Vacuum solutions of Einstein equations that depend on one coordinate

In the famous textbook written by Landau and Lifshitz all the vacuum metrics of the general theory of relativity are derived, which depend on one coordinate in the absence of a cosmological constant. Unfortunately, when considering these solutions the authors missed some of the possible solutions discussed in this article. An exact solution is demonstrated, which is absent in the book by Landau and Lifshitz. It describes space-time with a gravitational wave of zero frequency. It is shown that there are no other solutions of this type than listed above and Minkowski’s metrics. The list of vacuum metrics that depend on one coordinate is not complete without solution provided in this paper.

Hubble parameter and the potential of the cosmological scalar field

We consider a homogeneous isotropic Universe filled with cold matter (with zero pressure) and dynamic dark energy in a form of a scalar field. For known scalar field potential V(φ), the Friedmann equations are reduced to a system of the first order equation for the Hubble parameter H(z) and the second order equation for the scalar field as functions of the redshift z. On the other hand, knowledge of H(z) allows us to get the scalar field potential in a parametric form for a known cold matter content and three dimensional curvature parameter. We analyze when the accepted model mimics the dependence H(z) derived in the framework of the other models, e.g., hydrodynamic ones. Two examples of this mimicry are considered. The first one deals with the case when H2(z)~ Ωm(1+z)3+ΩΛ, but Ωm parameter overestimates the input of the cold matter (dark matter+baryons). The resulting scalar field potential is V(φ)=a+bsinh2(cφ), where the constants a,b,c depend on the Ω – parameters of the problem. In the other example we assume that some part of the dark matter has a non-zero equation of state p=wε, -1<w<1. In this case H2(z)~ Ωdm1(1+z)3(1+w)+ Ωb+Ωdm2)(1+z)3+ΩΛ. The corresponding potentials are defined for positive values of φ. For both signs of w potential V(φ) is a monotonically increasing function with typically an asymptotically exponential behavior; though for some choice of parameters we may have a singularity of V(φ)on a finite interval. Then we consider fitting of the potential for w from the interval [-0.2,0.2] for three different values of Ωdm2 by means of a simple formula Vfit(φ)=p0+p1exp(p2 φ). The dependencies pi(w) are presented and the approximation error is estimated.

Magnetic fields in limb solar flares on heights 2–14 Mm

We present the results of observations of two powerful limb solar flares which occured on 17 July 1981 and 14 July 2005. Spectral observations of these flares were carried out with the Echelle spectrograph of the Horizontal Solar Telescope of the Astronomical Observatory of Taras Shevchenko National University of Kyiv. In order to measure the magnetic fields in these flares, I ± V profiles of К СаІІ, HeI 4471.5 and Нα lines were studied. It was found that effective (averaged) magnetic field Вeff in the flares reached 1100–3000 G on heights 2–14 Mm. However, the spectral evidences to yet stronger fields of ~ 104 G range were found. In particular, the weak spectral evidences of large Zeeman splitting were found in first flare by HeI 4471.5 line; this evidences corresponds to superstrong magnetic field of 15.5 kG. In the second flare, Нα line has non-parallelism of bisectors of I ± V profiles which can reflect existence of 1550–3000 G fields in the flare. However, in frame of simple two-component model these observed values can correspond to true local (amplitude) magnetic fields Вmax in range 4.65–18 kG. Apparently, such superstrong magnetic fields arise in structures of a force-free type, with strong twisting of the field lines. It is precisely such field values that are necessary in solar flares for energy reasons. Indeed, solar flares emit energy in the range of 1027-1032 erg in a volume of the order of 1027 cm3. Elementary calculations show that in order to provide such energy in such a volume, the magnetic field strength should be at least 103 G. In addition, if we take into account that solar magnetic fields have the sub-telescopic (spatially unresolved) structure, then the local magnetic field intensities in the flares at the coronal level can be expected even higher.

Effect of the sourse ellipticity on light curves in extragalactic gravitational lens systems

In extragalactic gravitational lens system (GLS) several macro-images of a remote source (quasar) are observed. Gravitational microlensing leads to uncorrelated brightness variations of the macro-images. These variations can be separated from proper brightness changes of the source, which are repeated in each image with some relative delay. In most papers the gravitational microlensing effects in extragalactic GLS typically deal with centrally symmetric sources, though the real form of the source can be more complicated. In this paper we consider statistical signals of the source ellipticity in light curves of microlensed objects, which arise as a result of observations of many high amplification events. As a first step, we consider a qualitative version of the problem, when an elliptic source with Gaussian brightness distribution is crossed by a number of simple (fold) caustics with different orientations. Also we assume that the caustic network is isotropic, that is all orientations of the caustics and directions of their velocities are equally possible. We use the linear fold caustic approximation for the amplification of a small point source, when two critical images appear/disappear after the caustic crossing. For a rough estimate, the strength and velocity of the caustic are fixed by certain characteristic values. We estimate the averaged light curve after many caustic crossing events and compare maxima of brightness on the light curves for different eccentricities of the source. The ellipticity signal in the light curves is noticeable for a considerable oblateness of the source. Though we expect that the effect will be smeared out after taking into account the distribution of the caustic velocities and caustic strengths. Possible complications of the problem are indicated due to interplay of effects due to velocity distribution of stars in the lensing galaxy and bulk motion of the lensing galaxy as a whole.

Astronomical observatory of Taras Shevchenko National University of Kyiv in 2019

In 2019, the Astronomical Observatory had 48 full-time employees and 11 part-time employees. A total of 59 employees, including 34 scientists, including 24 full-time (6 doctors of sciences and 16 candidates of sciences) and 10 part-time employees (1 doctor and 3 candidates of sciences). The observatory consists of the Department of Astrophysics (Head of the Department, Doctor of Physical and Mathematical Sciences, Professor VI Zhdanov), the Department of Astrometry and Small Bodies of the Solar System (Head of the Department, Candidate of Physical and Mathematical Sciences Lukyanyk IV.), and 2 observation stations (the village of Lisnyky, the village of Pylypovychi). During the year, 4 budget topics were implemented. The main scientific results. The active nuclei of galaxies have been identified, which are potential sources of extremely high-energy cosmic rays, taking into account energy losses and the influence of magnetic fields on the way to Earth (distance up to 300 million light-years). A large array of observational data of small bodies of the solar system on the 6th (SAO RAS), 4.1th SOAR (Chile), 2.6th (KrAO), 2nd (Terskol), 2nd (OPTICON), 1.3th (AI SAN), 0.70th and 0.48th (v. Lisnyky) telescopes. The reliability of Stokes diagnostics methods of small-scale magnetic fields of the Sun’s photosphere in the interpretation of spectropolarimetric observations of the infrared line Si I 1082.7 nm on modern (VTT, SST, GREGOR) and future (DKIST, EST with a diameter of 4 m) ground telescopes estimated. Published 2 monographs, 65 scientific articles, 25 of them in foreign publications; made 75 reports at scientific conferences.

Astronomical observatory of Taras Shevchenko National University of Kyiv in 2020

In 2020, the Astronomical Observatory had 58 employees, of which 48 full-time and 10 part-time, scientists – 34 (6 doctors of sciences and 17 candidates of sciences). During the year, 4 budget and 3 contractual topics were implemented. The main scientific results. It is shown that the observed gamma radiation of the TeV range around the SGR 1900 + 14 magnetar – a neutron star with a superpowerful magnetic field – can be generated by two related sources: the undiscovered Hypernova residue, which generated SGR 1900 + 14 and / or the magnetar-wind nebula generated by this magnetar. As part of the implementation of joint international research projects, observations were made at the 6th BTA (SAO RAS), the 2nd HST (India), the 2.6th ZTSh (KrAO), the 2nd (Terskol), the 1.3th (Slovakia) and others telescopes, which resulted in a large array of photometric, polarimetric and spectral data of 9 comets, 6 asteroids, 8 satellites of Jupiter and Saturn and 1 centaur. According to the research results, 2 monographs, 76 scientific articles were published, 72 reports were made at scientific conferences.

On a possibility of transfer of the planet troyans to centaurs

Jupiter Trojans and Neptune Trojans have been selected from the Minor Planet center catalog for 2020. Numerical calculations of the evolution of orbits on intervals of up to 1 million years have been carried out. It has been established that all discovered by today Neptune Trojans and the numbered Jupiter Trojans are unlikely to transfer into the Centaur population during the next hundreds of thousands of years.

Determination of equatorial coordinates of bolide from observations with stationary low-sensitive home guard video camera

Method for determination of equatorial coordinates of a bright bolide detected with wide-angle low-sensitive home guard camera on 9 August 2020 above Kyiv is presented. Due to low sensitivity of the camera there were no objects for comparison in the frames with the bolide, and sky was obstructed more than a half by the crown of threes. For a search of objects of comparison with known equatorial coordinates we proposed to use the images of the Moon and Mars, which systematically got into frames during the next month – September. The corresponding formulae are presented. The precision of the bolide’s equatorial coordinates calculation were tenths of degree at field of view of the camera 100°, and the trajectory angular length was near 15°. The bolide was very slow, and according to calculations did not belong to the Perseid meteor shower, which was active during the observations.

Impact of the statistical effects on the Hubble constant value obtained from velocities of galaxies

We can obtain the Hubble constant value for the late Universe from the sample of radial velocities of galaxies and independent estimations of distances to them based on any statistical relation such as Cepheid variables, Tully-Fisher relation etc. Usually, the method of least squares is used when processing such data. However, the value of the Hubble constant is somewhat underestimated due to a statistical effect similar to the wellknown Malmquist bias. The main source of underestimation is associated with the deviation of the distances determined from the statistical dependence from their true values. The decrease of obtained Hubble constant value is about 5% for an error in the distance estimation of 20% and about 9% with an error of 30%. This impact cannot explain the recently discovered tensions between the values of Hubble constant obtained from the early and the late Universe. The estimation H0 = 67.4 km/s/Mpc obtained from observations in the recombination era account for about 92% of the average of the estimations based on observations of not very distant objects H0 = 73.3 km/s/ Mpc. Indeed, the described effect leads to underestimation of the largest of these values.

Hubble parameter in f(R)-gravity

In view of the famous problem with the “Hubble constant tension” there is a number of approaches to modify the cosmological equations and correspondingly modify Hubble parameter H(z) in order to to relieve the tension between the “early” and “late” Hubble constants. f(R)– gravity is one of such possible modifications. We discuss how to choose the Lagrangian in the f(R)– gravity on account of observational data within the homogeneous isotropic cosmology. The equation is obtained that enable us to derive f(R) for given Hubble parameter H(z). This yields a second order differential equation with corresponding degrees of freedom. If H(z) corresponds to that obtained from usual Friedmann equations, this equation yields a condition for f(R) to mimic the observable quantities of the standard ΛCDM with the above-mentioned freedom. To reduce this freedom on needs additional considerations, which involve the other observable quantities, such as those which appear in considerations of cosmological perturbations on the isotropic and homogeneous background. Also, we consider the reverse problem to find for given f(R). This is fulfilled within an approximation in case of small deviation of f(R) from the General Relativity value.