Numerical modeling of galaxy evolution

A very significant problem in the modeling of disk-galaxy formation in the cold dark matter (CDM) cosmology is the so-called `angular momentum problem'. This problem arises when we numerically model the collapse of baryons within a dark halo in the CDM model. The formed baryonic disk has much less angular momentum than observed disk galaxies due to the considerable loss of angular momentum during the progressive merger of small clumps. As a result of efficient radiative cooling, the gas component collapses too deeply within the dark halo. When two such systems are merging, the angular momentum of the material near the center is effectively transported outwards by the tidal force. This is a physical reason for this problem, however, there may be a numerical origin due to the nature of the Smoothed Particle Hydrodynamics (SPH) method widely used in galaxy formation models. To address the numerical origin of the `angular momentum problem' with a much higher-resolution SPH model, we are developing our Parallel Tree-SPH code. After evolving four initial models with different mass and force resolution, we compare the angular momentum content of SPH particles. We find that both mass and force resolutions clearly affect the evolution of radiative cosmological SPH models. In most previous radiative cosmological SPH models, a mass ratio between SPH and dark matter particles is .However, we find that this mass ratio is a crucial parameter when we consider the angular momentum content of SPH particles and it is better to make the mass ratio ∼ 1.0 in such models. This revised version was published online in August 2006 with corrections to the Cover Date.     

Main features of dynamical escape from three-dimensional triple systems

The dynamical evolution of triple systems with equal and unequal-mass components and different initial velocities is studied. It is shown that, in general, the statistical results for the planar and three-dimensional triple systems do not differ significantly. Most (about 85%) of the systems disrupt; the escape of one component occurs after a triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (about 15%) of stable or long-lived systems is formed if the angular momentum is non-zero. Averages, distributions and coefficients of correlations of evolutionary characteristics are presented: the life-time, angular momentum, numbers of wide and close triple approaches of bodies, relative energy of escapers, minimum perimeter during the last triple approach resulting in escape, elements of orbits of the final binary and escaper.     

Central energy equipartition in multimass models of globular clusters

In the construction of multimass King–Michie models of globular clusters, an approximated central energy equipartition between stars of different mass is usually imposed by scaling the velocity parameter of each mass class inversely with the stellar mass, as if the distribution function were isothermal. In this paper, this 'isothermal approximation' has been checked and its consequences on the model parameters studied by a comparison with models including central energy equipartition correctly. It is found that, under the isothermal approximation, the 'temperatures' of a pair of components can differ to a non-negligible amount for low concentration distributions. It is also found that, in general, this approximation leads to a significantly reduced mass segregation in comparison with that given under the exact energy equipartition at the centre. As a representative example, an isotropic three-component model fitting a given projected surface brightness and line-of-sight velocity dispersion profiles is discussed. In this example, the isothermal approximation gives a cluster envelope much more concentrated (central dimensionless potential   W = 3.3  ) than under the true equipartition  ( W = 5.9 × 10⁻²)  , as well as a higher mass function logarithmic slope. As a consequence, the inferred total mass (and then the global mass-to-light ratio) is a factor of 1.4 times lower than the correct value and the amount of mass in heavy dark remnants is 3.3 times smaller. Under energy equipartition, the fate of stars having a mass below a certain limit is to escape from the system. This limit is derived as a function of the mass and W of the component of giant and turn-off stars.     

Dark matter around binary galaxies: formation of collimated flows

We study here the dynamics of an extended shell of relatively low-mass (almost zero-mass) particles around massive binary systems by computer simulations in the framework of approximately restricted three-body problem with a set of several initial conditions concerning the massesM ₁ andM ₂ of the binary components surrounded byN test particles in uniform random distribution on a spherical envelope of radiusR expanding with a velocityV. We apply this model to binary galaxy systems with a halo of baryonic dark matter, e.g., massive black holes, globular clusters, and giant molecular clouds. It is shown that, initially, the shell expands homologously with decreasing velocity and then, falls back into the system forming zones of compressed matter. At some moment there could be a collapse or these particles onto the heavier component of the binary. Further in time, a number of particles escape from the system. We consider a number of different models with different initial parameters. For models with smallerR andV, about one-half of the particles escape from the system; while for larger values the shell disrupts as a whole. The escaping particles form a collimated flow in the plane of the orbit of the binary. The position of the flow and the directions of motions depend on the position of the heavier component of the binary at the moment of the closest approach of the particles and on the ratioM ₁/M ₂.     

Evolution of close binaries and origin of Algol-type systems

The evolution of close binary systems was followed for ten systems with the initial mass of the primary in the range 1–4M and with different initial mass ratios and initial separations. A brief discussion of the evolution of the contact component is presented for two separate cases: when the primary reaches its Roche lobe during central hydrogen burning (case A) and after the exhaustion of hydrogen in the center (case B).The models obtained are compared with observed semi-detached systems separately for massive (with total mass greater than 5M ) and low mass (with total mass below 4M ) binaries. It is shown that the contact components of the observed massive binaries are probably burning hydrogen in the core. On the contrary, the majority of contact components of the observed low-mass binaries are burning hydrogen in the shell. The observed distribution of such binaries as a function of different luminosity excesses of contact components seems to indicate that their origin is connected with case A rather than with case B.     

Binaries in the universe. possible dynamical mechanisms of formation,evolution and disruption of different kinds of constituents of the universe

We study the dynamics of extended shells of relatively low-mass particles around and inside the orbit of two heavy centres of gravity (a binary) by computer simulations. The binary components are surrounded byN = 16 000 small mass particles in uniform random distribution on few spherical envelopes with different radii expanding with respective velocities. Some shells are inside the orbit of binary.We apply this model to binary galaxy systems with baryonic dark matter, e.g., massive black holes. In principle, we can apply this model to different kinds of objects (from binary star systems until superclusters of galaxies).It is shown that the shell expands homologously with a decreasing velocity and then, falls back into the binary system forming zones of compressed matter. At some moment of time there could be a collapse of these particles on to the heavier component of the binary. Further in time, some part of particles which were outside the binary orbit escape from the system. Other particles which were initially inside of the orbit are captured by binary components.We consider a number of different models with different initial parameters. For models with smaller radii of shells, about one-half of the particles escape from systems; whereas for larger values the shell disrupts as a whole. Escaping particles form collimated flows in planes of orbits of binaries. Positions of flows and directions of motion depend on positions of heavier components of binaries at the moment of a closest approach of particles and on ratios of masses of binary components.We show that during evolution of our models different kinds of structures of systems often are very similar to the observed structures of galaxies: spiral and elliptical galaxies, interacting galaxies, different kinds of flows and jets. Totally systems are expanding - after 40 periods of rotation of the binary the system expands by 300 times.     

A quest for initial parameters of the semi-detached eclipsing binary μ1Sco

By assigning to the semi-detached system ¹Sco the age of the Sco OB2 association (to which the binary belongs), it is possible to search for its initial characteristics. A model in agreement with the observational data is achieved by assuming a mass and momentum loss from the system during the phase of mass transfer between the components.     

One example of mass exchange in case AB in system 5m ⊙+4m ⊙

Evolution of a binary system with masses of 5m and 4m , respectively, and with orbital period of 1.41 days is studied by means of non-stationary model calculations under assumptions of conservation of total mass and total orbital angular momentum of the system. As a result of mass exchange between the components we obtain a binary with masses of 8.46 and 0.54m . Physical parameters of the final product indicate possible connection with shell stars.It is also pointed out that the new secondary component can become rotationally unstable soon after the end of mass exchange.     

Determination of stray light and sunspot intensities based on the observation during the solar eclipse of 30 June, 1973

A program has been developed to evaluated the gravitational binding energy of a clumpy cluster composed ofN particles with a given mass dispersion, a given abundance of binaries and a given massive binary system at the centre. In application to clusters of galaxies nucleated by massivecD binaries, it is found that the gravitational binding energy is typically greater than the equivalent smooth distribution by a factor in the range 2–12. This suggests that the missing mass problem in clusters of galaxies can be reduced by an order of magnitude if the correct binding energy is used in the virial theorem.     

Orbit and physical characteristics of the components of the massive Algol V622 Per,a member of the open star cluster χ Per

Analysis of the radial velocities based on spectra of high (near the H _α line) and moderate (4420–4960 Å) resolutions supplemented by the published radial velocities has revealed the binarity of a bright member of the young open star cluster χ Per, the star V622 Per. The derived orbital elements of the binary show that the lines of both components are seen in its spectrum, the orbital period is 5.2 days, and the binary is in the phase of active mass exchange. The photometric variability of the star is caused by the ellipsoidal shape of its components. Analysis of the spectroscopic and photometric variabilities has allowed the absolute parameters of the binary’s orbit and its components to be found. V622 Per is shown to be a classical Algol with moderate mass exchange in the binary. Mass transfer occurs from the less massive (\({M_1} = 9.1 \pm 2.7{M_ \odot }\)) but brighter (\(\log {L_1} = 4.52 \pm 0.10{L_ \odot }\)) component onto the more massive (\({M_2} = 13.0 \pm 3.5{M_ \odot }\)) and less bright (\(\log {L_2} = 3.96 \pm 0.10{L_ \odot }\)) component. Analysis of the spectra has confirmed an appreciable overabundance of CNO-cycle products in the atmosphere of the primary component. Comparison of the positions of the binary’s components on the T _eff–log g diagram with the age of the cluster χ Per points to a possible delay in the evolution of the primary component due to mass loss by no more than 1–2Myr.     

Dynamical evolution of triple systems

This article reviews numerical experiments on the three-body problem carried out at the Leningrad University Astronomical Observatory during the past 20 years. Systematic studies of triple systems with negative total energy have yielded the following main results. Most (95%) of the systems decay; the decay always occurs after a close triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (5%) of quasi-stable systems is formed if the angular momentum is non-zero. The qualitative evolution in three-dimensional cases is the same as for planar systems. Small changes in initial conditions sometimes lead to substantial differences in the final outcome. The decay of triple systems is a stochastic process similar to radioactive decay. The estimated mean lifetime is 100 crossing times for equal-mass components and decreases for increasing mass dispersion.A classification of the close triple approaches which lead to immediate escape is given for equal-mass systems as well as for selected sets of unequal components. Detailed studies of close triple approaches by computer simulations reveal that the early evolutions is determined by the initial ratio of the interaction forces. The review concludes by discussing applications of the results to observational problems of stellar and extragalactic systems.     

Stellar Wind as a Stimulator of Accretion Activity in Young Binary Systems

A young binary system is considered, having a mass ratio of components M ₂/M ₁ 1, in which the low-velocity part of the stellar wind of the low-mass component (the so-called disk wind) can be partially captured by the gravitation of the primary component. It is shown that a large-scale redistribution of matter and angular momentum between the inner and outer parts of the gas-dust disk surrounding the binary system occurs as a result, with a consequent increase in the rate of accretion onto the primary component. In cases in which the orbital eccentricity of the secondary component is nonzero, modulation of the rate of accretion onto the primary component should be observed with a period equal to the orbital period, while in the case of a highly elongated orbit the mass accretion acquires a pulsed character. Since dust may be present in the disk wind from the secondary component, the capture of stellar wind will result in an increase in the effective geometrical thickness of the gas-dust disk. For this reason, the infrared (IR) emission excesses of such stars (especially in the near-IR range) and their intrinsic polarization can be considerably greater than in the case of a single star surrounded by a circumstellar disk of the same mass, and a periodic component may also be present in their behavior with time. Moreover, because of disruption of the axial symmetry in the dust distribution in the vicinity of the young binary system, the orbital period may also be present in its brightness variations. The role of these effects in the physics of young stars is discussed.     

Evolutionary computations of the early-type contact binary SV Centauri

Evolutionary models of the early-type contact binary SV Centauri are recalculated with contact condition taken into account. Two types of the contact condition are employed in the contact phase. With the initial masses of 13.4 and 7.0M for the component stars, the observed features such as the rate of mass transfer, the degree of contact, and the positions of both components in the H-R diagram can be reproduced. In agreement with the conclusion given in the previous paper (Nakamuraet al., 1978), this indicates that the binary system SV Cen is actually in the rapid phase of mass transfer preceding the reversal of the mass ratio.In contrast to the steadily increasing character of the rate of mass transfer shown in the previous paper, however, the rate of mass transfer suddenly turns to decrease as soon as the system evolves into the contact phase. This decreasing character continues until the rate drops to a minimum. In such contact phase the radius of the primary component remains almost unchanged, the secondary component increases its radius slowly, and the degree of contact increases in a definite way. Except a slight difference in the degree of contact evaluated, the use of different expressions for the contact condition does not produce practically any appreciable difference in the results.     

Dynamics of rotating triple systems

We investigate the dynamical evolution of 100 000 rotating triple systems with equal-mass components. The system rotation is specified by the parameter ω=?c²E, where c and E are the angular momentum and total energy of the triple system, respectively. We consider ω=0.1,1, 2, 4, 6 and study 20 000 triple systems with randomly specified coordinates and velocities of the bodies for each ω. We consider two methods for specifying initial conditions: with and without a hierarchical structure at the beginning of the evolution. The evolution of each system is traced until the escape of one of the bodies or until the critical time equal to 1000 mean system crossing times. For each set of initial conditions, we computed parameters of the final motions: orbital parameters for the final binary and the escaping body. We analyze variations in the statistical characteristics of the distributions of these parameters with ω. The mean disruption time of triple systems and the fraction of the systems that have not been disrupted in 1000 mean crossing times increase with ω. The final binaries become, on average, wider at larger angular momenta. The distribution of their eccentricities does not depend on ω and generally agrees with the theoretical law f(e)=2e. The velocities of the escaping bodies, on average, decrease with increasing angular momentum of the triple system. The fraction of the angles between the escaping-body velocity vector and the triple-system angular momentum close to 90° increases with ω. Escapes in the directions opposite to rotation and prograde motions dominate at small and large angular momenta, respectively. For slowly rotating systems, the angular momentum during their disruption is, on average, evenly divided between the escaping body and the final binary, whereas in rapidly rotating systems, about 80% of the angular momentum is carried away by the escaping component. We compare our numerical simulations with the statistical theory of triple-system disruption.     

Initial conditions and dynamics of triple systems

The dynamical evolution of triple systems with equal-mass components and zero initial velocities is studied. We consider two regions of initial conditions: a regionD of all possible configurations of triples and a circleR. The configurations are distributed uniformly within these regions. The calculations have been carried out until a time when escape or conditional escape (i.e. distant ejection) of one component takes place. The accuracy has been checked by doing time-reversed integration. Types of predictable and non-predictable systems are revealed. Averages for a number of evolution parameters are presented: the life-time, minimum perimeter during the last triple approach resulting in escape, semi-major axis and eccentricity of the final binary, and the smallest separation between the components during the evolution. It is shown that the statistical results for the regionsD andR do not differ significantly for the most part. Our results, which have been obtaned by a three-body regularization method, are in good agreement with previous work based on the RK4 integrator and Sundman's time smoothing.     

A two-parameter scheme for the evolution of symmetrical galaxies

In the present paper, a general evolutionary scheme for axisymmetrical rotationally supported equilibrium models for galaxies is considered. Its main phases are: an expansion phase of the initial protogalaxy, assumed to consist into an homogeneous gas sphere structured into clouds, from recombination to maximum expansion, during which it is surmized that angular momentum is acquired by tidal interactions by the expanding configuration; then a violent relaxation collapse phase, following maximum expansion and ending into a virialized deformed polytropic configuration; the reaching of virialization is considered as an adequate initial state for the new phase of virialized contraction of the gaseous component, due to the collisions of the constituent gas clouds, while the stellar component, due to the stars already formed according to a generalized Schmidt-type law during the early expansion and violent relaxation phases, is assumed to have reached a stabilized situation.The initial mean density and radius for both galaxy and component clouds expressed as functions of the density fluctuation spectrum at recombination, act as physical parameters determining the characteristics of the system at maximum expansion, together with the total amount of angular momentum acquired during the expansion phase. The main physical parameters at virialization are then completely specified when the initial distribution of the clouds inside the galaxy is assigned and the constants appearing in it are derived by normalization with the observed data.We find for systems of given mass that the larger the angular momentum per unit mass is: (1) the larger are the equatorial semiaxis at maximum expansion and at virialization and the lower the mean density; (2) the larger is the time elapsed up the maximum expansion and to virialization; while for systems of different mass, we obtain that to the larger mass correspond the larger time elapsed up to maximum expansion and to virialization, and the lower mean density.For the contraction phase following virialization, two limiting cases are considered: (A) either the star component already present at virialization is entirely neglected; (B) or it is thought to contract as the gas component. In such cases, it is found for systems of equal mass that lower angular momenta lead to final configurations characterized by no or small flat gaseous components (which may correspond to lenticulars and early type spirals) while the contrary is true for large angular momenta (corresponding to late type spirals and irregulars). As mass and angular momentum per unit mass decrease, according to an assumed lawj M, the allowed configurations on the late type side of the morphological sequence tend towards earlier and earlier types, until for masses low enough (10¹⁰ m ), only halo type configurations seem to exist. According to this view, the observed lack of spirals with masses below 10¹⁰ m and the wide mass range exibited by the stellar halo type galaxies might be interpreted. In general, it appears that in the limit of the approximations made, a morphological sequence of galaxies can be described by two parameters, mass and angular momentum.     

Evolution of globular cluster systems in three galaxies of the Fornax cluster

We studied and compared the radial profiles of globular clusters and of the stellar bulge component in three galaxies of the Fornax cluster observed with the WFPC2 of the Hubble Space Telescope ( HST ). The stars are more concentrated toward the galactic centres than globular clusters, in agreement with what has already been observed in many other galaxies: if the observed difference is the result of evolution of the globular cluster systems starting from initial profiles similar to those of the halo–bulge stellar components, a relevant fraction of their initial mass (74, 47 and 52 per cent for NGC 1379, 1399 and 1404, respectively) should have disappeared in the inner regions. This mass has probably contributed to the nuclear field population, local dynamics and high-energy phenomena in the primeval life of the galaxy. An indication in favour of the evolutionary interpretation of the difference between the globular cluster system and stellar bulge radial profiles is given by the positive correlation we found between the value of the mass lost from the globular cluster system and the central galactic black hole mass in the set of seven galaxies for which these data are available.     

On the dynamical evolution of the brown dwarf populationin open clusters

It is by now well established that open clusters contain a considerable fraction of brown dwarfs (BDs). This paper investigates the dynamical evolution of this substellar population by using simulations with Aarseth's (1994) NBODY5 code. A noticeable preferential escape of BDs is found, which may influence the determination of the IMF of substellar objects in dynamically evolved open clusters. This small dynamical-in-origin depletion may not explain, however, the scarcity of BDs observed in some evolved clusters, as the Hyades. On the other hand, BD cooling processes are able to reduce our ability to detect BDs in old clusters in a very significant way. Our results confirm that the probability of observing BDs in open clusters is almost the same over the whole cluster area because they are distributed quite uniformly even at late stages of the evolution of the cluster. This is expected to be a general feature as observed for low-mass stars in well studied open clusters (Pleiades, Praesepe). Our present calculations show that clusters as old as the Pleiades may have lost about 10% of their initial BD population but the number ratio of BDs to normal (not substellar) stars must remain almost unchanged. However, the long-term behavior of the relative percentage of BDs depends strongly on the initial mass function (IMF) assumed in the calculations. Clusters with a Salpeterian IMF evolve to reach relative percentages of BDs as low as 40% for a starting value around 70%. Our results suggest that BDs in clusters escape preferentially by evaporation. This revised version was published online in July 2006 with corrections to the Cover Date.     

A multi-term trial function stability analysis of isotropic relativistic star clusters

A multi-term trial function technique is developed for studying the dynamic stability of isotropic relativistic star clusters by using the variational principle originated by Ipser and Thorne (1968). The technique is applied ton=4 polytropic clusters, and low-temperature isothermal clusters. These two types of cluster have pronounced core-halo structures and they have both proved difficult to analyse with single-term trial function methods. Then=4 polytropic clusters are proved to be dynamically unstable if their central redshifts are greater thanz _c=0.412. This is quite close to the point on their sequence withz _c=0.41, where their fractional binding energy peaks. Strong evidence is obtained that all isothermal clusters with no dispersion in the stellar rest mass become dynamically unstable near the region where their fractional binding energy peaks, and that none of these clusters is dynamically stable if their central redshift exceedsz _c0.53.