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 globular cluster inside a rotating,layered, inhomogeneous elliptical galaxy

We consider the spatial motion of a globular cluster with a constant or variable mass inside a rotating, layered, inhomogenous elliptical galaxy with a constant or variable mass. An analog to the Jacobi integral is found, regions of possiblemotion are determined, and zero-velocity surfaces constructed. Stationary solutions (libration points) are determined, together with their stability according to the Lyapunov criterion. In the case of variable mass, the autonomization method is used to solve the equations of motion, and the autonomization criteria used to establish an analog of the Eddington-Jeans law for the variation of the density of the galaxy.     

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.     

Population synthesis for the luminosity functions of X-ray binaries made using the “Scenario Machine”

Using the “Scenario Machine” (a computer code based on the Monte-Carlo method, developed to calculate the evolution of a large ensemble of binaries), we have carried out population-synthesis calculations for X-ray binaries for the purpose of modeling the X-ray luminosity functions in various type galaxies. These calculations were focused on the evolution of magnetized neutron stars. The X-ray luminosity function is not universal, and depends on the star formation rate in the galaxy. In theoretical models, it is very important to take into account the evolution of the binaries and their lifetimes in their X-ray stages. We calculated the cumulative and differential X-ray luminosity functions in galaxies with a constant star formation rate, the cumulative luminosity functions for various time intervals since the peak star formation, and curves describing the evolution of the X-ray luminosity after a star formation burst in the galaxy.     

The nature hypervelocity stars

We list and analyze the main currently known mechanisms for accelerating the space motions of stars. A high space velocity of a star can be a consequence of its formation in the early stages of the evolution of a massive galaxy, when it was spheroidal and non-stationary, so that stars were born with velocities close to the escape velocity for the galaxy. Another possibility is that the star arrived from another galaxy with a velocity that is high for our Galaxy. The decay of unstable close multiple stars or supernova explosions in close binaries can also provide velocities of up to several hundreds of km/s to main-sequence stars and velocities of up to ∼1000 km/s to degenerate stars, neutron stars, and stellar-mass black holes. The merger of components of a binary system containing two neutron stars or a neutron star and a black hole due to gravitational-wave radiation can accelerate the nascent black hole to a velocity∼1000 km/s. Hypervelocity relativistic stars can be born due to asymmetric neutrino ejection during a supernova explosion. Stars can be efficiently accelerated by single and binary supermassive black holes (with masses from several millions to several billions of solar masses) in the nuclei of galaxies. Thanks to their gravitational field and fast orbital motion (in the case of binary objects), supermassive black holes are able to accelerate even main-sequence stars to relativistic velocities.     

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.     

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.     

<Emphasis Type="Italic">BVRI</Emphasis>Hα CCD photometry of the spiral galaxy NGC 3184

We have carried out BVRIHα CCD surface photometry of the spiral galaxy with active star formation NGC 3184 using the 1-m telescope of the Special Astrophysical Observatory. B and Hα data from the ING Archive (La Palma Observatory) were also used. We consider the structure and radial brightness distribution of the galaxy. Stellar populations in different regions of the galaxy are analyzed using two-color diagrams. We have identified and studied star-forming regions in NGC 3184 and estimated their ages based on evolutionary modeling.     

The stellar population and evolution of galaxies of the NGC 80 group

Seven early-type galaxies that are members of the massive X-ray group containing NGC 80 have been studied using two-dimensional spectroscopy with the 6-m telescope of the Special Astrophysical Observatory. We searched for evidence for the synchronous secular evolution of the galaxies in the group. The bulges of five of the seven galaxies appear to be old, with the average age of the bulge stars being 10–15 billion years. Signs of a relatively recent star-formation burst are observed in the small S0 galaxy IC 1548, whose average bulge age is 3 billion years and average core age is 1.5 billion years. A circumnuclear polar gas ring was also detected in this galaxy; in its outer regions, it makes a smooth transition to a gas disk that counter-rotates relative to the stars. IC 1548 probably underwent a close interaction, which resulted in its transformation from a spiral to a lenticular galaxy; the same interaction may also have induced the central burst of star formation. In the giant E0 galaxy NGC 83, a compact massive stellar-gas disk with a radius of about 2 kpc and very rapid rotation is observed, with ongoing star formation; the so-called “minor merger” is likely to have occurred there. We conclude that the NGC 80 group is in a state of formation, with the small NGC 83 subgroup “falling into” the large, old NGC 80 subgroup.     

Analysis of stellar trajectories in an open cluster model

A two-point model of an unisolated star cluster moving in a circular orbit in the Galactic plane is analyzed. The equations of stellar motion are linearized in the neighborhood of the singular point at the zero-velocity surface (ZVS), and also in the neighborhood of a point below the critical ZVS on a trajectory with less than the critical stellar ‘energy.’ We find the eigenvalues and eigenvectors of these equations and point out the instability of the two singular points on the critical ZVS; the separatrix connecting these points is determined numerically. For trajectories located below the critical ZVS, the absolute values of the eigenvalues of the linearized equations of motion increase with decreasing energy of the star and decreasing maximum distance between the trajectory and the cluster center of mass. This results in an increase of the numerical estimates of the maximum characteristic Lyapunov exponents for trajectories located closer to the center of mass of the cluster. We use Poincaré sections and the maximum characteristic Lyapunov exponents to analyze the properties of the stellar trajectories. A number of periodic orbits for different stellar energies are found, and the properties of the trajectories in the vicinity of these periodic orbits analyzed. Almost all the stellar trajectories considered are stochastic, with the degree of stochasticity increasing with decreasing stellar energy. Domains with different degrees of stochasticity are identified in the Poincaré maps.     

Formation of ring structures in galactic disks during close passages of galaxies

The formation of ring structures in galactic disks is investigated. It is shown that, in addition to the known mechanism of forming rings in “head-on” collisions between galaxies, ring structures can be formed during close passages of galaxies if the perturbing galaxy moves in a plane close to the equatorial plane of the perturbed disk galaxy, opposite to the direction of rotation of the disk. Numerical simulations of the formation of structures in the disk of a massive galaxy undergoing a passage with another galaxy are considered. The results of these cmputations show the formation of pronounced ring structures in the galactic disk when the initial inclination of the trajectory of the perturbing galaxy to the equatorial plane of the perturbed galaxy is no more than ~25°. However, the probability of close passages of galaxies with these parameters is small, as is the probability of head-on collisions. The characteristic time scale for the existence of pronounced rings is of order the dynamical time scale at the edge of the galaxy, 200–300 million years, close to the corresponding time for head-on collisions. The evolution of the rings has the same character in both cases: they gradually expand and move toward the periphery of the galaxy. The results of these simulations can also be applied to a close passage of one star by another star with a protoplanetary disk. According to the computation results, the characteristic time scale for the existence of pronounced rings in such a protoplanetary disk depends mainly on the size of the disk; this time scale can reach several tens of thousands of years for a disk radius of about 1000 AU. The formation of ring structures in such a disk could influence the formation and evolution of planetesimals, and possibly the character of the formation of planets and the distribution of their orbital semi-major axes.     

新的太阳系起源假说——再论巨星依次分离说

本文以太阳系星球的物质状态、形态面貌、体积、物质密度、运动速度、运动方向和角动量等作为根据,研究它们在宇宙空间上的分布特点、相互关系、内在联系以及规律的基础上,提出太阳系(乃至宇宙星球)是在46亿年前,宇宙中一个巨大灼热的星球,在高速度左旋旋转(公转和自转)运动的过程中,从尾部分离出来的物质,经过……恒星、行星和卫星依次波状旋转分离运动产生的。     

Interstellar medium surrounding the WO star in the galaxy IC 1613: New optical and radio observations

Observations of the nebula S3 associated with the WO star in the galaxy IC 1613 and of an extended region surrounding S3 are reported. The star and bright core of the nebula were observed with a multipupil fiber spectrograph mounted on the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. Images in the principle spectral lines and integrated spectra of the star and three compact clumps were obtained, and the radial-velocity field constructed. An extended region of the galaxy was observed with the Very Large Array at 21 cm. A giant ring or H I shell enclosing a large fraction of the stellar population in IC 1613 was discovered. The WO star and associated bipolar nebula, which we discovered earlier, lie at the inner edge of the H I ring. A local H I deficiency and two arclike H I ridges were also detected for the first time and probably represent the neutral component of the bipolar shell surrounding the WO star. The two arclike ridges may also have been produced by the collective stellar wind (and supernova explosions?) in OB association No. 9 from the list of Hodge. A scenario for the formation of the extended bipolar feature is discussed, based on the new data.     

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.     

Elliptical motion of a star in a close binary system

The motion of a rotating star in a close binary system with conservative mass exchange is considered. In contrast to the Paczyński-Huang model, the new model applied examines the relative motion of a star along an elliptical orbit in a close binary system, taking into account the mutual gravitation between the stars, reactive forces, the gravitation exered on the stars by the mass-transfer stream, and perturbations due to the rotation of the accreting star. The variations of the semi-major axis and eccentricity of the orbit and the orbital angular velocity of the accreting star as a function of the component-mass ratio q are determined. The results are applied to the BF Aurigae system.     

A region of violent star formation in the Irr galaxy IC 10: Structure and kinematics of ionized and neutral gas

We have used observations of the galaxy IC10 at the 6-m telescope of the Special Astrophysical Observatory with the SCORPIO focal reducer in the Fabry-Perot interferometer mode and with the MPFS spectrograph to study the structure and kinematics of ionized gas in the central region of current intense star formation. Archive VLA 21-cm observations are used to analyze the structure and kinematics of neutral gas in this region. High-velocity wings of the Hα and [SII] emission lines were revealed in the inner cavity of the nebula HL 111 and in other parts of the complex of violent star formation. We discovered local expanding neutral-gas shells around the nebulae HL 111 and HL 106.     

The motion of halo stars in dynamical numerical models of open clusters

Equations of motion containing a small parameter μ are derived for stars at the peripheries of open star clusters. The parameter μ is obtained for six numerical open-cluster models. The general analytical solution of these equations of motion for μ = 0 is found. An iterative method is used to derive the frequencies of the stellar motions for first-order expansions in μ of the solutions of the equations of motion for stars at the cluster periphery. Applications of the results are discussed.     

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.     

Magnetic activity of the star Corot-Exo-2a

Continuous photometric observations of the young active solar-type star Corot-Exo-2a using the “Corot” space telescope obtained over 142 days were used to analyze the star’s surface temperature inhomogeneities and to monitor their continuous evolution. This analysis was based on the iPH code, which reconstructs the distribution of temperature inhomogeneities on the surface of a star based on its light curve in a two-temperature approximation. We identified five time intervals in the positions of active areas, with corresponding flip-flop events, interpreted as activity periods. Their durations were between 55 and 15 days. The time scale for the active-longitude flip-flops of Corot-Exo-2a is a few tens of days, rather than years, as for other stars studied earlier. We detected motions of the active longitudes, possibly indicating differential rotation of the star. The phenomenon of flip-flops in the positions of active longitudes has a complex character. This is the first case apart fromthe Sun where we are able to follow the appearance and development of temperature inhomogeneities on a stellar surface in such detail. We determined typical timescales for variations of the activity parameter of the star in the ranges 17–20, 28–32, 33–38, and 51–55 days, which characterize changes of the brightness variation amplitude, the spotted surface area, positions of active areas, and brightness variations.     

Search for and study of hot circumstellar dust envelopes

Long-term (1984–2008) JHKLM photometry for 254 objects is presented. The observations were carried out in the standard JHKLM photometric system using an original method and a modern IR photometer designed and built at the Sternberg Astronomical Institute. Our program of studies included searches for and studies of relatively hot circumstellar dust envelopes. The most important results obtained using these observations include the following. We have detected relatively hot dust envelopes in a number of objects for the first time, including the RCB star UV Cas, RX Cas, several classical symbiotic stars, etc. A model has been calculated for the dust envelope of FG Sge, which formed around the star as a result of several successive cycles of dust condensation beginning in Autumn 1992. Several dust-condensation episodes have been traced in the envelopes of symbiotic systems (CH Cyg, V1016 Cyg, HM Sge, etc.), as well as the role of the hot component in the formation of the dust envelopes. We have established from variations of the IR emission that the cool components in the symbiotic novae V1016 Cyg and HM Sge, and possibly CH Cyg, are Miras. The binarity of V1016 Cyg and HM Sge has also been firmly established. The variability of a whole series of object has been studied, including the stellar components of close binary systems and several dozen Mira and semi-regular variables. The ellipsoidality of the components in the RX Cas system (a prototype W Ser star) and the cool component in the symbiotic systems CI Cyg and BF Cyg has been firmly established. We have obtained the first IR light curve for the eclipsing system V444 Cyg (WN5+O6), and determined the wavelength dependence of the obtained parameters of the WN5 star. Analysis of the IR light curves of several novae indicate the condensation of dust envelopes in the transition periods of Cygnus 1992, Aquila 1993, and Aquila 1995. The IR light curve of R CrB has been obtained over a long period and analyzed. IR observations of the nova-like variable V4334 Sgr have been carried out over four years, over which the star passed through four stages during its motion along its post-AGB evolutionary track; the star’s bolometric flux and optical depth of its dust envelope have been estimated, and the structure and mass of the dust layer determined. We have analyzed the IR variability of the symbiotic star V407 Cyg over 14 years, and found its cool component to be a Mira with a period of 745 days. The observed pulsations and trend are associated with the luminosity and temperature variations of the Mira, as well as the optical depth of the dust envelope. The size of the dust grains and mass-loss rate of the Mira have been determined. We have obtained JHKL light curves for the Seyfert galaxy NGC 4151 over 23 years. The IR brightness of the galaxy grew from 1985 through 1996 (by ∼0.9 ^m at 1.25 μm, ∼1 ^m at 1.65 μm, ∼1.1 ^m at 2.2 μm, and ∼1.3 ^m at 3.5 μm), while the galaxy simultaneously reddened. The “cool” variable source in NGC 4151 was still in the active state in 1998, although its luminosity had decreased by approximately 15%–20%. If the “cool” component of the variable source in this galaxy is a dust envelope heated by the central “hot” source, it should be optically thin to the radiation of this source: its mean optical depth is in the range 0.05–0.15. Emission from dust particles heated to temperatures of 600–800 K was observed in the near IR at a distance of several parsecs from the nucleus during the period of activity in 1995–1998; the inferred mass of emitting dust was 5–20 M _⊙. In 1994–2003, we observed a tendency for NGC 4151 to become bluer at 1.25–1.65 μm while simultaneously reddening at 2.2–3.5 μm. Beginning in Autumn 2000, the galaxy began to emerge from a minimum, which lasted from March 2000 through April 2001 in the IR; a flare of the galactic nucleus was observed and followed in detail in the IR in this same period. We confirm the IR variability of the nucleus of the Seyfert galaxy NGC 1068, which can be located in various stages of activity. The variability of NGC 1068 is associated with a complex source. A periodic component has been detected in the J brightness variations of the oxygen Mira V2108 Oph; we have shown that this star is immersed in a fairly dense dust envelope, and have calculated amodel for this envelope. We have calculated an (axially symmetrical) dust-envelope model for the carbon semi-regular variable RWLMi with a density distribution characteristic for the “superwind” stage. This envelope model is able to reproduce the observed fluxes over the entire observable spectrum, and displays a good agreement with the observational data. The three hot supergiants V482 Cas, QZ Sge, and HD 338926 may be variable in the IR. Long-term photometry of eight planetary nebulae in the near IR (1.25–5 μm) has enabled us to firmly establish the IR brightness and color variability of these nebulae on time scales from several tens of days to six-to-eight years. We have analyzed long-term JK photometry of the X-ray binary Cyg X-1 (V1357 Cyg). Periodicity with a characteristic time scale of ∼11.5 years is visible in the JK brightness variations of Cyg X-1 in 1984–2007, possibly due to periodic variations of the temperature, radius and luminosity of the optical component of the binary with P ∼11.5 yr. Fourteen-year IR light curves of five RV Tau stars (R Sge, RV Tau, AC Her, V Vul, and R Sct) and the yellow supergiant and protoplanetary-nebula candidate V1027 Cyg have been analyzed. A spherically symmetrical dust-envelope model has been calculated for V1027 Cyg.