Том 61, № 8 (2017)

Vertical oscillations of the gas at the outer edge of the accretion disk in a semi-detached binary due to interaction with the stream of matter from the inner Lagrangian point L₁ are considered. Mixing of the matter from the stream from L₁ with matter of the disk halo results in the formation of a system of two diverging shocks and a contact discontinuity, or so-called “hot line”. The passage of matter through the region of the hot line leads to an increase in its vertical velocity and a thickening of the disk at phases 0.7−0.8. Subsequently, the matter moving along the outer edge of the disk also experiences vertical oscillations, forming secondary maxima at phases 0.2−0.4. It is shown that, for systems with component mass ratios of 0.6, these oscillations will be amplified with each passage of the matter through the hotline zone, while the observations will be quenched in systems with component mass ratios ~0.07 and ~7. The most favorable conditions for the flow of matter from the stream through the edge of the disk arise for component mass ratios ~0.62. A theoretical relation between the phases of disk thickenings and the component mass ratio of the system is derived.

A star located in the close vicinity of a supermassive black hole (SMBH) in a galactic nucleus or a globular-cluster core could form a close binary with the SMBH, with the star possibly filling its Roche lobe. The evolution of such binary systems is studied assuming that the SMBH mainly accretes matter from the companion star and that the presence of gas in the vicinity of the SMBH does not appreciably influence variations in the star’s orbit. The evolution of the star–SMBH system is mainly determined by the same processes as those determining the evolution of ordinary binaries. The main differences are that the star is subject to an incident flux of hard radiation arising during the accretion of matter by the SMBH, and, in detached systems, the SMBH captures virtually all the wind emitted by its stellar companion, which appreciably influences the evolution of the major axis of the orbit. Moreover, the exchange between the orbital angular momentum and the angular momentum of the overflowing matter may not be entirely standard in such systems. The computations assume that there will be no such exchange of angular momentum if the characteristic timescale for mass transfer is shorter than the thermal time scale of the star. The absorption of external radiation in the stellar envelope was computed using the same formalism applied when computing the opacity of the stellar matter. The numerical simulations show that, with the adopted assumptions, three types of evolution are possible for such a binary system, depending on the masses and the initial separation of the SMBH and star. Type I evolution leads to the complete destruction of the star. Only this type of evolution is realized for low-mass main-sequence (MS) stars, even those with large initial separations from their SMBHs. Massive MS stars will also be destroyed if the initial separation is sufficiently small. However, two other types of evolution are possible for massive stars, with a determining role in the time variations of the parameters of the star–SMBH system being played by the possible growth of the massive star into a red giant during the time it is located in the close vicinity of the SMBH. Type II evolution can be realized for massive MS stars that are initially farther from the SMBH than in the case of disruption. In this case, the massive star fills its Roche lobe during its expansion, but is not fully destroyed; the star retreats inside its Roche lobe after a period of intense mass loss. This type of evolution is characterized by an increase in the orbital period of the system with time. As a result, the remnant of the star (its former core) is preserved as a white dwarf, and can end up at a fairly large distance from the SMBH. Type III evolution can be realized formassiveMSstars that are initially located still farther from their SMBHs, and also for massive stars that are already evolved at the initial time. In these cases, the star moves away from the SMBH without filling its Roche lobe, due to its intense stellar wind. The remnants of such stars can also end up at a fairly large distances from their SMBHs.

Analysis of collected photometric observations obtained with the Kepler Space Telescope were used to select and study 33 objects with parameters corresponding to those of the FK Com starHD199178; these can be considered candidate stars of this type. In this final study, the four objects with the best light curves, which show the properties of their regular rotational modulation most clearly, were selected for detailed studies. The photometric analysis is based on all data currently available in the Kepler archive (covering almost four years). The rotational periods and estimated parameters of the objects’ differential rotation are determined, and the longitudes of the dominant active regions on the surfaces found. For all four stars, the spot coverage is approximately 1% of the visible stellar surface area. The rotational periods and data on the stars’masses and radii fromtheMAST catalog are used to determine the rotation velocities projected onto the line of sight, which ranged from 12 to 21 km/s. Further studies will enable definite conclusions about how these stars are related to FK Com stars. If they are ultimately classified as FK Com stars, this will considerably increase the number of this rare type of star and the also number of rapidly rotating, single, late-type giants.

It is known from observations that the center of mass of the Moon does not coincide with the geometric center of its figure, and the line connecting these two centers is not aligned with the direction toward the center of the Earth, instead deviating toward the Southeast. This stationary deviation of the axis of the inertia ellipsoid of the Moon to the South of the direction toward the Earth is analyzed. A system of five linear differential equations describing the physical libration of the Moon in latitude is considered, and these equations are derived using a new vector method taking into account perturbations from the Earth and partly from the Sun. The characteristic equation of this system is obtained, and all five oscillation frequencies are found. Special attention is paid to the fifth (zero) frequency, for which the solution of the latitude libration equations are stationary and represents a previously unknown additional motion of the rotational axis of theMoon in a cone with a small opening angle. In contrast to the astronomical precession of the Earth, the rotation of the angular-velocity vector is in the positive direction (counter-clockwise), with the period T₃ = 27.32 days. On this basis, this phenomenon has been named “quasi-precession.” This quasi-precession leads to a stationary inclination of the major axis of the inertia ellipsoid of theMoon to the South (for an observer on Earth), making it possible to explain one component of the observed deviation of the center of mass of the Moon from the direction toward the Earth. The opening angle of the quasiprecession cone is approximately 0.834″.