## 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

## Highlights 2019-2020

We started an important scientific cooperation with Black Hole Initiative at Harvard University. We began utilization of the BHI KORAL code for performing simulations of time-dependent behaviour of accretion discs of different thickness. Our collaboration led to a discovery of a new type of accretion disc, the so-called puffy disc. This outstanding result was published in ApJ Letters [Lancova et. al, 2019, ApJL]. A consequent paper that discusses detailed observable properties of such disc is currently being in the process of completion.

Our collaboration with Dr. Straub (MPI, Germany; LUTH, France), Prof. Blaes (UCSB, US) and Dr. Jiri Horak (ASU, Prague) was focused on the treatment of accretion disc oscillations. The obtained results were published within various conference and impacted journal papers [e.g.,Torok et al. 2019 MNRAS]. The most important findings, that were described in recently completed manuscripts, were connected to application of detailed models of pressure-supported discs on the data of Galactic microquasars [Kotrlova et. al, 2020,A&A]. Other non-geodesic forces acting on discs that are associated to their oscillations were considered within our collaboration with the group of Prof. Stella (INAF, Italy) and Dr. Falanga (ISSI, China&Switzerland). We investigated photon propagation and influence of radiation pressure on dynamics of discs along with several other effects. The results were described in numerous conference presentations and several journal papers [e.g. De Falco, et al., 2020, Phys. Rev. D.].

Members of our group participated in the international team of the Chinese eXTP mission (white papers: Dense matter with eXTP, Accretion in Strong Field Gravity with eXTP, special issue of Sci. China Phys. Mech. Astron. 2019). Furthermore, we were involved in several other collaborative studies (e.g. with Prof. Miller, EN - Urbancova et al., 2019, ApJ). Last but not least, in the field of particle physics and quantum field theory we published findings indicating existence of kaonium [Lichard, 2020, Phys. Rev. D.].

## Research carried out in 2018

We continued our collaboration with the group of Prof. Omer Blaes (UCSB, Santa Barbara, USA) and Dr. Odele Straub (LUTH, France). Our colaboration includes both numerical and analytic treatement of oscillations of pressure supported accretion discs. Regarding this field of research we published partial results within several conference contributions. These are currently being gathered together for a journal publication that we expect to finish and submit during the present (2018/2019) winter.

The other non-geodesic forces acting on the discs and connected to their oscillations have been considered within our collaboration with the group of prof. Luigi Stella (INAF, Italy) and dr. Maurizio Falanga (ISSI, China&Switzerland). Our common research resulted in the paper accepted for publication in Phys. Rev. D and other paper being currently in the reviewing process. In 2018 we also started scientific cooperation with Black Hole Initiative at Harvard University in Cambridge. Within this collaboration we plan to utilize their KORAL numerical code for simulations of the time dependent behaviour of accretion discs with different thickness.

During the year 2018 we investigated oscillation modes of accretion structures with non-constant angular momentum profiles. We find that the oscillations and stability of thick accretion flows is strongly effected by the gradient of the angular momentum. Towards the Keplerian distributions, the oscillations become less ordered which may have a strong impact on their observability. These findings suitably complete our previous study of the constant-angular momentum flows, and we are in the process of completing a paper related to this study that is intended for submission in MNRAS. We began exploration of structure and dynamical stability of radiation-pressure dominated thin accretion discs with a strong external irradiation. We summarized basic equations governing the disc radial structure including both thermal and dynamical effects by means of a radiation four-force. We find that the irradiation strongly influences a heat generation in the disc. Due to strong gravitational lensing, the irradiation may play an important role not only for neutron stars but also for accreting black holes. These efffects, along with the effects of variable intensity and polarization of emerging radiation in optically thin media, represent the subject of an up-comming paper scheduled for the next year.

Furthermore we considered other non-geodesic effects that influence the behaviour and variability of accretion discs. We studied motion of a test particle under the influence of a radiation field and Poynting-Robertson drag in three-dimensional Kerr spacetime, and we extended previous studies that had considered motion in equatorial plane only. Our analytical and numerical calculations show that the orbits of particles are strongly affected by the effects of general relativity. We demonstrated the existence of a critical hypersurface where gravity is balanced by the radiation forces [De Falco, et al, 2019, Phys. Rev. D, accepted for publication].

Within the same context we submitted a paper in which a disc in the equatorial plane is simulated using the Shakura-Sunyaev model including the Poynting-Robertson drag force. The most important new property is the existence of a critical radius which separates the disc into two parts – the outer part has the same properties as the Shakura-Sunyaev standard model, but the inner part, where the PR drag dominates, has a significantly smaller density, and the motion of the matter is faster. The radial distance of the transition depends mainly on the luminosity of the central object [Bakala et al, A&A, submitted].

We continued in our effort in confronting the accretion disc models with the observational data. We focused namely on the expectation of scaling of the observed QPO frequencies with the compact object mass ("the one over M scaling"). We identified an interesting behaviour of the neutron star data which can be compared to the case of black hole sources. We find that in the millisecond pulsar XTE J1807.4-294 the HF QPO time scale is clearly longer than those in the other NS LMXBs. Consequently models of QPOs imply that the X-ray pulsars' mass has to be about 50% higher than mass typical for other sources. The mass of this source is thus relatively close to the lowest masses of stellar mass black holes (Torok et al., MNRAS, submitted).

In the context of black hole HF QPOs we investigated the implications of QPO models that arise for the exceptional extragalactic X-ray source XMMUJ134736.6+173403. Our findings strongly support evidence for the presence of an active galactic nucleus black hole (AGN BH). Assuming the orbital origin of QPOs we calculated the upper and lower limit on AGN BH mass M, M = 10^7-10^9Msun. Comparing that to mass estimates of other sources, XMMUJ134736.6+173403 appears to be the most massive source with commensurable QPO frequencies, and its mass represents the current observational upper limit on AGN BH mass based on QPO observations [Goluchova, et al., A&A Letters, accepted for publication].

We completed the systematic study of behaviour of frequencies of perturbed geodesic motion which compares Kerr and Hartle-Thorne spacetimes and discusses the relevance of these spacetimes to numerical solutions of external spacetimes of astrophysical rotating axisymmetric objects [Urbancova et al., ApJ, submitted]. Last but not least, we started scientific cooperation with Black Hole Initiative at Harvard University in Cambridge. Within this collaboration we plan to utilize their KORAL numerical code simulations of the time dependent behaviour of accretion discs with different thickness.

## Scientific Studies Carried Out in 2017

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.