The motion of a star with variable mass inside a layered inhomogeneous elliptical galaxy

We consider the motion of a variable-mass star inside a layered, inhomogeneous, rotating elliptical variable-mass galaxy. Under certain conditions, the differential equations of motion of a star inside the galaxy admit autonomization. The autonomized differential equations in this problem are similar to those for the motion of a constant-mass star. We have found analogs for the Jacobi integral and the Eddington-Jeans law for the variation of the density of the galaxy in its center and layers.     

The libration points for the motion of a star inside an elliptical galaxy

We consider the three-dimensional motion of a star inside an inhomogeneous, rotating, elliptical galaxy with a homothetic density distribution. The libration points inside a triaxial, rotating, inhomogeneous, gravitating ellipsoid are determined and their stability studied. We determine zero-velocity surfaces and regions of possible motion both inside and outside the galaxy. The motions are shown to be stable in the sense given by Hill. The obtained zero-velocity surfaces enable the construction of a Roche model for a galaxy in the form of either a triaxial ellipsoid or an oblate ellipsoid of rotation.     

The motion of a star in the vicinity of a globular cluster in an elliptical galaxy

The spatial motion of a star in the vicinity of a globular cluster located in an inhomogeneous, rotating elliptical galaxy (EG) is considered. Perturbations due to the gravitation of the galaxy are taken into account, taking it to be a two-layer system together with its halo: an inner ellipsoid, representing the lumious part of the galaxy, and a homeoid, representing space filled with dark matter between inner and outer ellipsoidal boundaries. The ellipsoids are taken to be homothetic and to have a common center, with the boundary of the outer ellipsoid coincident with the boundary of the galactic halo. The luminous part of the EG and the homeoid have different densities. The motion of the star near a globular cluster occurs outside the luminous part of the EG, but inside the homeoid. The concept of the “vicinity of the globular cluster” is concretized using the concept of a “sphere of influence” (and the gravitational sphere and Hill gravitational sphere). Stellar motions inside and outside the sphere of influence of the globular cluster are considered, and the region of possible motions is determined. A quasi-integral and surfaces of minimum energy are found, which under certain conditions can be transformed into an analog of the Jacobi integral and surfaces of zero velocity. The Lyapunov stability of the stationary solutions obtained is established. The results are applied to model EGs whose parameters coincide with those of NGC 4472 (M49), NGC 4636, and NGC 4374, which contain a large number of globular clusters, and are presented in the form of figures and tables. Using these galaxies as examples, it is shown that studying stellar motions, and also determining the libration points and establishing their stability, requires use of an exact, rather than an approximate, expression for the potential of the luminous part of the elliptical galaxy.     

Steady-state solutions for the motion of a globular cluster in an inhomogeneous, rotating elliptical galaxy

Steady-state solutions for the motion of a passively gravitating globular cluster (GC) inside an inhomogeneous, rotating, ellipsoidal elliptical galaxy (EG) are considered. It is assumed that an EG with a halo is comprised of a triaxial ellipsoid consisting of two layers. The first is formed by an inner, uniform ellipsoid representing the luminous part of the galaxy, while the second corresponds to the space between an inner and outer ellipsoid, which is uniformly filled with dark matter. The triaxial ellipsoids are taken to be homothetic and to have a common center; the space between them is called a homeoid. The outer boundary of the homeoid is the boundary of the galaxy halo. The densities of the luminous part of the EG and the homeoid are different. This picture of an EG is in agreement with our current understanding of galactic structure. The motion of the GC occurs outside the luminous part of the EG, but inside the homeoid, which is treated like a perturbing body. Steady-state solutions (libration points) are found for the GC, and its Lyapunov stability determined. The elliptical galaxies NGC 4472 (M49), NGC 4636, and NGC 4374, which contain a large number of GCs, are used as examples. Analysis of these galaxies shows that the exact expression for the potential of the luminous part of the EG must be used to find the libration points and study their stability, rather than an approximate expression for this potential.     

The motions of galaxies in the field of the cosmic vacuum

The general solution and general integral of the equations of motion in the field of the cosmic vacuum are constructed. It is shown that the resulting motions of galaxies are along either hyperbolic or rectilinear paths. The laws of motion of galaxies in the field of the cosmic vacuum are formulated. Various forms of the Hubble law are considered. A strict adherence to the Hubble law is not possible for most initial conditions in the sense of the Lebesgue measure. Therefore, it becomes meaningless to search for explanations to deviations from the Hubble law due to any physical factor, apart from the repulsive force of the cosmic vacuum. Phase portraits for the galaxy motions are constructed. It is shown that the Hubble constant should be determined observationally using the most distant galaxies, since the accuracy of the result will be reduced otherwise.     

Multicolor CCD photometry of the dusty,giant, late-type spiral galaxy NGC 5351

The paper reports the results of BV RI surface photometry of the giant galaxy NGC 5351 based on CCD observations obtained on the 1-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. Analysis of the structure and radial brightness distribution in the galaxy shows that NGC 5351 has a complex and, in some places, asymmetric structure. The galaxy possesses a large quantity of dust. The average internal extinction due to dust is A_V=1.2^m±0.4^m. After correcting for the effect of this dust, the parameters of the galaxy are typical of late-type spirals. The compositions of the stellar population in various parts of the galaxy are estimated using two-color diagrams. Star-forming regions in NGC 5351 are identified and studied. Most of the star-forming regions are located in the ring of the galaxy. Evolutionary modeling is used to estimate the ages of regions of violent star formation. An elliptical companion galaxy to NGC 5351 was found. The rotation curve of the galaxy is modeled and its mass estimated. The disk of NGC 5351 is self-gravitating within its optical radius.     

Is there a relationship between the density of primordial black holes in a galaxy and the rate of cosmological gamma-ray bursts?

The rate of accretion of matter from a solar-type star onto a primordial black hole (PBH) that passes through it is calculated. The probability that a PBH is captured into an orbit around a star in a galaxy is found. The mean lifetime of the PBH in such an orbit and the rate of orbital captures of PBHs in the galaxy are calculated. It is shown that this rate does not depend on the mass of the PBH. This mechanism cannot make an appreciable contribution to the rate of observed gamma-ray bursts. The density of PBHs in the galaxy can reach a critical value—the density of the mass of dark matter in the galaxy.     

Gas dynamics of a central collision of two galaxies: Merger, disruption, passage, and the formation of a new galaxy

Results of numerical simulations of a collision of the gaseous components of two identical disk galaxies during a head-on collision of the galaxies in the polar direction are presented. When the relative velocity of the galaxy collision is small, their gaseous components merge. At high relative velocities (100–500 km/s), the massive stellar components of the galaxies (M _g = 10⁹ M _⊙) pass through each other nearly freely, leaving behind the gaseous components, which are decelerated and heated by the collision. If the overall gaseous component of the colliding galaxies is able to cool to the virial temperature during the collision, a new galaxy forms. At velocities V ≥ 500 km/s, the gaseous component does not have time to cool, and the gas is scattered into intergalactic space, supplying it with heavy elements produced in supernovae in the colliding galaxies. High-velocity (V ≥ 100 km/s) collisions of identical low-mass galaxies (M _g ≤ 10⁹ M _⊙) whose mass is dominated by the mass of gas lead to the disruption of their stellar components. The overall gaseous component forms a new galaxy when V ≤ 500 km/s, and is scattered into intergalactic space if the velocity becomes higher than this. A galaxy collision increases the star-formation rates in the disk galaxies by nearly a factor of 100. Rotation of the colliding galaxies in the same direction increases the changes of the disruption of both the stellar and gaseous components of the galaxies. The merger of galaxies during their collision can explain the presence of gaseous disks rotating opposite to the rotation of the stellar component in some ordinary elliptical galaxies. Moreover, galaxy mergers can help explain the origin of a comparatively young stellar population in some elliptical galaxies.     

Is Dark Matter Needed in Galaxies?

Arguments indicating that galaxies and galaxy clusters should be considered open, forming systems are presented. Galaxies interact with the intergalactic medium, and are not in virial equilibrium (determined by gravitation and rotation). The usual interpretation of the rotation curves of the outer regions of galaxies beyond the visible stellar disk—that they imply the presence of a massive dark-matter halo— could be erroneous in this case: if the intergalactic medium is being accreted in these regions, the orbital speeds of clouds of neutral hydrogen will not be determined purely by the gravitation of the mass inside their orbits. Galaxy clusters accrete matter (intergalactic gas and galaxies) from the filaments of the large-scale structure at whose intersections they are located. Only their inner regions can approach virial equilibrium. Therefore, the high speeds of galaxies and the high temperature of the intergalactic gas in clusters does not necessarily imply the presence of a high mass of dark matter in galaxy clusters.     

Activity of the Seyfert galaxy NGC 4151 in the near-IR in 1994–2011

We present the results of our infrared J H K L photometry of the Seyfert galaxy NGC 4151 during its active period in 1995–2011. The variable IR source was still in its active state in 2011, though its observed luminosity had almost halved compared to the maximum of 1995–1996. If the “cool” component of the galaxy’s variable source is a dust shell heated with the central “hot” source, its optical depth at 1.25 µm varied from 0.3 to almost 1.0, its temperature from 700 to 950 K, its size from 20 to 40 pc, and its mass from 2 to 40M _⊙ during our observations. A component with a period of 317 ± 5 days can be revealed in the flux variations observed in 1994–2011.     

Does the LMC possess a dark bulge?

A series of numerical dynamical models for the LMC are constructed in order to fit the observed rotational velocities and stellar velocity dispersions at various galactocentric distances. The models include a three-dimensional spherical disk and nonevolving spherical components with various relative masses. The two LMC rotation curves presented by Kim et al. (1998) and Sofue (2000), which differ strongly in the inner region of the galaxy, are compared. The latter curve requires the presence of a massive dark bulge. Models based on the rotation curve of Sofue (2000) cannot account for the observed velocity dispersion or the presence of a long-lived bar in the galaxy. A model with no dark bulge is in good agreement with the observations if we assume that the disk dominates over the halo in terms of the mass within the optical radius (about 7 kpc).     

The active galaxy NGC 3862 in a compact group in the cluster A1367

We study a compact group of 18 galaxies in the cluster A1367 with redshifts z = 0.0208–0.025. The group’s center of activity in the radio is the galaxy NGC 3862, whose radio flux is an order of magnitude stronger than for the other members of the group. We present coordinates derived from the Palomar plate archive together with recessional velocities, and analyze other characteristics of the group’s galaxies. The results of 1400 MHz observations of NGC 3862 with the RATAN-600 radio telescope are presented. These observations indicate that the galaxy’s radio emission is variable.     

BVRI surface photometry of the galaxy NGC 3726

We present BVRI surface photometry of the late-type spiral galaxy NGC 3627. The distributions of the color indices and extinction-independent Q indices show that the observed photometric asymmetry in the inner part of the galaxy, including the bar, is due to an asymmetric distribution of absorbing material. The bluest regions of star formation are located in a ring surrounding the bar. The background-subtracted color indices of individual blue knots are used to estimate the ages of young stellar aggregates. In combination with previously published photometric data, our measurements indicate that the R-band profile of the disk is rather flat in its inner part (r<50″) and becomes steeper further from its center. We estimate the mass of the disk and dark halo by decomposing the rotation curve. The mass-to-light ratio M/L _B for the stellar disk is ≈1.4. The galaxy possesses a massive dark halo; however, the mass of the disk exceeds that of the halo in the inner part of the galaxy, which displays a regular spiral structure.     

Stellar subsystems of the galaxy NGC 2366

Hubble Space Telescope archive data are used to perform photometry of stars in seven fields at the center and periphery of the galaxy NGC 2366. The variation of the number density of stars of various ages with galactocentric radius and along the minor axis of the galaxy are determined. The boundaries of the thin and thick disks of the galaxy are found. The inferred sizes of the subsystems of NGC 2366 (Z _thin = 4 kpc and Z _thick = 8 kpc for the thin and thick disks, respectively) are more typical for spiral galaxies. Evidence for a stellar halo is found at the periphery of NGC 2366 beyond the thick disk of the galaxy.     

Polycyclic aromatic hydrocarbons in the dwarf galaxy IC 10

Archival infrared Spitzer Space Telescope observations are used to study the dust component of the ISM in the irregular galaxy IC 10. The dust distribution in the galaxy is compared to the distributions of the Hα and [S II] emission, neutral gas and CO clouds, and ionizing radiation sources. The distribution of polycyclic aromatic hydrocarbons (PAHs) in the galaxy is shown to be highly non-uniform, with the fraction of these particles in total dust mass reaching 4%. On the whole, PAHs avoid bright H II regions and correlate with the atomic and molecular gas. This pattern suggests that they form in the dense interstellar gas. It is suggested that the observed metallicity dependence of the PAH abundance shows up not only globally (at the level of the entire galaxy), but also locally (at least, at the level of individual H II regions). No conclusive evidence for shock destruction of PAHs in the IC 10 galaxy has been found.     

Dynamical evolution of galaxy clusters in the framework of the <Emphasis Type="Italic">N</Emphasis>-body problem. The formation of supermassive cD galaxies

We have carried out numerical simulations of the dynamical evolution of galaxy clusters taking into account merging when the relative velocities of the colliding galaxies are low. In particular, we study the evolution of the structure, mass spectrum, and velocity spectrum of a cluster of a thousand galaxies, as well as the growth of the central supermassive cD galaxy. The initial velocity dispersion of the galaxies and the rotation of the cluster were taken into account. The observed logarithmic spectrum dN ～ \(\tfrac{{dM}}{M}\) was adopted as the initial mass spectrum. The dynamical evolution of galaxy clusters, allowing for the possible merging of colliding galaxies, results in the emergence of a central supermassive galaxy, whose mass continuously increases due to mergers. This occurs only if the mass of the central galaxy becomes greater than ～0.1 of the total mass of the cluster. The observation of cD galaxies with relative masses of ～0.01 suggests that they initially formed in the cluster core, merged with nearby galaxies, and accreted intergalactic gas. The model indicates that a logarithmic galaxy mass spectrum is preserved during the cluster evolution, despite the substantial decrease in the number of galaxies in the cluster with time. The model can also reproduce the observed mass distribution with distance from the cluster center, M _r ～ r ^1.7.     

地震作用下丰满重力坝的塑性损伤

基于混凝土塑性损伤本构模型,将可以表征材料和结构渐进破坏的损伤变量作为内变量,考虑了混凝土拉压异性的损伤变量,利用有限元软件ABAQUS,对丰满混凝土重力坝在经受地震作用下的结构损伤区域的发展变化进行安全性评价。在数值计算过程中,对于受地震荷载作用所引起的地面水平运动而导致大坝水位水平运动对坝体的影响,通过扩充后的广义Westergaard公式予以计算模拟。通过分析得到了丰满大坝在地震作用下的塑性损伤破坏情况,并评价了丰满大坝的安全性,亦说明利用损伤力学对大坝进行安全性评价是一个可行的方法。     

Applicability of a Constitutive Model to Jointed Block Mass

Summary ?Deformational behaviour of jointed rocks is governed both by the properties of the joints and the intact rock. The applicability of a constitutive model to predict the stress-strain behaviour of a jointed block mass is discussed in this note. The stress-strain curves predicted by the model are compared with the experimental curves from physical model tests. It is observed that the model predicts the tangent modulus of the mass very closely. The failure strains are, however, underestimated, which may be due to the constant value of shear stiffness, resulting in linear stress-strain response by the model. The non-linear response of stress-strain curves can be obtained by using a variable value of the shear stiffness of the joints. A simple approach has been presented to assign variable stiffnesses, based on direct shear test results on joints. It is found that by assuming a variable stiffness the axial strains can also be predicted accurately. The transverse strain, however, remains highly underestimated by the model.     

Expulsion of dust from dark-matter halos at high redshifts

The conditions required for the expulsion of dust grains from primordial galaxies (dark-matter halos) are considered. The initial configuration is taken to be a dark-matter halo with the profile of a modified isothermal sphere; the baryons are taken to be in equilibrium with the corresponding virial temperature. The baryon density profile is calculated assuming hydrostatic equilibrium. A star-formation rate corresponding to a star-forming efficiency of 10% is assumed. The dust is transported from the galaxy by the radiation of stars concentrated in the central regions. Due to friction via collisions with gas in central regions, a fairly high luminosity is required in order for the radiation pressure to be strong enough to expel dust from the galaxy—the ratio of the luminosity to the total mass of the galaxy can reach unity.     

MT Ser, a binary blue subdwarf

We have classified and determined the parameters of the evolved close binary MT Ser. Our moderate-resolution spectra covering various phases of the orbital period were taken with the 6-m telescope of the Special Astrophysical Observatory. The spectra of MT Ser freed from the contribution of the surrounding nebula Abell 41 contained no emission lines due to the reflection effect. The radial velocities measured from lines of different elements showed them to be constant on a time scale corresponding to the orbital period. At the same time, we find effects of broadening for the HeII absorption lines, due to the orbital motion of two hot stars of similar types. As a result, we classify MT Ser as a system with two blue subdwarfs after the common-envelope stage. We estimate the component masses and the distance to the object from the Doppler broadening of the HeII lines. We demonstrate that the age of the ambient nebula, Abell 41, is about 35 000 years.