found a surprisingly simple analytic relation that reproduces observational data of a group of several sources. This formula can be related to a model of oscillating torus which was recently proposed by our research group. In a future work we would like to explore this model's predictions for black holes, in particular for Galactic microquasars.

## Scientific Studies Carried Out in the Period 2012-2015

**Our main focus has been directed to the improvement of our understanding of astrophysical effects taking place in the close vicinity** **of black holes and neutron stars. A particular attention has been devoted to estimating parameters of these objects****. In this field, we have been engaged in ****several research areas overlaping in the following complex topics.**

#### Properties and Structure of Neutron and Strange Stars

We have carried out research work focused on exploration of main properties of neutron stars described by up-to-date equations of state (EoS). We have developed an advanced numerical code for modeling of realistic oblate neutron stars in Hartle-Thorne spacetimes. It has been applied to explore relations between the angular momentum, quadrupole moment, and the compactness of rotating neutron and strange stars. We have found universal relations between the so-called Kerr factor and the compactness of the star, which are almost independent of EoS.

Using the code, we have also investigated the estimates of mass and spin of neutron stars based on various models of high frequency (kHz) QPOs. We have shown that fitting of the measured QPO frequencies results in specific mass-spin relations rather than preferred combinations of mass and spin (even when a single EoS is considered). We have furthermore investigated the appearance of innermost stable circular orbit (ISCO) determined by EoS. It has been found that neutron stars exhibiting ISCO can be divided into two distinct groups of slow and fast rotators. For a large sub-variety of QPO models, this applies to QPO sources as well.

#### Properties of Astrophysical Black Holes and Exotic Compact Objects

We have undertaken several studies devoted to estimations of black hole spin in Galactic microquasars based on kHz QPO models. We have investigated the impact of non-geodesic effects related to pressure forces on estimations of spin that have been previously derived based on geodesic approximation of the accreted fluid motion. For the prominent 3:2 parametric resonance model, the non-geodesic effects can cause an unexpected dramatic shift in the predicted QPO frequencies, but only for rapidly rotating black holes. We have therefore suggested that sources with a near-extreme spin should exhibit a higher spread of 3:2 QPO frequencies than other sources. This can be verified by future measurements.

We have also made similar investigations for several other QPO models revealing that in some cases the influence of non-geodesic effects can be quite significant. Moreover, we have calculated spin estimates implied by a number of kHz QPO models for the alternative case, in which the microquasar contains a super-spinning object instead of a black hole. We have concluded that only two QPO models are compatible with the realistic expectation of the (super)spin.

#### Modelling the Variability and Spectra of Accreting Compact Objects

We have contributed to development of some of the individual QPO models and exploration of their observable predictions. We have carried out a study of orbital motion around a magnetized rotating neutron star calculating the magnetic-field-induced corrections to frequencies of the orbital motion. The study has included a discussion of their relevance to QPO models. We have conducted a complex research oriented on proper simulations of data predicted by various developed QPO models that take into account strong gravity effects acting on photon propagation as well as technical capabilities of the present and future observational X-ray instruments. We have payed a special attention to the simulated signal behaviour for the past Rossi X-ray Timing (RXTE) mission and the proposed Large Observatory For x-ray Timing (LOFT) mission. Among other things, we have made comparison of the signal produced by hot accreted spots and the signal produced by axisymmetric epicyclic disc oscillation modes. We have identified key differences in signals that could be recognized via the proposed future technology. We have in particular recognized the importance of the harmonic content of the signal.