An introduction to the theory of internal structure of supermassive compact celestial bodies

Different in principle from the contemporary standard black hole accretion models, a new approach to the understanding of the internal structure of highly compact stationary supermassive celestial bodies has been worked out. The equations of equilibrium configurations of baryonic protomatter (ECBP) have been discussed. In a particular case of ideal degenerated neutron gas in absence of a process of inner distortion of the space and time, it has been shown that the theory suggested by Ter-Kazarian (1989c) leads to the same results as those obtained by Oppenheimer and Volkoff (1939) based on Einstein's theory. The numerical integration of equations of ECBP in the most simple case of equilibrium single-component configurations of degenerated ideal gas of neutrons in a presence of one-dimensional space-like inner distortion of space-time continuum is carried out. It has been shown that the stable stationary supermassive cores are formed in the central parts of the considered configurations. As the models of active galactic nuclei (AGNs) one has considered only the configurations that consisted of these cores surrounded by accretion disks. The fundamental difference from the standard black-hole accretion models is the fact that the central cores are in a stable equilibrium state with certain radial distributions of density and pressure and with a number of integral characteristics. The significant effect of metric singularity cut-off has been established, due to the action of which a singularity of metric ceased to be significant. The numerous integrations have also revealed the other fact of great importance, the presence within the outlined theory of a rigorous restriction on the upper limit of possible values of total masses of considered equilibrium configurations, which is to beM3.5×10⁸ M . In the last section one has proceeded to the direct modelling of concrete AGNs (for 61 sources), the whole point of which comes to the solving of the inverse problem. The results of all calculations that have been carried out in the present work are summarized in Tables I–VII and represented by means of numerous figures. Finally, one should emphasize the important fact of the existence of BL Lac objects OJ 287, 3C 66A, and B2 1308+32, the observed time-scale for flux variations of which are inconsistent with contemporary black hole aceretion models. The case is quite different within the scope of the suggested theory. It seems that a decisive significance for these objects has the action of metric singularity cut-off effect. Due to this their observed sizes are less than the sizes of corresponding spheres of the event horizon. This may serve as a further indication that the suggested theory is preferable to the standard models.     

On the stability of compact supermassive objects

Proceeded from the gravitation equations proposed by one of authors it was argued in a previous paper that there can exist supermassive compact configurations of degenerated Fermi‐gas without events horizon. In the present paper we consider the stability of these objects by a method like the one used in the theory of stellar structure. It is shown that the configurations are stable.     

On population of hazardous celestial bodies in the near-Earth space

In recent years, following the Chelyabinsk event of February 15, 2013, the lower size limit for presumably dangerous near-Earth objects has been decreased manyfold (essentially, from 140 m to ~10 m). This has drawn an increased attention to the properties of the population of decameter-sized bodies, in particular, the bodies that approach the Earth from the sunward side (daytime sky). The current paper is concerned with various properties of this population. The properties of the ensemble are analyzed using both observational data from other authors and theoretical estimates obtained by cloning virtual bodies. This question is of great practical importance, as the means for detecting such bodies (for example, the SODA project) need to be developed with consideration for the requirements imposed by the population properties. We have shown that the average rate of entering near-Earth space (NES), i.e., at distances less than ~1 million km from the Earth, for decameter-sized and larger bodies from the daytime sky (elongation values of entry points less than 90°) is approximately 620 objects per year for elongation angles of the detection point <90° and approximately 220 objects per year for elongation angles of the detection point <45°.     

Virial oscillations of celestial bodies

A general approach to the solution of the perturbed oscillation problem for celestial bodies is considered. The solution sought describes unperturbed virial oscillations (zero approximation) affected by external perturbing effects. In the general case, these perturbations can be expressed by an arbitrary given function of time, Jacobi's function and its first derivative. Standard methods and modes of perturbation theory are used for solution of the problem.It is shown that while studying the evolution of a celestial body as a dissipative system in the framework of perturbed virial oscillations, the analytical expression for perturbing function can be derived, assuming the celestial body to be an oscillating electrical dipole emitting electromagnetic energy.The general covariant form of Jacobi's equation is derived and its spur is examined. It is shown that the scalar form of Jacobi's equation appears to be more universal than Newton's laws of motion from which it is derived.     

On the modern approach to the problem of detecting hazardous celestial bodies

The problem of detecting dangerous (in the sense of a collision with the Earth) celestial bodies of natural origin and the modern concept of building a system of detection of such bodies are discussed. The concept includes two items: remote detection of large (>50 m) hazardous objects providing warning time of several tens of days, which is sufficient to allow the active counteraction and detection of hazardous bodies larger than 10 m in near-Earth space providing warning time of few hours, which is sufficient to issue a warning and to carry out mitigation activities. Some examples of this approach and prospects of the international cooperation are discussed.     

Rotational dynamics of celestial bodies

In this paper the ‘class of near homoaxial rotations’ is defined, being suitable for treatment of problems of nonuniform rotation of stars. This class is represented by a proper form of the so-called ‘velocity tensor’, the latter describing efficiently the motion of a deformable finite material continuum in the common frame. The ‘class of particular near homoaxial rotations’ is then defined, characterized by simple transformation equations of the velocity tensor in two noninertial frames; namely, in a ‘frame rotating uniformly’ relative to the common frame, and in a ‘frame rotating nonuniformly’ relative to it. A sufficient condition is also derived so that a near homoaxial rotation be reducible to a particular one. ‘Preferred frames’ are then defined in the sense that they preserve a near homoaxial rotation in its class when referring thismotion; that is, such frames keep invariant the intertial class of the motion. Finally, a method is proposed for constructing a nonuniformly rotating preferred frame, to which a near homoaxial rotation is referred simply as ‘radial distortion’.     

Rotational dynamics of deformable celestial bodies

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Rotational dynamics of celestial deformable bodies

In a previous paper of this series (Tokis, 1974b), we have discussed the solution of the Eulerian equation which governs the axial rotation, applied to the effects of viscous friction exhibited in binary systems which consist of a close pair of fluid bodies of arbitrary structure. The aim of the present paper will be to give an application of those results to the Earth-Moon system. It is shown that synchronism between the axial rotation of the Earth and the revolution of the Moon will occur at the value of 650 h, in a time scale which depends strongly on the value of the mean viscosity of the Earth (regarded as spherical or spheroidal). In particular, the variation of rotational angular velocity of the Earth over the next ten centuries commencing from 1900 A.D., depends sensitively on the value of viscosity. On the other hand, the time for synchronism of axial rotation of the Moon is not affected by the viscosity for values between 10²⁴g cm^?1 s^?1 and 10²⁷g cm^?1 s^?1.     

Resonance rotation of celestial bodies and Cassini's laws

Celestial body rotation about its center of mass, taking into account the body orbit evolution, is considered. Non-linear evolution equations of motion are constructed. Empirical Cassini's laws describing the Moon motion result from these equations as their stationary points. Bifurcation conditions of steady motions are written out and conditions of their stability are investigated. Hypothesis of Mercury's resonance motion analogous to the motion by Cassini is discussed. Consequences of this hypothesis are considered.The first information including the results mentioned in the paper was previously published in preprint [1].     

Gravitational lens effect of degenerate neutrino celestial bodies

We took the degenerate neutrino celestial body (NCO) to be transparent. We solved the geodesic equation for the light rays emitted by sources inside and outside the body. We then derived the expression for the amplication factor K by a transparent gravitational lens, and evaluated K and the redshift under the metric of the NCO. Our calculations show that, for light travelling in certain directions from sources in certain positions, the brightness may be amplified several hundred times. We point out that some quasars may be galactic nuclei inside NCOs.     

Yukawa-type potential effects in the anomalistic period of celestial bodies

Several contemporary modified models of gravity predict the existence of a non-Newtonian Yukawa-type correction to the classical gravitational potential. We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We derive two equations to approximate the periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period) under the influence of the non-Newtonian radial acceleration. Kinematically, this influence produces apsidal motion. We performed numerical estimations for Mercury, for the companion star of the pulsar PSR 1913+16, and for the extrasolar Planet b of the star HD 80606. We also considered the case of the artificial Earth satellite GRACE-A, but the results present a low degree of reliability from a practical standpoint.     

On the possibility of the guidance of small asteroids to dangerous celestial bodies using the gravity-assist maneuver

In this paper, the method of changing the trajectories of hazardous asteroids with orbits known for some years to be on a possible collision course with the Earth is considered. The method relies on the use of small asteroids (asteroid-projectiles) directed at hazardous celestial bodies by giving the projectile a sufficiently small velocity impulse ensuring the Earth gravity assist. As a result, the asteroid-projectile vector can be controllably changed over a wide range. Apophis is considered as an example of the target asteroid. The technical feasibility of this method is discussed. It is noted that despite the potential use of this elegant method, its practical implementation requires further research and development.     

Simulation of the solar wind interaction with non-magnetic celestial bodies

Laboratory experiments are described to simulate the solar wind flowing around nonmagnetic planets for three cases: non-conducting and ideally conducting planets, and a planet with a gaseous shell. A glass sphere was used as a model of a non-conducting planet (the Moon). Spatial distributions of plasma density and magnetic field strength that have been obtained agree with the data from measurements in space. However, the magnetic field does not increase before the rarefaction wave in the model experiment. A field increase was observed only for a conducting lunella: this argues in favour of the existence of a high conduction region on the Moon. A wax ball was used to model phenomena on the day-side of non-magnetic celestial bodies with a gaseoue shell (Venus, comets). Its surface easily evaporates in the plasma flow, and ionized evaporation products form an artificial ionosphere. The magnetic field frozen in the plasma flow is shown to be a determinative factor in the formation of a sharp ionospheric boundary. The supersonic plasma flow that interacts with the ionosphere gives rise to a stationary shock wave.     

A method for modelling the surface of irregular celestial bodies

Die Funktion R9 der Oberfläche von unregelmäßigen Himmelskörpern (kleine Monde wie Phobos und Deimos, Kometenkerne oder kleine Asteroiden) wird nach Kugelfunktionen entwickelt. Es wird eine Methode angegeben, nach der die Entwicklungskoeffizienten durch Vergleich der berechneten Konturen mit den Konturen bestimmt werden, die aus einer Folge von Abbildungen des Körpers gewonnen wurden. Bei gegebenen Entwicklungskoeffizienten kann diese Methode für Orientierungssysteme von Raumschiffen beim Anflug auf den Himmelskörper verwendet werden. Weiterhin können physikalische Größen, wie das Volumen, die Schwerpunktskoordinaten, Trägheitsmomente und Gravitationsfeld analytisch berechnet werden. Unter der Voraussetzung, daß das Gravitationspotential experimentell bestimmt werden kann, wird eine Methode zur Berechnung des radialen Dichteprofiles des Körpers beschrieben.     

Dynamo mechanism for turbulent wave in celestial bodies

It is well known that under cosmic conditions the various modes of plasma turbulence waves (including MHD waves) are easily excited. In this paper we are trying to show that the turbulent wave also generates a source-term for the magnetic induced equations as does the turbulent fluid with nonzero helicity. By expanding the turbulent field in Fourier series, we have obtained dynamo equation for turbulent wave and a reasonable solution which indicates that the poloidal field may be built-up in the turbulent source region. Perhaps, we may think that the poloidal field of Equation (9) is the analytical form of the magnetic field in a turbulent source region of celestial bodies.     

Tidal evolution of inclinations and rotations of celestial bodies

The cosmogonic role of tidal effects in planetary rotations is considered. According to the cosmogonic modern theory by Eneev-Kozlov [3], the evolution of a protoplanetary cloud resulted in protoplanets of enormous initial sizes. Due to this, the tidal evolution of planetary rotations played a great part; it developed with rate by a few orders of magnitude higher than that of the evolution in contemporary epoch. The compression of protoplanets to their present sizes had played a certain (in some cases, dominating) role. These two factors effected in a present variety of planetary inclinations and rotations.