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The thermodynamic properties of electron gas under the extreme conditions of high temperature, high matter density, and/or a strong magnetic field largely determine the behaviour of matter in upper layers of neutron stars and accretion columns of magnetized neutron stars in binary systems. A strong magnetic field in these objects makes the motion of electrons across the field essentially quantum. The possible electron degeneracy and relativism of electrons are also important. When studying accretion onto a magnetar in a binary system, the intensive generation of electron-positron pairs in the quantizing magnetic field should also be taken into account. We consider in detail the thermodynamic properties of a gas of free electrons in strong magnetic fields, taking into account their relativism and degeneracy, as well as the equilibrium creation of electron-positron pairs in a high-temperature plasma in the presence of a quantizing magnetic field., Comment: 33 pages, 15 figures

The problem of the motion of two gravitating bodies in the presence of dark energy (DE), considered as a perturbing factor, is investigated. In addition to the orbit precession frequency obtained in previous studies, the correction to the orbital motion frequency was calculated, and the oscillations of the semi-major axis and the eccentricity of the orbit caused by the influence of DE were studied.

The results of three-dimensional numerical simulation of heat transfer in the outer layers of magnetized neutron stars are presented. Determining the structure of the magnetic field on a neutron star surface is an important task of modern astrophysics. In the presence of strong magnetic fields, the medium becomes anisotropic, and the laws of heat conduction change. The tensor coefficient of thermal conductivity for magnetized degenerate plasma was obtained by Bisnovatyi-Kogan and Glushikhina by solving the Boltzmann equation with the Chapman–Enskog method. In this paper, the temperature distribution on the surface of a magnetized neutron star is obtained for magnetic fields of the dipolar and quadrupolar type, as well as for their superposition. To numerically solve the stationary temperature distribution problem in the outer layers of a magnetized neutron star, the basic (support) operator numerical method was extended to a three-dimensional case. The problem was solved on the grid which consists of tetrahedra.

In this paper, we investigate the influence of the plasma surrounding the gravitational lens on the effect of microlensing. In presence of plasma around the lens, the deflection angle is determined by both the gravitational field of the lens and the chromatic refraction in the inhomogeneous plasma. We calculate microlensing light curves numerically for point-mass lens surrounded by power-law density distribution of plasma. A variety of possible curves is revealed, depending on the plasma density and frequency of observations. In the case of significant influence of plasma, the shape of microlensing light curve is strongly deformed in comparison with vacuum case. If the refractive deflection is large enough to compensate or to overcome the gravitational deflection, microlensing images can completely disappear for the observer. In this case, the remarkable effect occurs: formation of a 'hole' instead of a 'hill' in the center of microlensing light curve. Observational prospects of 'hill-hole' effect in different microlensing scenarios are discussed., Comment: Published in MNRAS

Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions are obtained for a uniform sphere with a hollow spherical volume and central mass inside the sphere. Solutions are also obtained for an arbitrary number of spherical layers with the same density, but with different equilibrium distribution functions., 8 pages, 1 figure

Propagation of strong shock wave in the expanding universe is studied using approximate analytic, and exact numerical solution of self-similar equations. Both solutions have similar properties, which change qualitatively, depending on the adiabatic powers $\gamma$. In the interval $1\gamma_{cr}$ a pressure becomes zero at finite radius, and a spherical void appears around the origin in both solutions. All matter is collected in thin layer behind the shock wave front. The structure of this layer qualitatively depends on $\gamma$. At the inner edge of the layer the pressure is always zero, but the density on this edge is jumping from zero to infinity at $\gamma \approx 1.4$ in both solutions., Comment: Keywords: cosmology, strong shock wave, self-similar solution. arXiv admin note: text overlap with arXiv:1808.02112

1. Peculiar Milestone: SN and GRB. 2. GW: BH+BH, NS+NS. 3. BH Shadow. 4. “Cyclotron” lines and polarisation. 5. Flight to other planets.

Determination of a magnetic field structure on a neutron star (NS) surface is an important problem of a modern astrophysics. In a presence of strong magnetic fields a thermal conductivity of a degenerate matter is anisotropic. In this paper we present 3D anisotropic heat transfer simulations in outer layers of magnetized NSs, and construct synthetic thermal light curves. We have used a different from previous works tensorial thermal conductivity coefficient of electrons, derived from the analytical solution of the Boltzmann equation by the Chapman-Enskog method. We have obtained a NS surface temperature distribution in presence of dipole-plus-quadrupole magnetic fields. We consider a case, in which magnetic axes of a dipole and quadrupole components of the magnetic field are not aligned. To examine observational manifestations of such fields we have generated thermal light curves for the obtained temperature distributions using a composite black-body model. It is shown, that the simplest (only zero-order spherical function in quadrupole component) non-coaxial dipole-plus-quadrupole magnetic field distribution can significantly affect the thermal light curves, making pulse profiles non-symmetric and amplifying pulsations in comparison to the pure-dipolar field., accepted for publication in MNRAS, 12 pages, 7 figures

The solution of Boltzmann equation for plasma in magnetic field, with arbitrarily degenerate electrons and non-degenerate nuclei, is obtained by Chapman-Enskog method. Functions, generalizing Sonin polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in non-quantized magnetic field is calculated. For non-degenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained, which are compared with results of previous authors. The Lorentz approximation, with neglecting of electron-electron encounters, is asymptotically exact for strongly degenerate plasma. We obtain, for the first time, in three polynomial approximation, with account of electron-electron collisions, analytical expressions for the heat conductivity tensor for non-degenerate electrons, in presence of a magnetic field. Account of the third polynomial improved substantially the precision of results. In two polynomial approximation our solution coincides with the published results. For strongly degenerate electrons we obtain, for the first time, an asymptotically exact analytical solution for the heat conductivity tensor in presence of a magnetic field. This solution has considerably more complicated dependence on the magnetic field than those in previous publications, and gives several times smaller relative value of a thermal conductivity across the magnetic field at $\omega\tau\gtrsim 0.8$., Comment: 23 pages, 3 figures. arXiv admin note: text overlap with arXiv:0710.0854 by other authors

The application of the Lagrangian completely conservative implicit operator-difference scheme for the simulation of magnetorotational (MR) processes in astrophysics is described. Results of 2D simulations of MR core-collapsed supernova explosion are represented.

We consider the low-mass flare stars which form the bulk of the population in the galactic bulge as a source of the positrons needed to form the observed narrow annihilation line from the galactic bulge. Estimates based on the observed flares in low-mass stars, together with observations of the annihilation line in solar flares, show that the rate of production of positrons in flares in the stars in the bulge may be sufficient to explain the formation of the narrow stationary annihilation line observed from the region of the galactic bulge.

In this paper we investigate the relation between the potential and geometric time delays in gravitational lensing. In the original paper of Shapiro (1964), it is stated that there is a time delay in the radar signals between Earth and Venus that pass near a massive object (the Sun), compared to the path taken in the absence of any mass. The reason for this delay is connected with the influence of gravity on the coordinate velocity of a light ray in a gravitational potential. The contribution from the change of the path length, which happens to be of second order, is considered as negligible. Nevertheless, in the gravitational lens theory the geometrical delay, related to the change of path length, is routinely taken into account along with the potential term. In this work we explain this apparent discrepancy. We address the contribution of the geometric part of the time delay in different situations, and introduce a unified treatment with two limiting regimes of lensing. One of these limits corresponds to the time delay experiments near the Sun where the geometrical delay is shown to be negligible. The second corresponds to the typical gravitational lens scenario with multiple imaging where the geometrical delay is shown to be significant. We introduce a compact, analytical, and quantitative criteria based on relation between the angular position of source and the Einstein radius. This criterion allows one to find out easily when it is necessary to take the geometrical delay into account. In particular, it is shown that the geometrical delay is non-negligible in the case of good alignment between source, lens and observer, because in such a case it becomes a first order quantity (the same order as the potential term)., Comment: 21 pages, 5 figures

Periodic changes in a thermal soft X-ray flux of a rotating neutron star indicate a non-uniform distribution of the surface temperature. A possible cause of this phenomenon is a suppression of the heat flux across the magnetic field lines in a crust and an envelope of magnetized neutron stars. In this paper we study three-dimensional effects, associated with non-axisymmetric magnetic fields in neutron stars. We calculate the surface temperature distribution by solving numerically a three dimensional heat transfer equation in a magnetized neutron star crust. We adopt an anisotropic (tensorial) electron thermal conductivity coefficient, which is derived as an analytical solution of the Boltzmann equation with a Chapman-Enskog method. To calculate the surface temperature distribution, we construct a local one-dimensional plane-parallel model ("Ts-Tb"-relationship) of a magnetized neutron star envelope. We then use it as an outer boundary condition for the three-dimensional problem in the crust to find the self-consistent solution. To study possible observational manifestations from anisotropic temperature distributions we calculate light curves with a composite black-body model. Our calculations show, that a non-axisymmetric magnetic field distribution can lead to the irregular non-sinusoidal shape of a pulse profile as well as in some cases a significant amplification of pulsations of the thermal flux in comparison to the pure-dipolar magnetic field configurations., Comment: Proceedings paper from "High Energy Phenomena in Relativistic Outflows VII" (HEPRO7, 9-12 July 2019, Facultat de Fisica, Universitat de Barcelona, Spain), accepted by Proceedings of Science (PoS)

Cosmic expansion influences the angular size of black hole shadow. The most general way to describe a black hole embedded into an expanding universe is to use the McVittie metric. So far, the exact analytical solution for the shadow size in the McVittie metric, valid for arbitrary law of expansion and arbitrary position of the observer, has not been found. In this paper, we present the first analytical solution for angular size of black hole shadow in McVittie metric as seen by observer comoving with the cosmic expansion. We use a method of matched asymptotic expansions to find approximate solution valid within the entire range of possible positions of observer. As two particular examples, we consider black hole in de Sitter and matter dominated universe., Comment: 13 pages, 2 figures

Advancements in the black hole shadow observations may allow us not only to investigate physics in the strong gravity regime, but also to use them in cosmological studies. In this paper, we propose to use the shadow of supermassive black holes as a standard ruler for cosmological applications assuming the black hole mass can be determined independently. First, observations at low redshift distances can be used to constrain the Hubble constant independently. Secondly, the angular size of shadows of high redshift black holes is increased due to cosmic expansion and may also be reachable with future observations. This would allow us to probe the cosmic expansion history for the redshift range elusive to other distance measurements. Additionally, shadow can be used to estimate the mass of black holes at high redshift, assuming that cosmology is known.

1. Peculiar Milestone: SN and GRB. 2. GW: BH+BH, NS+NS. 3. BH Shadow. 4. “Cyclotron” lines and polarisation. 5. Flight to other planets.

We analytically investigate the influence of a cosmic expansion on the shadow of the Schwarzschild black hole. We suppose that the expansion is driven by a cosmological constant only and use the Kottler (or Schwarzschild-deSitter) spacetime as a model for a Schwarzschild black hole embedded in a deSitter universe. We calculate the angular radius of the shadow for an observer who is comoving with the cosmic expansion. It is found that the angular radius of the shadow shrinks to a non-zero finite value if the comoving observer approaches infinity., Comment: 11 pages, 7 figures

An exact analytic solution of self-similar equations is obtained for propagation of a strong shock in a flat expanding Friedman universe. The time and radial dependences of the density and velocity of the polytropic gas behind the shock wave are obtained. The shock velocity in the expanding medium decreases as ~t−1/5, slower than the shock velocity in the static uniform medium (~t−3/5), and its radius increases ~t4/5, more rapidly than in a uniform non-gravitating medium (~t2/5). So, the shock propagates in the direction of a decreasing density at a larger speed than in a static medium due to accelerating action of the decreasing density, even in the presence of self-gravity.

In the paper we discuss the results of simulations of magnetorotational supernova explosion. Due to the nonuniform core collapse the rotation of the core becomes differential. In the case when initial poloidal magnetic field is nonzero it starts to amplify with time. At the initial stage of the amplification of the magnetic field its growth is linear. Later the exponential growth of all components of the magnetic field show the development of Magneto-Rotational-Instability of special type (Tayler-type instability). We call it Magneto-Differential-Rotational-Instability (MDRI).

Dark energy limits a radius of big clusters of galaxies, and may accelerate hot gas outflowing from the cluster as a wind. Collision of accelerated winds, in presence of a magnetic field, produce a situation favorable for acceleration of EHECR.

The question of why the observed periods of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) cluster in the range 2–12 s is discussed. The possibility that AXPs and SGRs are the descendants of high-mass X-ray binaries that have disintegrated in core-collapse supernova explosions is investigated. The spin periods of neutron stars in high-mass X-ray binaries evolve towards the equilibrium period, which is a few seconds, on average. After the explosion of its massive companion, the neutron star becomes embedded in a dense gaseous envelope, and accretion from this envelope leads to the formation of a residual magnetically levitating disk. It is shown that the expected mass of the disk in this case is 10−7–10−8 M⊙, which is sufficient to support accretion at the rate 1014–1015 g/s over a few thousand years. During this period, the star manifests itself as an isolated X-ray pulsar with a number of parameters similar to those of AXPs and SGRs. The periods of such pulsars can cluster if the lifetime of the residual disk does not exceed the spin-down timescale of the neutron star.

A mechanism of formation of gravitational waves in the Universe is considered for a nonspherical collapse of matter. Nonspherical collapse results are presented for a uniform spheroid of dust and a finite-entropy spheroid. Numerical simulation results on core-collapse supernova explosions are presented for the neutrino and magnetorotational models. These results are used to estimate the dimensionless amplitude of the gravitational wave with a frequency \nu ~1300 Hz, radiated during the collapse of the rotating core of a pre-supernova with a mass of 1:2M(sun) (calculated by the authors in 2D). This estimate agrees well with many other calculations (presented in this paper) that have been done in 2D and 3D settings and which rely on more exact and sophisticated calculations of the gravitational wave amplitude. The formation of the large-scale structure of the Universe in the Zel'dovich pancake model involves the emission of very long-wavelength gravitational waves. The average amplitude of these waves is calculated from the simulation, in the uniform spheroid approximation, of the nonspherical collapse of noncollisional dust matter, which imitates dark matter. It is noted that a gravitational wave radiated during a core-collapse supernova explosion in our Galaxy has a sufficient amplitude to be detected by existing gravitational wave telescopes.

1. Peculiar Milestone: SN and GRB. 2. GW: BH+BH, NS+NS. 3. BH Shadow. 4. “Cyclotron” lines and polarisation. 5. Flight to other planets.

A solution for cosmological expansion in the presence of dark matter is presented, and observational results from which a conclusion on the present value of the cosmological constant is obtained, are discussed. A solution is obtained for hydrodynamic outflow of polytropic gas from a gravitating center, in the presence of uniform Dark Energy (DE). The antigravity of DE is enlightening the outflow and makes the outflow possible at smaller initial temperature at the same density. The main property of the wind in the presence of DE is its unlimited acceleration after passing the critical point. Applying this solution to winds from galaxy clusters, we suggest that a collision of a strongly accelerated wind with another galaxy cluster, or with another galactic cluster wind, could lead to the formation of highest energy cosmic rays.

The theory of gravitational lensing is well developed for light propagation in vacuum in the approximation of weak deflection. We discuss two ways of extending the studies of usual gravitational lens theory which were recently theoretically developed. One way is to go beyond the weak deflection approximation and consider relativistic images formed by the photons performing one or several revolutions around the central object. Another way is to consider the propagation of light in a plasma instead of vacuum, in the presence of gravity. In this case the lensing angle depends on the plasma distribution and the photon frequency. The gravitational deflection of a light ray even in a homogeneous plasma differs from the vacuum (Einstein) angle and depends on the photon frequency. We also discuss the recent results on the influence of a plasma on positions and magnifications of relativistic images.

We consider the Kepler two-body problem in presence of the cosmological constant $\Lambda$. Contrary to the classical case, where finite solutions exist for any angular momentum of the system $L$, in presence of $\Lambda$ finite solutions exist only in the interval $0, Comment: 15 pages, 3 figures

We obtain a solution for the hydrodynamic outflow of the polytropic gas from the gravitating center, in presence of the uniform Dark Energy (DE). The antigravity of DE is enlightening the outflow and make the outflow possible at smaller initial temperature, at the same density. The main property of the wind in presence of DE is its unlimited acceleration after passing the critical point. In application of this solution to the winds from galaxy clusters we suggest that collision of the strongly accelerated wind with another galaxy cluster, or with another galactic cluster wind could lead to the formation of a highest energy cosmic rays., Comment: 13 pages, 7 figures

Strong discontinuities in solutions of the gas dynamic equations under isentropic conditions, i.e., with continuity of entropy at the discontinuity, are examined. Solutions for a standard shock wave with continuity of energy at the discontinuity are compared with those for an isentropic 'shock wave'. It is shown that numerical simulation of astrophysical problems in which high-amplitude shock waves are encountered (supernova explosions, modelling of jets) with conservation of entropy, rather than of energy, leads to large errors in the shock calculations. The isentropic equations of gas dynamics can be used only when there are no strong discontinuities in the solution or when the intensity of the shocks is not high and they do not significantly affect the flow., 10 pages, 5 figures

The motion of classical spinning test particles in the equatorial plane of a Kerr black hole is considered for the case where the particle spin is perpendicular to the equatorial plane. We review some results of our recent research of the innermost stable circular orbits (ISCO) [P.I. Jefremov, O.Yu. Tsupko and G.S. Bisnovatyi-Kogan, Phys.Rev. D 91 124030 (2015)] and present some new calculations. The ISCO radius, total angular momentum, energy, and orbital angular frequency are considered. We calculate the ISCO parameters numerically for different values of the Kerr parameter $a$ and investigate their dependence on both black hole and test particle spins. Then we describe in details how to calculate analytically small-spin corrections to the ISCO parameters for an arbitrary values of $a$. The cases of Schwarzschild, slowly rotating Kerr and extreme Kerr black hole are considered. The use of the orbital angular momentum is discussed. We also consider the ISCO binding energy. It is shown that the efficiency of accretion onto an extreme Kerr black hole can be larger than the maximum known efficiency (42 %) if the test body has a spin., Paper is written for special issue of the journal dedicated to the centenary of Prof. K.P. Staniukovich. Some results of our previous paper arXiv:1503.07060 are used

We discuss in detail our new results in the field of gravitational lensing in a plasma. We show that gravitational deflection by a point mass in a homogeneous plasma differs from vacuum deflection and depends on the frequency of the photon. This frequency dependence resembles the properties of a refractive prism spectrometer, whose strongest action takes place for very long radio waves. We also derive the photon deflection angle by a point mass in an inhomogeneous plasma. Then we consider a more general case of photon deflection by a mass distribution in an inhomogeneous plasma. Our approach allows us to consider two effects simultaneously: the gravitational deflection in a plasma which differs from the vacuum case (a new effect), and the non-relativistic effect (refraction) connected with the plasma inhomogeneity.

We consider various physical processes that affect the thermal balance of an X-ray jet. We focus on the rapid cooling of dense jets via bremsstrahlung, and all processes are considered from the viewpoint of their contributions to the jet thermal balance. Jet heating by Compton scattering of hard X-ray photons from the hot corona, the effect of shocks in the jet on heating of the jet, and the transformation of jet kinetic energy into heat via Coulomb collisions between protons of the jet and corona are considered. Numerical values have been obtained for the Galactic microquasar SS 433 based on previous results for modeling the X-ray spectrum of this source. Collisions of the jet particles with the ambient gas turns out to be the most important jet heating mechanism for this source.

We study physics of clusters of galaxies embedded in the cosmic dark energy background. Under the assumption that dark energy is described by the cosmological constant, we show that the dynamical effects of dark energy are strong in clusters like the Virgo cluster. Specifically, the key physical parameters of the dark mater halos in clusters are determined by dark energy: 1) the halo cut-off radius is practically, if not exactly, equal to the zero-gravity radius at which the dark matter gravity is balanced by the dark energy antigravity; 2) the halo averaged density is equal to two densities of dark energy; 3) the halo edge (cut-off) density is the dark energy density with a numerical factor of the unity order slightly depending on the halo profile. The cluster gravitational potential well in which the particles of the dark halo (as well as galaxies and intracluster plasma) move is strongly affected by dark energy: the maximum of the potential is located at the zero-gravity radius of the cluster., 8 pages, 1 figure

The oscillations of a magnetized incompressible cylinder with a uniform magnetic field along its axis and the resulting electromagnetic field are studied. Two types of characteristic oscillations, torsional and Alfven, are found to exist in the linear approximation. In the case of an infinite cylinder with torsional oscillations, no electromagnetic field is generated. In the case of Alfven oscillations, an electromagnetic field develops around the cylinder with a local flux density that falls off exponentially with radial distance from the axis of the cylinder and has a time average of zero. The results are interpreted physically.

One of the difficulties of numerical simulations of cold supersonic astrophysical flows is a big difference in different types of energy. Gravitational and/or kinetic energy of the gas could be much larger than its internal energy. In such a case, it is possible to get large numerical errors in the simulations. To avoid this difficulty, conservation of entropy equation was used instead of energy conservation equation. The entropy conservation equation does not contain the gravitational and kinetic energy. The application of the isentropic set of equations is correct when the flow does not contain shocks or the amplitude of the shocks (shock wave Mach number) is not large. We estimate the violation of the energy conservation low when the “shock wave” is isentropic.

We consider the low-mass flare stars which form the bulk of the population in the galactic bulge as a source of the positrons needed to form the observed narrow annihilation line from the galactic bulge. Estimates based on the observed flares in low-mass stars, together with observations of the annihilation line in solar flares, show that the rate of production of positrons in flares in the stars in the bulge may be sufficient to explain the formation of the narrow stationary annihilation line observed from the region of the galactic bulge.