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In this paper, we study and compare the optical and X-ray counterparts of subparsec supermassive black hole binaries (SMBHBs). With that aim, we simulated the profiles of optical spectral lines emitted from the broad line region (BLR) as well as X-ray spectral lines emitted from the relativistic accretion disks around both black holes and compared them with each other. The obtained results showed that SMBHBs could cause a specific, but different variability of the lines from the optical part and Fe K$\alpha$ line, leaving potentially detectable imprints in their profiles. Since these imprints depend on the orbital phase of the system, they could be used for reconstructing the Keplerian orbits of the components in the observed SMBHBs. Moreover, such signatures in the optical and X-ray line profiles of the observed SMBHBs could be used as a tool for the detection of these objects as well as for studying their properties., Comment: 18 pages, 1 table, 10 figures. Accepted for publication in Advances in Space Research

Here we investigate the giant radio galaxy DA 240, which is a FR II source. Specifically, we investigate its flux density, as well as the spectral index distribution. For that purpose, we used publicly available data for the source: Leahy's atlas of double radio-sources and NASA/IPAC Extragalactic Database (NED). We used observations at 326 MHz (92 cm) and at 608 MHz (49 cm) and obtained spectral index distributions between 326 and 608 MHz. For the first time we give spectral index map for these frequencies. We found that the synchrotron radiation is the dominant radiation mechanism over most of the area of DA 240, and also investigated the mechanism of radiation at some characteristic points, namely its core and the hotspots. The results of this study will be helpful for understanding the evolutionary process of the DA 240 radio source., Comment: 9 pages, 5 figures. Accepted for publication in Contrib. Astron. Obs. Skalnate Pleso (Invited lecture at V Meeting on Astrophysical Spectroscopy - A&M DATA 2023)

In this paper we investigate a Yukawa gravity modification of the Newtonian gravitational potential in a weak field approximation. For that purpose we derived the corresponding equations of motion and used them to perform two-body simulations of the stellar orbits. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center (GC) and showed that it is close to the general relativity (GR) prediction. Using this observational fact, we evaluated parameters of the Yukawa gravity (the range of Yukawa interaction $\Lambda$ and universal constant $\delta$) with the Schwarzschild precession of the S-stars assuming that the observed values as indicated by the GRAVITY Collaboration will have a small deviation from GR prediction. GR provides the most natural way to fit observational data for S-star orbits, however, their precessions can be fitted by Yukawa gravity. Our main goal was to study the possible influence of the strength of Yukawa interaction, i.e. the universal constant $\delta$, on the precessions of S-star orbits. We analyze S-star orbits assuming different strength of Yukawa interaction $\delta$ and find that this parameter has strong influence on range of Yukawa interaction $\Lambda$. For that purpose we use PPN equations of motion in order to calculate the simulated orbits of S-stars in GR and Yukawa gravity. Using MCMC simulations we obtain the best-fit values and uncertainties of Yukawa gravity parameters for S-stars. Also, we introduce a new criterion which can be used for classification of gravitational systems in this type of gravity, according to their scales. We demonstrated that performed analysis of the observed S-stars orbits around the GC in the frame of the Yukawa gravity represent a tool for constraining the Yukawa gravity parameters and probing the predictions of gravity theories., Comment: 25 pages, 2 tables, 5 figures. Published in J. Cosmol. Astropart. P

The goal of this paper is to investigate the flux and spectral index distribution of FR II radio galaxy 4C 14.11. We focused on the distribution of flux and spectral indices over the lobes, as well as in their hot spots. For that purpose, we used publicly available observations of this radio galaxy given at 1450 and 8440 MHz. Particularly, we used Leahy's Atlas of radio-emitting double radio sources, Jodrell Bank Centre for Astrophysics in Manchester, as well as NASA/IPAC Extragalactic Database. We found that the non-thermal (synchrotron) radiation dominates over the areas of the lobes. Distinction between hot spots and rest of the lobes are much smaller in the spectral index than in the flux. We also found that over the inner parts of both lobes, spectral index $\alpha$ is flat in average and significantly higher than 1.2, indicating that 4C 14.11 is old AGN., Comment: 8 pages, 5 figures, 1 FITS file. Accepted for publication in Adv. Space Res

After giving a short overview of previous results on constraining of Extended Gravity (EG) by stellar orbits, we discuss the Schwarzschild orbital precession of S2 star assuming the congruence with predictions of General Relativity (GR). At the moment, the S2 star trajectory is remarkably fitted with the first post-Newtonian (pN) approximation of GR. In particular, both Keck and VLT (GRAVITY) teams declared that the gravitational redshift near its pericenter passage for the S2 star orbit corresponds to theoretical estimates found with the first pN approximation. In 2020, the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center (GC) and showed that it is close to the GR prediction. Based on this observational fact, we evaluated parameters of the EG theories with the Schwarzschild precession of the S2 star. Using the mentioned method, we estimate the orbital precession angles for some EG models including power-law f(R), general Yukawa-like corrections, scalar-tensor gravity (STG), and non-local gravity (NLG) theories formulated in both metric and Palatini formalism. In this consideration we assume that a gravitational field is spherically symmetric, therefore, alternative theories of gravity could be described only with a few parameters. Specifically, considering the orbital precession, we estimate the range of parameters of these EG models for which the orbital precession is like in GR. We then compare these results with our previous results, which were obtained by fitting the simulated orbits of S2 star to its observed astrometric positions. In case of power-law f(R), generic Yukawa-like correction, STG and NLG theories, we were able to obtain a prograde orbital precession, like in GR. According to these results, the method is a useful tool to evaluate parameters of the gravitational potential at the GC., Comment: 19 pages, 7 figures. Accepted for publication in Universe

In this study we investigate possible applications of observed S2 orbit around Galactic Center for constraining the Yukawa gravity at scales in the range between several tens and several thousands astronomical units (AU) to obtain graviton mass constraints. In our model we suppose that bulk distribution of matter (includes stellar cluster, interstellar gas distribution and dark matter) exists near Supermassive Black Hole (SMBH) in our Galactic Center. We obtain the values of orbital precession angle for different values of mass density of matter and we require that the value of orbital precession is the same like in General Relativity (GR). From that request we determine gravity parameter $\lambda$ and the upper value for graviton mass. We found that in the cases where the density of extended mass is higher, the maximum allowed value for parameter $\lambda$ is smaller and the upper limit for graviton mass is higher. It is due to the fact that the extended mass causes the retrograde orbital precession. We believe that this study is a very efficient tool to evaluate a gravitational potential at the Galactic Center, parameter $\lambda$ of the Yukawa gravity model, and to constrain the graviton mass., Comment: 7 pages, 6 figures, 2 tables. Accepted for publication in Eur. Phys. J. D

We use the Fundamental Plane of Elliptical Galaxies to constrain the so-called Hybrid Gravity, a modified theory of gravity where General Relativity is improved by further degrees of freedom of metric-affine Palatini formalism of $f(\cal R)$ gravity. Because the Fundamental Plane is connected to the global properties of elliptical galaxies, it is possible to obtain observational constraints on the parameters of Hybrid Gravity in the weak field limit. We analyze also the velocity distribution of elliptical galaxies comparing our theoretical results in the case of Hybrid Gravity with astronomical data for elliptical galaxies. In this way, we are able to constrain the Hybrid Gravity parameters $m_\phi$ and $\phi_0$. We show that the Fundamental Plane, i.e. $v_c/\sigma$ relations, can be used as a standard tool to probe different theories of gravity in the weak field limit. We conclude that Hybrid Gravity is able to explain elliptical galaxies with different stellar kinematics without the dark matter hypothesis., Comment: 7 pages, 5 figures. Accepted for publication in Eur. Phys. J. D

Here we study the potential observational signatures of supermassive black hole binaries (SMBHBs) in the Fe K$\alpha$ line profiles emitted from the accretion disks around their components. We simulated the Fe K$\alpha$ line emission from the relativistic accretion disks using ray tracing method in Kerr metric. The obtained profiles from the SMBHBs are then compared with those in the case of the single supermassive black holes (SMBHs). We considered two models of the SMBHBs: a model when the secondary SMBH is embedded in the accretion disk around the primary, causing an empty gap in the disk, and a model with clearly separated components, where the accretion disks around both primary and secondary give a significant contribution to the composite Fe K$\alpha$ line emission of a such SMBHB. The obtained results showed that both models of SMBHBs can leave imprints in the form of ripples in the cores of the emitted Fe K$\alpha$ line profiles, which may look like an absorption component in the line profile. However, in the case of the composite line profiles emitted from two accretion disks, these ripples could have much higher amplitudes and strongly depend on orbital phase of the system, while for those emitted from a disk with an empty gap, the corresponding ripples mostly have lower amplitudes and do not vary significantly with orbital phase. The present day X-ray telescopes are not able to detect such signatures in the observed X-ray spectra of SMBHBs. However this will be possible with the next generation of X-ray observatories, which will also enable application of such effects as a tool for studying the properties of these objects., Comment: 16 pages, 5 figures, 1 table. Presented as invited talk at the 12th Serbian Conference on Spectral Line Shapes in Astrophysics (http://www.scslsa.matf.bg.ac.rs/press12/day5/Jovanovic.pdf) and accepted for publication in "Contributions of the Astronomical Observatory Skalnat\'e Pleso (CAOSP)"

Non-local theories of gravity have recently gained a lot of interest because they can suitably represent the behavior of gravitational interaction in the ultraviolet regime. Furthermore, at infrared scales, they give rise to notable cosmological effects which could be important to describe the dark energy behavior. In particular, exponential forms of the distortion function seem particularly useful for this purpose. Using Noether Symmetries, it can be shown that the only non-trivial form of the distortion function is the exponential one, which is working not only for cosmological mini-superspaces, but also in a spherically symmetric spacetime. Taking this result into account, we study the weak field approximation of this type of non-local gravity, and comparing with the orbits of S2 stars around the Galactic center (NTT/VLT data), we set constraints on the parameters of the theory. Non-local effects do not play a significant role on the orbits of S2 stars around Sgr A*, but give richer phenomenology at cosmological scales than the $\Lambda$CDM model. Also, we show that non-local gravity model gives better agreement between theory and astronomical observations than Keplerian orbits., Comment: 11 pages, 6 figures. Accepted for publication in Phys. Rev. D

Recently, the LIGO-Virgo collaboration discovered gravitational waves and in their first publication on the subject the authors also presented a graviton mass constraint as $m_g < 1.2 \times 10^{-22}$ eV (Abbott et al., 2016). In the paper we analyze a potential to reduce upper bounds for graviton mass with future observational data on trajectories of bright stars near the Galactic Center. Since gravitational potentials are different for these two cases, expressions for relativistic advance for general relativity and Yukawa potential are different functions on eccentricity and semimajor axis, it gives an opportunity to improve current estimates of graviton mass with future observational facilities. In our considerations of an improvement potential for a graviton mass estimate we adopt a conservative strategy and assume that trajectories of bright stars and their apocenter advance will be described with general relativity expressions and it gives opportunities to improve graviton mass constraints. In contrast with our previous studies, where we present current constraints on parameters of Yukawa gravity (Borka et al., 2013) and graviton mass (Zakharov et al., 2016) from observations of S2 star, in the paper we express expectations to improve current constraints for graviton mass, assuming the GR predictions about apocenter shifts will be confirmed with future observations. We concluded that if future observations of bright star orbits during around fifty years will confirm GR predictions about apocenter shifts of bright star orbits it give an opportunity to constrain a graviton mass at a level around $5 \times 10^{-23}$ eV or slightly better than current estimates obtained with LIGO observations., Comment: 16 pages, 1 Figure, 1 Table, corrected minor typos

We demonstrate that the existence of a Noether symmetry in $f(R)$ theories of gravity gives rise to a further gravitational radius, besides the standard Schwarzschild one, determining the dynamics at galactic scales. By this feature, it is possible to explain the baryonic Tully-Fisher relation and the rotation curve of gas-rich galaxies without the dark matter hypothesis., Comment: 9 pages, 2 figures, to be published in JCAP

The fundamental plane (FP) of galaxies can be recovered in the framework of $f(R)$ gravity avoiding the issues related to dark matter to fit the observations. In particular, the power-law version $f(R)\propto R^n$, resulting from the existence of Noether symmetries for $f(R)$, is sufficient to implement the approach. In fact, relations between the FP parameters and the corrected Newtonian potential, coming from $R^n$, can be found and justified from a physical point of view. Specifically, we analyze the velocity distribution of elliptical galaxies and obtain that $r_c$, the scale-length depending on the gravitational system properties, is proportional to $r_e$, the galaxy effective radius. This fact points out that the gravitational corrections induced by $f(R)$ can lead photometry and dynamics of the system. Furthermore, the main byproduct of such an approach is that gravity could work in different ways depending on the scales of self-gravitating systems., Comment: 18 pages, 3 tables, 8 figures. Accepted for publication in Phys. Dark Universe

We use radio-continuum all-sky surveys at 1420 and 408 MHz with the aim to investigate properties of the Galactic radio source Lupus Loop. The survey data at 1435 MHz, with the linear polarization of the southern sky, is also used. We calculate properties of this supernova remnant: the brightness temperature, surface brightness and radio spectral index. For determining borders and calculation of its properties, we use the method we have developed. The non-thermal nature of its radiation is confirmed. The distribution of spectral index over its area is also given. A significant correlation between the radio spectral index distribution and the corresponding polarized intensity distribution inside the loop borders is found, indicating that the polarization maps could provide us information about the distribution of interstellar medium, and thus could represent one additional way to search for new Galactic loops., Comment: 12 pages, 7 figures. Accepted for publication in Rev. Mex. AA

Here we present a short overview and main results of our investigations of several effects which can induce shifts in the broad Fe K$\alpha$ line emitted from relativistic accretion disks around single and binary supermassive black holes. We used numerical simulations based on ray-tracing method in the Kerr metric to study the role of classical Doppler shift, special relativistic transverse Doppler shift and Doppler beaming, general relativistic gravitational redshift, and perturbations of the disk emissivity in the formation of the observed Fe K$\alpha$ line profiles. Besides, we also investigated whether the observed line profiles from the binary systems of supermassive black holes could be affected by the Doppler shifts due to dynamics of such systems. The presented results demonstrate that all these effects could have a significant influence on the observed profiles of the broad Fe K$\alpha$ line emitted from relativistic accretion disks around single and binary supermassive black holes., Comment: 9 pages, 5 figures, 1 table. Accepted for publication in Astrophysics and Space Science

We investigate the possibility to explain theoretically the observed deviations of S2 star orbit around the Galactic Centre using gravitational potentials derived from modified gravity models in absence of dark matter. To this aim, an analytic fourth-order theory of gravity, non-minimally coupled with a massive scalar field is considered. Specifically, the interaction term is given by analytic functions $f(R)$ and $f(R,\phi)$ where $R$ is the Ricci scalar and $\phi$ is a scalar field whose meaning can be related to further gravitational degrees of freedom. We simulate the orbit of S2 star around the Galactic Centre in $f(R)$ (Yukawa-like) and $f(R,\phi)$ (Sanders-like) gravity potentials and compare it with NTT/VLT observations. Our simulations result in strong constraints on the range of gravity interaction. In the case of analytic functions $f(R)$, we are not able to obtain reliable constraints on the derivative constants $f_1$ and $f_2$, because the current observations of S2 star indicated that they may be highly mutually correlated. In the case of analytic functions $f(R,\phi)$, we are able to obtain reliable constraints on the derivative constants $f_0$, $f_R$, $f_{RR}$, $f_{\phi}$, $f_{\phi\phi}$ and $f_{\phi R}$. The approach we are proposing seems to be sufficiently reliable to constrain the modified gravity models from stellar orbits around Galactic Centre., Comment: 9 pages, 6 figure to appear in Phys. Rev. D

We consider possible signatures for Yukawa gravity within the Galactic Central Parsec, based on our analysis of the S2 star orbital precession around the massive compact dark object at the Galactic Centre, and on the comparisons between the simulated orbits in Yukawa gravity and two independent sets of observations. Our simulations resulted in strong constraints on the range of Yukawa interaction $\Lambda$ and showed that its most probable value in the case of S2 star is around 5000 - 7000 AU. At the same time, we were not able to obtain reliable constrains on the universal constant $\delta$ of Yukawa gravity, because the current observations of S2 star indicated that it may be highly correlated with parameter $\Lambda$ in the range $(0 <\delta < 1)$. For $\delta > 2$ they are not correlated. However, the same universal constant which was successfully applied to clusters of galaxies and rotation curves of spiral galaxies ($\delta=1/3$) also gives a satisfactory agreement with the observed orbital precession of the S2 star, and in that case the most probable value for the scale parameter is $\Lambda \approx 3000 \pm 1500$ AU. Also, the Yukawa gravity potential induces precession of S2 star orbit in the same direction as General Relativity for $\delta > 0$ and for $\delta < -1$, and in the opposite direction for $-1 <\delta < 0$. The future observations with advanced facilities, such as GRAVITY or/and European Extremely Large Telescope, are needed in order to verify these claims., Comment: 16 pages, 8 figures, accepted for publication in JCAP

The average brightness temperatures and surface brightnesses at 22 MHz are derived for the four main Galactic radio-continuum loops (Loops I, II, III and IV, hereafter radio-loops). Also the radio-continuum spectra for the radio-loops are presented. Adding the average brightness temperatures at 22 MHz derived here with the average brightness temperatures derived from spectra published previously at 408, 820 and 1420 MHz we obtained clearly non-thermal spectral indices for all radio-loops. Our derived spectral indices are slightly shallower than those measured by previous works., Comment: 11 pages, 2 tables, 9 figures. Accepted for publication in Open Astronomy Journal

In this paper we estimated the temperatures and brightnesses of the Monoceros radio loop at 1420, 820 and 408 MHz. Linear spectrum is estimated for mean temperatures versus frequency between 1420, 820 and 408 MHz. The spectral index of Monoceros loop is also obtained. The brightness temperatures and surface brightnesses of the loop are computed using data taken from radio-continuum surveys at the three frequencies. The spectral index of the loop is also obtained from $T-T$ plots between 1420 - 820, 1420 - 408 and 820 - 408 MHz. The obtained results confirm non-thermal origin of the Monoceros radio loop., Comment: 9 pages, 7 tables, 5 figures. Accepted for publication in Astron. Nachr