Study of local hydrodynamic characteristics of upward slug flow

Results of an experimental study of local velocity, fluctuation and void fraction profiles in liquid plugs of an upward vertical gas-liquid flow as well as of wall shear stress distribution both under gas slugs and in liquid plugs, are presented. The conditional sampling technique allowed to obtain instantaneous profiles of the above hydrodynamical quantities, which illuminated the real physical picture of the flow in a liquid plug. The toroidal vortex adjacent to the bottom of a gas slug is shown to determine significantly the development of the flow in a liquid plug. The intensity of this vortex is determined only by the relative velocity of the gas bubble with respect to the liquid.     

The role of external factors in the evolution of galaxies

We consider the evolution of galaxies in dense galactic clusters. Observations and theoretical estimates indicate that this evolution may be specified to a large extent by collisions between galaxies, as well as interactions between the gaseous components of disk galaxies and intergalactic gas. We analyze collisions between disk galaxies with gaseous components using a simple model based on a comparison of the duration of a collision and the characteristic cooling time for the gas heated by the collision, and also of the relative masses of stars and gas in the colliding disk galaxies. This model is used to analyze scenarios for collisions between disk galaxies with various masses as a function of their relative velocities. Our analysis indicates that galaxies can merge, lose one or both of their gaseous components, or totally disintegrate as a result of a collision; ultimately, a new galaxy may form from the gas lost by the colliding galaxies. Disk galaxies with mass M _G and velocities exceeding ～300 (M _G/10¹⁰ M _⊙)^1/2 km/s in intergalactic gas in clusters with densities ～10^?27 g/cm³ can lose their gas due to the pressure of inflowing intergalactic gas, thereby developing into E(SO) galaxies.     

Evolution of the components of the close binary WR 20a

We have analyzed the evolution of the components of the unique massive binary system WR 20a, which consists of a Wolf-Rayet nitrogen star and an Of star with an extremely small separation. The estimated masses of the components are 83 and 82 M _⊙, which are among the highest stellar mass inferred. We have carried out numerical modeling of the evolution of the components, taking into account the mass loss due to the stellar wind inherent to massive stars. In a scenario in which the systemis detached from the time the components reach the main sequence until its present state, the initial component masses are inferred to be close to 110 M _⊙, if the initial masses of the stars were equal, or 120 and 100 M _⊙, if they were different. Currently, the components are evolved main-sequence stars, whose surfaces are relatively little enriched by helium. The further evolution of the system will result in one of the components filling its Roche lobe and evolution within a common envelope. As a result, the components may coalesce, leading to the formation of a single massive black hole the supernova explosion. Otherwise, depending on the masses of the resulting black holes, either a binary system with two black holes or two free black holes will be formed. In the latter case, gamma-ray bursts will be observed.     

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.     

The stellar epoch in the evolution of the Galaxy

We consider the astrophysical evolution of the Galaxy over large time scales, from early stages (an age of ～10⁸ yrs) to the end of traditional stellar evolution (～10¹¹ yrs). Despite the fact that the basic parameters of our stellar system (such as its size, mass, and general structure) have varied little over this time, variations in the characteristics of stars (their total luminosity, color, mass function, and chemical composition) are rather substantial. The interaction of the Galaxy with other stellar systems becomes an important factor in its evolution 100–1000 Gyr after its origin; however, we take the Galaxy to be isolated. In the model considered, the basic stages of Galactic evolution are as follows. The Galaxy forms as the result of the contraction (collapse) of a protogalactic cloud. The beginning of the Milky Way’s life—the relaxation period, which lasts about 1–2 Gyr—is characterized by active star formation and final structurization. The luminosity and colors of the Galaxy are correlated to the star formation rate (SFR). The young Galaxy intensely radiates high-energy photons, which are mostly absorbed by dust and re-emitted at IR wavelengths. In the subsequent period of steady-state evolution, the gas content in the Galactic disk gradually decreases; accordingly, the SFR decreases, reaching 3–5M _⊙/yr at the present epoch and decreasing to 0.03M _⊙/yr by an age of 100 Gyr. Essentially all other basic parameters of the Galaxy vary little. Later, the decrease in the SFR accelerates, since the evolution of stars with masses exceeding 0.4M _⊙ (i.e., those able to lose matter and renew the supply of interstellar gas) comes to an end. The Galaxy enters a period of “dying”, and becomes fainter and redder. The variation of its chemical composition is manifested most appreciably in a dramatic enrichment of the interstellar gas in iron. The final “stellar epoch” in the life of the Galaxy is completed ～10¹³ yrs after its formation, when the evolution of the least massive stars comes to an end. By this time, the supplies of interstellar and intergalactic gas are exhausted, the remaining stars become dark, compact remnants, there is no further formation of new stars, and the Galactic disk no longer radiates. Eventually, infrequent outbursts originating from collisions of stellar remnants in the densest central regions of the Galaxy will remain the only source of emission.     

The formation and evolution of the most massive stars

We consider the formation of massive stars under the assumption that a young star accretes material from the protostellar cloud through its accretion disk while losing gas in the polar directions via its stellar wind. The mass of the star reaches its maximum when the intensity of the gradually strengthening stellar wind of the young star becomes equal to the accretion rate. We show that the maximum mass of the forming stars increases with the temperature of gas in the protostellar cloud T ₀, since the rate at which the protostellar matter is accreted increases with T ₀. Numerical modeling indicates that the maximum mass of the forming stars increases to ～900 M _⊙ for T ₀ ～ 300 K. Such high temperatures of the protostellar gas can be reached either in dense star-formation regions or in the vicinity of bright active galactic nuclei. It is also shown that, the lower the abundance of heavy elements in the initial stellar material Z, the larger the maximum mass of the star, since the mass-loss rate due to the stellar wind decreases with decreasing Z. This suggests that supermassive stars with masses up to 10⁶ M _⊙ could be formed at early stages in the evolution of the Universe, in young galaxies that are almost devoid of heavy elements. Under the current conditions, for T ₀ = (30–100) K, the maximum mass of a star can reach ～100M _⊙, as is confirmed by observations. Another opportunity for the most massive stars to increase their masses emerges in connection with the formation and early stages of evolution of the most massive close binary systems: the most massive stars can be produced either by coalescence of the binary components or via mass transfer in such systems.     

The evolution of close binary systems with intermediate-mass black holes and ultra-luminous X-ray sources

The results of numerical studies of the evolution of a close binary system containing a black hole with a mass of ～3000M_⊙ are presented. Such a black hole could form in the center of a sufficiently rich and massive globular cluster. The secondary could be a main-sequence star, giant, or degenerate dwarf that fills or nearly fills its Roche lobe. The numerical simulations of the evolution of such a system take into account the magnetic wind of the donor together with the wind induced by X-ray irradiation from the primary, the radiation of gravitational waves by the system, and the nuclear evolution of the donor. Mass transfer between the components is possible when the donor fills its Roche lobe, and also via the black hole’s capture of some material from the induced stellar wind. The computations show that the evolution of systems with solar-mass donors depends only weakly on the mass of the accretor. We conclude that the observed ultra-luminous X-ray sources (L _X ? 10³⁸ erg/s) in nearby galaxies could include accreting black holes with masses of 10²?10⁴M_⊙. Three scenarios for the formation of black holes with such masses in the cores of globular clusters are considered: the collapse of superstars with the corresponding masses, the accretion of gas by a black hole with a stellar initial mass (<100M_⊙), and the tidal accumulation of stellar black holes. We conclude that the tidal accumulation of stellar-mass black holes is the main scenario for the formation of intermediate-mass black holes (10²?10⁴M_⊙) in the cores of globular clusters.     

A dipolar vortex model for the obscuring tori in active galactic nuclei

Motivated by currently available direct observations of occulting tori in Seyfert galaxies and ongoing discussions about tori as important structural components in Active Galactic Nuclei, we discuss the possibility that the “spinning up” of a torus by radiation or winds could transform it into a dipolar toroidal vortex. The vortex motion balances the torus’ self-gravitation, and can explain the existence of cool, thick tori inferred from observations. In turn, the toroidal vortex can be a source of matter to feed the accretion disk. The resulting instability could result in flares accompanied by the ejection of matter. Our numerical estimates of the model parameters for luminosities close to the Eddington limit are consistent with the observational data.     

The Fragmentation in a Protoplanetary Disk and the Properties of the Resultant Self-Gravitating Clumps

We study the fragmentation properties in the protoplanetary disk and properties of the resultant self-gravitating clumps using our newly constructed disk model. Our disk model includes the mass inflall term from a molecular cloud core and the photoevaporation winds effect. We adopt the conventional fragmentation criterion to judge whether a protoplanetary disk can fragment. In this work, we follow our previous work to investigate the properties of the resultant self-gravitating clumps. In our calculation, the initial masses of the resultant self-gravitating clumps lie in the range of tens of M_J to more than one hundred of M_J, where M_J is the Jupiter mass. These initial masses can seemingly account for the masses of extrasolar planets in magnitude. We also calculate the subsequent gas accretion of clumps in 1.27 × 10⁴ yr after the formation of self-gravitating clumps. We find that the subsequent gas accretion of self-gravitating clumps is very efficient, and the clump masses grow to hundreds of M_J and the physical radii R_c of clumps increase to about 10 AU. Additionally, we also calculate the orbital migration of clumps. We find that most clumps have short migration timescale to be accreted onto the protostar, and only a small fraction of clumps have long migration timescale (>10⁶ yr) to successfully become gas giant planets. These results are consistent with previous studies.     

Rotational mass loss by Be stars

We have carried out a numerical study of rotational mass loss by rapidly rotating Be stars assuming preservation of rigid-body rotation during their main-sequence evolution. Evolutionary models are computed for stars with solar chemical composition and initial masses of 3, 10 and M_⊙. As a result of their rapid initial rotation, these stars can lose one to four percent of their initial mass during the main-sequence stage. The amount of mass lost increases with the initial mass of the star. The matter lost by Be stars can form gas-dust disks with masses comparable to the masses of planets, which, in principle, makes possible the formation of planetary systems around such stars.     

Evolution of Stars Paired with Intermediate-Mass Black Holes

Under certain conditions, stars close to intermediate-mass black holes (IMBHs) can form close binary systems with these objects, in which the Roche lobe can be filled by the star and intense accretion of the star’s matter onto the IMBH is possible. Recently, accreting IMBHs have been associated with hyperluminous X-ray sources (HLXs), whose X-ray luminosities can exceed 10⁴¹ erg/s. In this paper, the evolution of star—IMBH binary systems is investigated assuming that the IMBH mainly accretes the matter of its companion star, and that the presence of gas in the vicinity of the IMBH does not appreciably affect changes in the orbit of the star. The computations take into account all processes determining the evolution of ordinary binary systems, as well as the irradiation of a star by hard radiation during the accretion of its matter onto the IMBH. The absorption of external radiation in the stellar envelope was calculated applying the same formalism that is used to calculate the opacity of the stellar matter. The computations also assumed that, if the characteristic time for the mass transfer is less than the thermal time scale of the star, there is no exchange betwween the orbital angular momentum of the system and the angular momentum of the matter flowing onto the IMBH.

Numerical simulations have shown that, under these assumptions, three types of evolution are possible for such a binary system, depending on the mass of the IMBH and the star, as well as on the star’s initial distance from the IMBH. The first type ends with the destruction of the star. For low-mass main sequence (MS) stars, only this option is realized, even in the case of large initial distances from IMBH. For massive MS stars, the star is also destroyed if the mass of the IMBH is high and the initial distance of the star from the IMBH is sufficiently small.

The second type of evolution can occur for massive MS stars, which are initially located farther from the IMBH than in the first type of evolution. In this case, the massive star fills its Roche lobe during its evolutionary expansion, after which a stage of intense mass transfer begins. It is in this phase of the evolution that the star- IMBH system can manifest itself as a HLX, when its X-ray luminosity L_X exceeds 10⁴¹ erg/s for a fairly long time. Numerical simulations show that the initial mass of the donor star in systems with M_BH = (10³?10⁵)M_⊙ must be close to ～10 M_⊙ in this case. The characteristic duration of the HLX stage is 30 000–70 000 years. For smaller initial donor masses close to ～5M_⊙, L_X does not reach 10⁴¹ erg/s in the stage of intense mass transfer, but can exceed 10⁴⁰ erg/s. The duration of this stage of evolution is 300 000–800 000 years. A characteristic feature of this second type of evolution is an increase in the orbital period of the system over time. As a result, after a period of intense mass loss, the star “retreats” inside the Roche lobe. A remnant of the star in the form of a white dwarf is left behind, and can end up fairly far from the IMBH.

The third type of evolution can occur for massive MS stars that are initially even farther from the IMBH, as well as for massive stars that are already evolved at the initial time. In this case, conservative mass exchange in the presence of intense stellar wind leads to the star moving away from the IMBH, without filling its Roche lobe at all. For massive stars with sufficiently strong stellar winds (for example, stars with masses ～50M_⊙), the accretion rate of matter onto the IMBH in this case can reach values that are characteristic of HLXs. As in the case of the second type of evolution, the stellar remnant can remain at a fairly large distance from the IMBH.

     

The evolutionary status of the most massive WNh stars in close binary systems. NGC 3603-A1

The evolution of the components of the unique, massive, close binary system NGC 3603-A1, which consists of stars of spectral types WN6ha and WN6h, is analyzed. The component masses are estimated to be 116 and 89M _⊙, close to the highest measured stellar masses. Numerical modeling of the evolution of the components has been carried out, taking into account mass loss via the stellar winds of the two massive stars. It is shown that the maximum possible initial component masses are close to 140 and 125M _⊙. The components are currently slightly evolved main-sequence stars, with a comparative low degree of helium enrichment at their surfaces. Further evolution of the system will lead to filling of the Roche lobe of the primary and subsequent evolution in a common envelope. This may lead to the merger of the components, with the evolution of the system ending in the formation of a singlemassive black hole after the second supernova explosion. Otherwise, depending on the masses of the resulting black holes, either a binary system of two black holes or two unbound black holes may form, accompanied by gamma-ray bursts.     

Evolution of the first supernovae in protogalaxies: Dynamics of mixing of heavy elements

The paper considers the evolution of the supernova envelopes produced by Population III stars with masses ofM _* ?? 25?C200M _?? located in non-rotating protogalaxies with masses of M ?? 10⁷ M _?? at redshifts z = 12, with dark-matter density profiles in the form of modified isothermal spheres. The supernova explosion occurs in the ionization zone formed by a single parent star. The properties of the distribution of heavy elements (metals) produced by the parent star are investigated, as well as the efficiency with which they are mixed with the primordial gas in the supernova envelope. In supernovae with high energies (E ? 5 × 10⁵² erg), an appreciable fraction of the gas can be ejected from the protogalaxy, but nearly all the heavy elements remain in the protogalaxy. In explosions with lower energies (E ? 3 × 10⁵² erg), essentially no gas and heavy elements are lost from the protogalaxy: during the first one to threemillion years, the gas and heavy elements are actively carried from the central region of the protogalaxy (r ?? 0.1r _v , where r _v is the virial radius of the protogalaxy), but an appreciable fraction of the mass of metals subsequently returns when the hot cavity cools and the envelope collapses. Supernovae with high energies (E ? 5 × 10⁵² erg) are characterized by a very low efficiency of mixing of metals; their heavy elements are located in the small volume occupied by the disrupted envelope (in a volume comparable with that of the entire envelope), with most of the metals remaining inside the hot, rarified cavity of the envelope. At the same time, the efficiency of mixing of heavy elements in less energetic supernovae (E ? 3 × 10⁵² erg) is appreciably higher. This comes about due to the disruption of the hot cavity during the collapse of the supernova envelope. However, even in this case, a clear spatial separation of regions enriched and not enriched in metals is visible. During the collapse of the supernova envelope, the metallicity of the gas is appreciably higher in the central region ([Z] ?? ?1 to 0) than at the periphery ([Z] ?? ?2 to ?4) of the protogalaxy; most of the enriched gas has metallicities [Z] ?? ?3.5 to ?2.5. The masses of enriched fragments of the supernova envelope remain appreciably lower than the Jeans mass, except in regions at the center of the protogalaxy upon which the surrounding enriched gas is efficiently accreted. Consequently, the birth of stars with metallicities close to those characteristic of present-day Galactic stars is very probable in the central region of the protogalaxy.     

Evolution of stars near bright quasars

We consider the evolution of stars that are located in the near vicinity of bright quasars and illuminated by their hard radiation. The absorption of the external radiation flux in the stellar envelope was calculated applying the formalism used to determine the opacity of the stellar material. The simulations show that the external irradiation heats the outer layers of the star, altering their structure and reducing the thickness of the convective envelope in low-mass stars, but leaves the inner layers essentially unaffected. In addition, the irradiation substantially increases the mass loss in the stars. This is important for our understanding of the evolution of quasar masses, since this increased mass loss by nearby stars can supply the quasar with additional accreting gas. The results can also be applied to detached binaries in which a low-mass star is irradiated by a very massive companion.     

Evolution of close stellar binaries with black holes under the action of gravitational radiation and magnetic and induced stellar winds of the donor

We show that semi-detached close binary systems with massive (4–25M_⊙) black holes are formed in the evolution of massive stellar binaries in which the initial mass of the primary exceeds ～25M_⊙. The mass exchange in such systems is maintained by the nuclear evolution of the donor and by its magnetic and induced stellar winds. The donor in such systems can be a main-sequence star, subgiant, non-degenerate helium star, or white dwarf. The evolution of corresponding systems with black-hole masses of 10M_⊙ is investigated.     

Supermassive black holes and galaxy kinematics

The statistical relation between the masses of supermassive black holes (SMBHs) in disk galaxies and the kinematic properties of their host galaxies is analyzed. Velocity estimates for several galaxies obtained earlier at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and the data for other galaxies taken from the literature are used. The SMBH masses correlate well with the rotational velocities at a distance of R ≈ 1 kpc, V ₁, which characterize the mean density of the central region of the galaxy. The SMBH masses correlate appreciably weaker with the asymptotic velocity at large distances from the center and the angular velocity at the optical radius R ₂₅. We have found for the first time a correlation between the SMBH mass and the total mass of the galaxy within the optical radius R ₂₅, M ₂₅, which includes both baryonic and “dark” mass. The masses of the nuclear star clusters in disk galaxies (based on the catalog of Seth et al.) are also related to the dynamical mass M ₂₅; the correlations with the luminosity and rotational velocity of the disk are appreciably weaker. For a given value of M ₂₅, the masses of the central cluster are, on average, an order of magnitude higher in S0-Sbc galaxies than in late-type galaxies, or than the SMBH masses. We suggest that the growth of the SMBH occurs in the forming “classical” bulge of the galaxy over a time < 10⁹ yr, during a monolithic collapse of gas in the central region of the protogalaxy. The central star clusters form on a different time scale, and their stellar masses continue to grow for a long time after the growth of the central black hole has ceased, if this process is not hindered by activity of the nucleus.     

Variations of the H2O maser emission of W51M in 1981–1998

The results of spectral monitoring of the maser source W51M carried out in the water-vapor line at 1.35 cm (22GHz) on the 22-m telescope of the Pushchino Radio Astronomy Observatory in 1981–1998 are reported and interpreted. Long-term variations of the maser flux with a period of 12–13 years are found. W51M may be a rotating and simultaneously expanding toroidal cloud of gas and dust around a young star with a mass of the order of ～15M _⊙, with numerous high-velocity jets of maser condensations flowing out in two broad cones along the polar axis of the torus. A stellar wind with a velocity of about 2000–3000 km/s is responsible for the maser pumping.     

A dynamo in a torus as an explanation of magnetic fields in the outer rings of galaxies

It is currently generally believed that magnetic fields in the disks of spiral galaxies are generated by the dynamo mechanism, which is based on the joint action of differential rotation and the alpha effect, associated with turbulent motions in the interstellar gas. Together with their disks, outer rings are also encountered in galaxies, where magnetic fields may be present. In earlier studies, the generation of magnetic fields has been described in a planar approximation, whose essence is that the size of rings perpendicular to the plane of the galaxy is much smaller than their size in the radial direction. However, it is plausible that these sizesmay sometimes be comparable, so that it would be more logical to suppose that a ring has a toroidal form. A model for a dynamo in a toroidal ring is constructed in this study. This model describes the magnetic field using two functions, corresponding to the toroidal component of the field and the part of the vector potential characterizing its poloidal component. The possible generation of magnetic field in various cases is shown, with both quadrupolar symmetry (close to the fields obtained in the planar approximation) and dipolar symmetry (when two layers with oppositely directed magnetic fields form in the ring). The parameter values for which the generation of fields with one or the other type of symmetry is possible are estimated. The results can also be used to describe the evolution of the magnetic fields in other toroidal astrophysical objects.     

Close binaries containing Supermassive Black Holes

We consider the evolution of binary systems formed by a Supermassive Black Hole (SMBH) residing in the center of a galaxy or a globular cluster and a star in its immediate vicinity. The star is assumed to fill its Roche lobe, and the SMBH accretes primarily the matter of this star. The evolution of such a system is mainly determined by the same processes as for an ordinary binary. The main differences are that the donor star is irradiated by hard radiation emitted during accretion onto the SMBH; in a detached system, nearly all the donor wind is captured by the black hole, which strongly affects the evolution of the semi-major axis; it is not possible for companions of the most massive SMBHs to fill their Roche lobes, since the corresponding orbital separations are smaller than the radius of the last stable orbit in the gravitational field of the SMBH. Moreover, there may not be efficient exchange between the orbital angular momentum and the angular momentum of the overflowing matter in such systems. Our computations assumed that, if the characteristic timescale for mass transfer is smaller than the thermal timescale of the star, no momentum exchange occurs. Absorption of incident external radiation in the stellar envelope was treated using the same formalism that was used when computing the radiative transfer in the stellar atmosphere. Numerical simulations show that Roche-lobe overflow is possible for a broad range of initial system parameters. The evolution of semi-detached systems containing a star and a SMBH nearly always ends with the dynamical disruption of the star. Stars with masses close to the solar mass are destroyed immediately after they fill their Roche lobes. During the accretion of matter of disrupted stars, the SMBH can achieve quasar luminosities. If the SMBH accretes ambient gas as well as gas stripped from stars, the star is subject to additional radiation in the detached phase of its evolution, strengthening its stellar wind. This leads to an increase of the semi-major axis and subsequent decrease of the probability of Roche-lobe overflow during the subsequent evolution of the system.     

松动岩体工程特性研究——以雅砻江楞古水电站松动岩体为例

为了对松动岩体的工程特性进行系统研究,以楞古水电站厂址区边坡为例,对该边坡岩体进行了详细的地质编录和物理勘探试验,重点对节理裂隙的空间发育规律、镶嵌结构和碎裂结构岩体的发育深度及空间分布、软弱结构面发育分布规律以及边坡已有变形破坏特征这四个方面进行了系统的统计和分析,认为松动岩体是区域断裂活动和浅表生改造的结果,岩体工程效应差、变形模量低;同时结合应力测试、声波测速、高密度电磁勘探等试验成果进行分析,结果显示松动岩体具低波速（波速大部分小于3 000 m/s）、低应力（最大主应力不超过20 MPa）、强透水性（透水性系数大于10 L/（min·m·m））。认为岩体破碎主要受断层及节理裂隙影响,分析了岩体破裂松动的演化过程及特征。