The paper is devoted to the problem of the origin of the Moon. The discussed modern scenarios for the formation of the Earth–Moon system are: simultaneous formation of the Earth and the Moon in the circumsolar gas-dust disk; impact partial destruction of the Earth by a massive asteroid; gravitational capture of the Moon by the Earth; and destruction of the double Moon at the beginning when approaching the Earth with possible subsequent absorption components of smaller mass by the Earth. We offer two-stage scenario of gravitational capture of the Moon by the Earth in the early stages of Solar System. In the first stage, using a hybrid numerical model in the formulation of the three-body problem (Sun, Earth and Moon) and N-bodies, the search and selection of temporary orbits of the Moon around the Earth is carried out. Using the backward integration method in the N-body problem formulation, the influence of tidal forces on pumping of orbital moment of the Moon ( P_orb^M ) relative to the Earth at its own moment P_s^M is estimated. The simulation shows that actions tidal forces alone are not enough to capture the Moon by the Earth in a short time scale of 100 years ( Δ P_s^M∼10^ - 6P_orb^M ). At the second stage, the factor is considered viscous-dissipative environment leading to additional “slowing down” of the Moon, due, for example, to collisions with asteroids and the transition of tidal energy into heat, which helps the Moon get rid of excess kinetic energy and gain constant orbit around the Earth.

This article raises the question of the possibility of identifying stellar pairs in which one of the components belongs to the family of near-nuclear central S-stars and the other belongs to a population of hypervelocity stars (HVSs). In the recent past, they could be genetically linked in a single parent binary star (BS), and today its components are separated by hundreds or more parsecs as a result of dynamic capture of a BS by the field of a supermassive black hole (SMBH). There is interest in the mutual reconstruction of populations of S-stars and HVSs calculated in the context of the classical Hills scenario, based on the principle of supplementing their observational data. The paper is based on a report presented at the astrophysical memorial seminar “Novelties in Understanding the Evolution of Binary Stars,” dedicated to the 90th anniversary of Professor M.A. Svechnikov.

This paper continues the search for mechanisms for the formation of free planets and considers the problem of the dynamic capture of a planetary system by the vicinity of a supermassive black hole (SMBH) with a mass of one million solar masses. A simplified model of a planetary system is used, which includes a solar-mass parent star, a giant planet with the mass of Jupiter, and $$N$$ small bodies such as asteroids, comets, and dwarf planets (ACP objects) co-orbital with the giant planet. Statement of numerical simulation is reduced to the problem of four bodies, duplicated $$N$$ times. The spectra of scattering velocities of the ACP objects are studied depending on the collision parameters: pericentric distance and angle of approach of the planetary system to the SMBH. The effectiveness of the gravitational scattering of the planetary system on the SMBH is noted: up to 50% of all small planetary bodies receive the status of free objects, including ~1% of hypervelocity ACPs with velocities up to a thousand and more kilometers per second. The share of ACP objects destroyed or swallowed by SMBHs is analyzed. We present the estimate for the frequency of collisions of planetary systems with SMBHs, based on which the existence of a well-populated component of free planets, asteroids and comets in dense galactic nuclei is assumed.

We present a three-dimensional model of the evolution of the asteroid–cometary–planetary (ACP) component of the Solar System under the gravitational influence of Jupiter. We demonstrate the origin of the Kuiper belt of the Sun, the Oort cloud of the Sun and Jupiter, as well as the ACP “spear,” which becomes elongated with time and transforms into a “ring” of ACP objects along the trajectory of the Sun orbiting the Galaxy center. When generalizing to the case of the Galaxy, we conclude that a noticeable portion of ACP objects turn out to be unbound with the host stars and form a field of free asteroids, comets, and planets of the Galaxy. Galaxies with small masses (M < 108 M⊙) lose a part of their unbound ACP material to the intergalactic space of their clusters and possess galactic ACP spears.

Central, or “circumnuclear,” stars of the Galaxy, known as S stars, are studied. These stars can be used to investigate the gravitational potential near the Galactic center, which hosts a supermassive black hole (SMBH), as well as to impose constraints on estimates of the mass and position of this SMBH. The evolutionary relationship between S stars and hypervelocity stars is analyzed in the classical Hills scenario, which considers the dynamical capture of a binary star in the field of a SMBH. Numerical simulations in the three-body and N-body problems are used to obtain consistent statistics for the populations of S stars and high-velocity stars, and to estimate their lifetimes, including the time scale for the capture of an S star in the neighborhood of the central SMBH. The mass spectrum of the S stars is also analyzed, and the distribution of the semi-major axes for their orbits around the SMBH is derived. A comparison of the computed and observed distributions is used to place constraints on the time scale and cross section for the capture of binaries in the vicinity of the SMBH. The genetic relationship between high-velocity stars and S stars as former components of binary-star systems is confirmed.

The dynamical capture of a binary system consisting of a supermassive black hole (SMBH) and an ordinary star in the gravitational field of a central (more massive) SMBH is considered in the three-body problem in the framework of a modified Hills scenario. The results of numerical simulations predict the existence of objects whose spatial speeds are comparable to the speed of light. The conditions for and constraints imposed on the ejection speeds realized in a classical scenario and the modified Hills scenario are analyzed. The star is modeled using an N-body approach, making it possible to treat it as a structured object, enabling estimation of the probability that the object survives when it is ejected with relativistic speed as a function of the mass of the star, the masses of both SMBHs, and the pericenter distance. It is possible that the modern kinematic classification for stars with anomalously high spatial velocities will be augmented with a new class—stars with relativistic speeds.

A simple model for the dynamics of stars located in a sphere with a radius of one-tenth of the central parsec, designed to enable estimation of the probability of capture in the close vicinity (r < 10−3 pc) of a supermassive black hole (SMBH) is presented. In the case of binary stars, such a capture with a high probability results in the formation of a hyper-velocity star. The population of stars in a sphere of radius <0.1 pc is calculated based on data for the Galactic rotation curve. To simulate the distortion of initially circular orbits of stars, these are subjected to a series of random shock encounters (“kicks”), whose net effect is to “push” these binary systems into the region of potential formation of hyper-velocity stars. The mean crossing time of the border of the close vicinity of the SMBH (r < 10−3 pc) by the stellar orbit can be used to estimate the probability that a binary system is captured, followed by the possible ejection of a hyper-velocity star.

The probability of forming a Galactic hypervelocity star is estimated for the scenario of Hills, which describes the dynamical capture of one component of a binary star by the gravitational field of the supermassive black hole in the Galactic center, leading to the ejection of the other component. Ten thousand initial orientations of the binary orbits were considered, and the semi-major axes of the binary orbits were varied in a wide range from 11.3 R ⊙ to 425 R ⊙ . Two series of computations were carried out, in which the mass of the supermassive black hole was taken to be 10 6 M ⊙ and 3.4 × 10 6 M ⊙ . Numerical simulations of encounters of the binary and black hole in the framework of the three-body and N-body problems are used to localize regions favorable for the formation of hypervelocity stars. The motion of the ejected star in the regular field of the Galaxy is calculated, and the conditions under which the star escapes the Galaxy defined. The probability of escaping the Galaxy is caluclated as a function of various parameters the initial separation of the binary components and the distance of the binary from the black hole. On average, the probability of forming a hypervelocity star is higher for closer encounters and more tightly bound binary pairs.

The formation of hypervelocity stars due to the dynamical capture of one component of a closebinary system by the gravitational field of a supermassive black hole (SMBH) is modeled. The mass of the black hole was varied between 10 6 and 10 9 M ⊙ . In the model, the problem was considered first as a three-body problem (stage I) and then as an N-body problem (stage II). In the first stage, the effect of the inclination of the internal close-binary orbit (the motion of the components about the center of mass of the binary system) relative to the plane of the external orbit (the motion of the close binary around the SMBH) on the velocity with which one of the binary components is ejected was assessed. The initial binary orbits were generated randomly, with 10 000 orbits considered for each external orbit with a fixed pericenter distance r p . Analysis of the results obtained in the first stage of the modeling enables determination of the binary-orbit orientations that are the most favorable for high-velocity ejection, and estimation of the largest possible ejection velocities V max . The boundaries of the region of stellar disruption derived from the balance of tidal forces and self-gravitation are discussed using V max - r p plots, which generalize the results of the first stage of the modeling. Since a point-mass representation does not enable predictions about the survival of stars during close passages by a SMBH, there is the need for a second stage of the modeling, in which the tidal influence of the SMBH is considered. An approach treating a star like a structured finite object containing N bodies ( N = 4000) enables the derivation of more accurate limits for the zone of efficient acceleration of hypervelocity stars and the formulation of conditions for the tidal disruption of stars.

Tidal torque constants are calculated for each component of 112 close eclipsing binaries of the DMS type (detached components located within the main sequence) from the catalogue by Svechnikov and Perevozkina (1999) on the basis of the evolutionary models by Claret (2004), which are the first to present constants for investigation of tidal effects in close binaries. This study applies conversion of a grid of model tracks into that of isochrones with an arbitrarily small time step based on optimal nonlinear interpolation. The small time-step criterion guarantees application of the linear interpolation procedure to estimate the age of the DMS components and find an individual set of tidal-evolution constants for the close binary under study that refers to the estimated time point. The theoretical values of the apsidal motion period calculated from the individual internal structure constants for each close binary are well consistent with the observations. This confirms the validity of the evolutionary stellar models by Claret and the numerical algorithm proposed here.

Numerical simulations of the dynamical evolution of a galaxy cluster in the framework of the N -body problem taking into account dark matter are presented. These simulations are aimed at studying the role of intergalactic gas in the cluster (the ICM) in the formation of a central, supermassive cD galaxy. The numerical models indicate that deceleration of the galaxies by intergalactic gas supports the observed high temperature of this gas, and accelerates the formation of a supermassive cD galaxy in the cluster core. The accretion of interstellar gas by the cluster core can support a high accretion rate by the central, supermassive black hole associated with the nucleus of the cD galaxy. As a result, this nucleus harbors a bright quasar. The mass of the black hole can grow with time to values 10 10 M ⊙ , as are observed for the brightest quasars.

NumericalN-body studies of the dynamical evolution of a cluster of 1000 galaxies were carried out in order to investigate the role of dark matter in the formation of cD galaxies. Two models explicitly describing the darkmatter as a full-fledged component of the cluster having its own physical characteristics are constructed. These treat the dark matter as a continuous underlying substrate and as “grainy” matter. The ratio of the masses of the dark and luminous matter of the cluster is varied in the range 3–100. The observed logarithmic spectrum dN ∼ dM / M is used as an initial mass spectrum for the galaxies. A comparative numerical analysis of the evolution of the mass spectrum, the dynamics of mergers of the cluster galaxies, and the evolution of the growth of the central, supermassive cD galaxy suggests that dynamical friction associated with dark matter accelerates the formation of the cD galaxy via the absorption of galaxies colliding with it. Taking into account a dark-matter “substrate” removes the formation of multiple mass-accumulation centers, and makes it easier to form a cD galaxy that accumulates 1–2% of the cluster mass within the Hubble time scale (3–8 billion years), consistent with observations.

We analyze the distribution of close binary stars in the orbital semimajor axis—primary mass plane. The reduced spatial density of stars with semimajor axes below 10R⊙ is confirmed. We identify the area in this plane occupied by precursors of W UMa stars, assuming that the driving force causing the components to approach each other is their magnetic stellar wind. This scenario enables us to estimate the rate of formation (0.02/year) and lifetime (108 yr) of W UMa stars. We derive a theoretical estimate of the ratio of the number of blue stragglers, N BS , and of horizontal-branch stars, N HB , in globular clusters based on the hypothesis that all blue stragglers are the result of component mergers in W UMa contact binaries. This ratio is N BS /N HB =0.4, close to the observed value for 62 Galactic globular clusters. We discuss possible reasons for the considerable dispersion of the observed estimates of this ratio for different clusters in our Galaxy.