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The evolution of perturbations in a two-layer spherical shell and a plane layer with a two-step density distribution has been simulated numerically. The clumps formed by instability are shown to have qualitatively different structures, depending on the ratio of the densities in the inner and outer layers of the shell. Inhomogeneities bordered by a dense gas are formed in shells with an outwardly decreasing density. If, however, a denser gas is in the outer layer, then cores surrounded by a more rarefied material appear. These results are used to analyze the expansion of the HII region RCW 82. Since the inhomogeneities observed in the 13CO emission in the outer parts of this region have sharply delineated boundaries, our calculations argue for the model of the expansion of a shell with an outwardly decreasing density. The interaction of an accelerating shell with clumps in front of it has also been investigated. The deformations of a clump during its penetration into the shell and the formation of a groove in the shell gradually fillingwith a cold gas have been revealed. Thereafter, the shell material collapses to form a cumulative jet. As applied to the HII region RCW 82, we conclude that the existence of jets is possible if there are inhomogeneities with a scale of ∼1018 cm in the interstellar medium. The lack of data on such jet flows at the boundary of this region is an additional argument for the model where the inhomogeneous structure of the boundaries is attributable to the development of Rayleigh-Taylor instability.

The oxygen density in the central zone of the ejecta of nine type IIP supernovae (SNe IIP) at the nebular phase has been determined from the [O I] 6300, 6364 A doublet lines. In combination with the known estimates for two supernovae, the results of measurements show that the oxygen densities on day 300 are distributed in a narrow range, (2.3 ± 1) × 109 cm−3. This result does not depend on the distance, extinction, and model assumptions. Analysis of the density distribution found leads to the conclusion that the SN IIP explosion energy increases with stellar mass.

The data on the peculiar velocities of 1493 RFGC flat spiral galaxies processed using the POTENT method allowed the density distribution of matter, including dark matter, on 75-Mpc scales to be reconstructed. Well-known attractors (the Great Attractor, the Perseus—Pisces and Coma superclusters) and voids are separated from the distribution. In general, the density distribution is close to that of IRAS galaxies, suggesting that the luminous-to-dark matter density ratio is constant. The masses of the main attractors were estimated.

The problem of the spatial motion of a star inside an inhomogeneous rotating elliptical galaxy with a homothetic density distribution is considered. Periodic solutions are constructed by the method of a small Poincare parameter. Linear variational equations with periodic coefficients are used to analyze the Lyapunov stability of these solutions.

We established a criterion for the Hill stability of motions in the problem of many spherical bodies with a spherical density distribution. The region of Hill stability was determined. The sizes of this region are comparable to the total volume of all of the bodies in the system, which sharply increases the probability of mutual collisions. This result may be considered as a confirmation that a supermassive core can be formed at the center of a globular star cluster. The motions in the n-body problem are shown to be unstable according to Hill.

We developed an efficient method for determining the surface-density distribution in a self-gravitating disk with an isolated central point mass from a specified angular-velocity distribution in the disk. An upper limit for the galactic-disk mass is shown to exist at a given black-hole mass. This limit significantly depends on the choice of rotation curves.

The motion of a neutron superfluid condensate in a pulsar is studied. Several theorems of general-relativistic hydrodynamics are proved for a superfluid. The average density distribution of vortex lines in pulsars and their general-relativistic curvature are derived., Comment: 18 pages, 1 figures

The plane motion of a mass point inside an inhomogeneous rotating ellipsoidal body with a homothetic density distribution is considered. The force function of the problem is expanded in terms of the ellipsoid's second eccentricities up to the fourth order, which are taken as small parameters. We derive an expression for the perturbing function and solve the equations of perturbed motion in orbital elements.