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1.
The kinematics of stars in open-cluster models are investigated. The central regions of these model clusters are fairly “cool, ” leading to gravitational instability in the cluster cores. A temporary virilization is observed in the model clusters, during which an appreciable fraction of the fluctuation energy of the cluster is temporarily transformed into the kinetic energy of the peculiar motions of stars. The duration of this stage can reach ∼108 yr. The origins of this temporary virialization of the model clusters are discussed. The instability of the intrinsic fluctuations of the phase density in the centers of six clusters and model clusters is investigated. Several new regions of unstable phase-density fluctuations are found, in addition to those already known. The observed and model clusters can move toward a stable equilibrium state when the density of the cluster core both decreases and increases. The structure of regions of instability of the phase-density fluctuations in the centers of the six clusters is studied. Resonance curves for the amplitudes of steady-state phase-density fluctuations in the center of NGC 6705 are constructed. Analysis of the structure of the regions of instability indicates an appreciable rate of fluctuation-energy loss due to relaxation effects. The instability increments and widths of regions of instability fall off with increasing distance of the cluster from the Galactic center. An important role in the formation of regions of instability may be played by resonances between the frequency of the orbital motion of the cluster in the Galaxy and the frequencies of intrinsic phase-density fluctuations in the centers of the clusters considered.  相似文献   

2.
Instability of proper fluctuations of the phase density at the centers of six open clusters is demonstrated. The boundaries of the region of instability in terms of the mean mass densities of the cluster cores are determined. Estimates for a number of dynamical parameters (the potential, velocity dispersion of the stellar motions, mass density, phase-density fluctuation period, time for the development of instability of the fluctuations, etc.) are obtained for the central parts of these clusters, as well as for numerical dynamical models for open clusters. Equation that can be used to estimate the dynamical mass of a cluster taking into account the influence of the external field of the Galaxy and the non-stationarity of the cluster is derived. Allowance for these effects makes it possible to decrease the dynamical masses of clusters compared to the virial masses assuming isolated systems. Astrophysical applications of the results are discussed.  相似文献   

3.
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.  相似文献   

4.
We have obtained the stellar velocity dispersion in three mutually perpendicular directions in the halos and cores of clusters as a function of time for several non-stationary open-cluster models. During the dynamical evolution of the open-cluster models, the velocity dispersions undergo oscillations that do not decay during 5–10 violent-relaxation timescales, τ vr . We estimated the time for synchronization of the rotation of the open-cluster models and their motion around the center of the Galaxy, t s , which, depending on the model parameters, is t s ? (5–27)τ vr . Synchronization mechanisms for the models are discussed. The disruption of the systems in the force field of the Galaxy is strongly affected by tidal friction. We have also estimated the time for the formation of a spherical stellar-velocity distribution in the cluster models, t σ ? (6 ? 25)τ vr . The impact of instability in the stellar motions in a cluster on the formation of a spherical velocity distribution in the open-cluster models is discussed. We have noted a tendency for a weakening of the dependence of the coarse phase density of the cluster on small initial perturbations of the stellar phase coordinates in the model cluster cores for times about five times longer than the violent-relaxation time.  相似文献   

5.
Numerical simulations of the dynamical evolution of a galaxy cluster in the framework of the N-body problem taking into account dark matter are presented. These simulations are aimed at studying the role of intergalactic gas in the cluster (the ICM) in the formation of a central, supermassive cD galaxy. The numerical models indicate that deceleration of the galaxies by intergalactic gas supports the observed high temperature of this gas, and accelerates the formation of a supermassive cD galaxy in the cluster core. The accretion of interstellar gas by the cluster core can support a high accretion rate by the central, supermassive black hole associated with the nucleus of the cD galaxy. As a result, this nucleus harbors a bright quasar. The mass of the black hole can grow with time to values 1010 M ⊙, as are observed for the brightest quasars.  相似文献   

6.
In dynamical models for open clusters, virial equilibrium is not achieved over the violent relaxation time scale τvr. The stars form an equilibrium distribution in (?, ?ζ, l) space, where ? and l are the energy and angular momentum per unit stellar mass in the combined field of the Galaxy and cluster and ?ζ is the energy of motion perpendicular to the Galactic plane per unit mass of cluster stars in the gravitational field of the Galaxy. This distribution of stars changes little when t>τvr. The stellar phase-space distribution corresponding to this type of equilibrium and the regular cluster potential vary periodically (or quasi-periodically) with time. This phase-space equilibrium is probably possible due to an approximate balance in the stellar transitions between phase-space cells over times equal to the oscillation period for the regular cluster field.  相似文献   

7.
Estimates of a number of dynamical parameters of 103 open star clusters are presented: the density contrast in the cluster core, stellar velocity dispersion, taking into account the influence of the external field of the Galaxy and non-stationarity of the cluster, oscillation periods of the cluster and the cluster core, etc. Analytical solutions to the gross dynamical equations are obtained for simple cluster models. These solutions are used to estimate a number of quantities characterizing the degree of non-stationarity of the cluster, such as the amplitude of oscillations of the cluster virial coefficient and of the radius of the cluster core, etc. Astrophysical applications of these results are discussed.  相似文献   

8.
The evolution of Population I stars with initial masses 60 M ⊙ ≤ M ZAMS ≤ 120 M ⊙ is computed up to the Wolf-Rayet stage, when the central helium abundance decreases to Y c ≈ 0.05. Several models from evolutionary sequences in the core helium-burning stage were used as initial conditions when solving the equations of radiative hydrodynamics for self-exciting stellar radial pulsations. The low-density envelope surrounding the compact core during the core helium burning is unstable against radial oscillations in a wide range of effective temperatures extending to T eff ～ 105 K. The e-folding time of the amplitude growth is comparable to the dynamical time scale of the star, and, when the instability ceases growing, the radial displacement of the outer layers is comparable to the stellar radius. Evolutionary changes of the stellar radius and luminosity are accompanied by a decrease in the amplitude of radial pulsations, but, at the effective temperature T eff ≈ 105 K, the stellar oscillations are still nonlinear, with a maximum expansion velocity of the outer layers of about one-third the local escape velocity. The period of the radial oscillations decreases from 9 hr to 4 min as stellar mass decreases from M = 28 M ⊙ to M = 6 M ⊙ in the course of evolution. The nonlinear oscillations lead to a substantial increase of the radii of the Lagrangian mass zones compared to their equilibrium radii throughout the instability region. The instability of Wolf-Rayet stars against radial oscillations is due to the action of the κ mechanism in the iron-group ionization zone, which has a temperature of T ～ 2 × 105 K.  相似文献   

9.
It is known from observations that the center of mass of the Moon does not coincide with the geometric center of its figure, and the line connecting these two centers is not aligned with the direction toward the center of the Earth, instead deviating toward the Southeast. This stationary deviation of the axis of the inertia ellipsoid of the Moon to the South of the direction toward the Earth is analyzed. A system of five linear differential equations describing the physical libration of the Moon in latitude is considered, and these equations are derived using a new vector method taking into account perturbations from the Earth and partly from the Sun. The characteristic equation of this system is obtained, and all five oscillation frequencies are found. Special attention is paid to the fifth (zero) frequency, for which the solution of the latitude libration equations are stationary and represents a previously unknown additional motion of the rotational axis of theMoon in a cone with a small opening angle. In contrast to the astronomical precession of the Earth, the rotation of the angular-velocity vector is in the positive direction (counter-clockwise), with the period T 3 = 27.32 days. On this basis, this phenomenon has been named “quasi-precession.” This quasi-precession leads to a stationary inclination of the major axis of the inertia ellipsoid of theMoon to the South (for an observer on Earth), making it possible to explain one component of the observed deviation of the center of mass of the Moon from the direction toward the Earth. The opening angle of the quasiprecession cone is approximately 0.834″.  相似文献   

10.
Enstatites (Mg2Si2O6) are important rock forming silicates of the pyroxene group whose structures are characterised by double MgO6 octahedral bands and single silicate chains. Orthoenstatite transforms to protoenstatite above 1273 K with a doubling of the a axis and a rearrangement of the silicate chains with respect to the Mg2+ ions. Lattice dynamical calculations based on a rigid-ion model in the quasi-harmonic approximation provide theoretical estimates of elastic constants, long wavelength phonon modes, phonon dispersion relations, total and partial density of states and inelastic neutron scattering cross-sections of protoenstatite. The computed elastic constants are in good agreement with experimental data. The computed density of states of a chain silicate such as protoenstatite is distinct from that of olivines (forsterite, Mg2SiO4 and fayalite, Fe2-SiO4) with isolated silicate tetrahedra. The band gaps in the density of states in forsterite are largely due to the separation in the frequency ranges of the external and internal vibrations of the isolated silicate group, whereas in protoenstatite these gaps are filled by the vibrations of the bridging oxygens of the silicate chain. The computed density of states is used to calculate the specific heat, the mean square atomic displacements and temperature factors. Validity of these calculations are supported by Raman scattering measurements. Polarised and unpolarised Raman spectra are obtained from small single crystals of protoenstatite (Li,Sc)0.6Mg1.4Si2O6 stable at room temperature using the 488 nm or 514.5 nm lines of an Ar+ ion laser and a micro-Raman spectrometer with backscattering geometry. The Raman spectra were analysed and interpreted based on the lattice dynamical model. The experimental Raman frequencies and mode assignments (based on polarised single crystal spectra) are in good agreement with those obtained from lattice dynamical calculations.  相似文献   

11.
A model of a multivariate covariance function with an ellipsoidal directional correlation scale has been developed. The axes of the ellipsoidal scale are related to the eigenvalues and eigenvectors of a matrix B which characterizes the ellipsoid of the range of influence. The matrix B is found to be related to a matrix T which can be estimated directly from sparse sampling data and can be used to determine estimates of the matrix B. The method has been applied to both two-dimensional and three-dimensional cases. The numerical results show that the satisfactory accuracy is obtained with sparse sampling data from an anisotropic random function.  相似文献   

12.
We studied the upper-bound ultimate bearing capacity of smooth strip shallow footings with symmetrical and asymmetrical horizontal confinements on purely frictional sand within the framework of upper-bound limit analysis. The subsoil follows the associated flow rule, and no surcharge on the soil surface is assumed. The contact between the soil and the horizontal confinement walls is assumed to be perfectly rough. The upper-bound solutions for the objective functions are obtained using nonlinear sequential quadratic programming. The results for the different internal friction angles φ are provided in terms of the variation of two parameters, namely, the bearing capacity factor Nγ and the correction factor of bearing capacity Kγ, with respect to the change in the clear spacing between the edge of smooth footing and the rigid vertical walls. The values of Nγ and Kγ increase with φ and decrease with the clear spacing between the edge of the smooth footing and the rigid vertical walls. Nγ and Kγ are more sensitive to this confining effect as φ increases. The numerical results, a comparative analysis with the results from previous studies, and design charts are also included.  相似文献   

13.
We have used a newly developed ab initio constant-pressure molecular dynamics with variable cell shape technique to investigate the zero temperature behaviour of high pressure clinoenstatite (MgSiO3-C2/c) from 0 up to 30 GPa. The optimum structure at 8 GPa, as well as structural trends under pressure, compare very well with experimental data. At this pressure, we find noticeable “fluctuations” in the chain configuration which suggests the structure is on the verge of a mechanical instability. Two distinct compressive behaviours then appear: one below and another above 8 GPa. This phenomenon may be related to the observed transition to a lower symmetry P21/c phase which involves a reconfiguration of the silicate chains, and suggests that the C2/c structure at low pressures found here, may be an artifact of the dynamical algorithm which preserves space group in the absence of symmetry breaking fluctuations. Comparison with calculations in other magnesium silicate phases, indicates that the size and shape of the silicate units (isolated and/or linked tetrahedra and octahedra) are generally well described by the local density approximation; however, the weaker linkages provided by the O-Mg-O bonds, are not as well described. This trend suggests that, as in the recently studied case of H2O-ice, the structural properties of more inhomogeneous systems, like enstatite, may be improved by using gradientcorrected density functionals.  相似文献   

14.
We present the results of our study of the physical and dynamical parameters of the multiple system HD 222326. A new method for determining the individual radial velocities of components in wide binary and multiple systems in the case of small radial-velocity differences (δV r ≤ the FWHMfor the line profiles) is suggested and tested for both model systems and the binary HD 10009. This testing yielded the component radial velocities V r 1,2 for HD 10009, enabling us to derive the center-of mass velocity, V γ, for the first time. We determined the radial velocities of the components of HD 222326 from high-resolution spectra, and refined the orbital parameters of the subsystems using speckle-interferometric observations. A combined spectroscopic and speckle interferometric analysis enabled us to find the positions of the components in the spectral type—luminosity diagram and to estimate their masses. It is likely that the components are all in various evolutionary stages after leaving the main sequence. We analyzed the dynamical evolution of the system using numerical modeling in the gravitational three-body problem and the known stability criteria for triple systems. The system is probably stable on time scales of at least 106 years. The presence of a fourth component in the system is also suggested.  相似文献   

15.
The results of several sets of measurements of the frequency of radio signals during coronal-sounding experiments carried out from 1991 to 2000 using the ULYSSES and GALILEO spacecraft are presented and analyzed. The S-band signals (carrier frequency f = 2295 MHz) were received at the three 70-m widely spaced ground stations of the NASA Deep Space Network. As a rule, the frequency-fluctuation spectra at frequencies above 1 mHz are power-laws. At small heliocentric distances, R < 10R⊙ (R⊙ is the solar radius), the spectral index is close to zero; this corresponds to a spectral index for the one-dimensional turbulence spectrum p1 = 1. The index of the frequency-fluctuation spectra in the region of the supersonic solar wind at distances R > 30 R⊙ is between 0.5 and 0.7 (p1 = 1.5–1.7). The results demonstrate a substantial difference between the turbulence regimes in these regions: in the region of the established solar wind, the power-law spectra are determined by nonlinear cascade processes that pump energy from the outer turbulence scale to the small-scale part of the spectrum, whereas such cascade processes are absent in the solar wind acceleration region. Near the solar minimum, the change in the turbulence regime of the fast, high-latitude solar wind occurs at greater distances than for the slow, low-latitude solar wind. Spectra with a sharp cutoff at high frequencies have been detected for the first time. Such spectra are observed only at R < 10 R⊙ and at sufficiently low levels of the electron density fluctuations. The measured cutoff frequencies are between 10 and 30 mHz; the cutoff frequency tends to increase with heliocentric distance. The variance of the plasma-density fluctuations has been estimated for the slow, low-latitude solar wind. These estimates suggest that the relative fluctuation level at distances 7 R⊙ < R < 30 R⊙ does not depend on heliocentric distance. The cross correlation of the frequency fluctuations recorded at widely spaced ground stations increases with the index of the frequency-fluctuation spectrum. At distances R ≈ 10 R⊙, the rate of temporal changes in irregularities on the scale of several thousand kilometers is less than or comparable to the solar wind velocity.  相似文献   

16.
Accretion disks around young binary stars are subject to strong forces exerted by the system components. Gas–dynamical interactions excite strong non-linear perturbations in the disk, which can give rise to turbulence. This study considers a mechanism for the excitation of turbulence based on the instability of non-linear waves in a rotating flow. It is shown that the spectrum of non-linear perturbations excited in the inner part of the disk leads to turbularization of the flow. Estimates of the Shakura–Syunyaev index, α ～ 0.01?0.05, are obtained for use in numerical models of accretion disks.  相似文献   

17.
A numerical study incorporating three-dimensional Eulerian large deformation finite element analyses is performed to investigate the pullout process of horizontal square plate anchors in both hypothetical weightless soil and soil with self-weight. The validity of the numerical model is established through verification against published experimental and numerical results. The failure mechanisms during the pullout process under different conditions are then investigated. Three types of failure mechanism are observed; of which only two have been reported in the literature. The third mechanism identified in this study, which is a partially localized flow mechanism, is operative when the soil overburden ratio is not high enough to mobilize the full flow mechanism. The influence of soil self-weight is directly investigated by incorporating the density of the soil in the finite element model and maintaining the gravitational acceleration field throughout the analysis. The critical overburden ratio corresponding to the full transition to a localized plastic flow mechanism is identified in this study. The effect of the soil rigidity index (E/su) on the anchor uplift capability has not been systematically investigated in earlier studies. Contrary to the general failure mechanism and the full flow mechanism described in the literature, the capacity factor corresponding to this new mechanism increases with increasing E/su. The capacity factors for square plate anchors corresponding to different anchor embedment ratios, overburden ratios and E/su are provided in the form of design charts.  相似文献   

18.
A series of dynamical models of the Galaxy is constructed assuming that the entire disk is near the gravitational-stability limit. This imposes constraints on the dynamical and kinematic parameters of the main subsystems (the disk, bulge, and halo). The disk surface density in the solar neighborhood should not exceed 58 M⊙/pc2. Further, we find that the observed local decrease in the rotational velocity at 6 kpc ? r ? 10 kpc is not associated with details of the radial distribution of matter in the Galaxy and instead results from dynamical processes or some other factors responsible for noncircular motions. It follows from the presence of a long-lived bar and the observed distribution of the stellar-velocity dispersion that the central maximum in the rotation curve at radius r ? 300 pc cannot be associated with a very concentrated bulge core. The best agreement between the observational data and the parameters of the dynamical models is achieved for a radial disk scale length of L ? 3 kpc. The relative contribution of the disk to the circular rotational velocity at r = 2.2L is 73%.  相似文献   

19.
The stability of multiple systems with known orbital elements and with subsystems occupying adjacent hierarchy levels is analyzed using six stability criteria and numerical simulations of their dynamical evolution. All the stability criteria considered are in qualitative agreement with the numerical computations. Of the 16 systems studied, 11 are confirmed to be stable and five (HD 40887, HD 136176, HD 150680, HD 217675, and HD 222326) may be unstable on time scales of ～106 yr or less. The small dynamical ages of the unstable systems may indicate that they have captured components during encounters between close binaries and field or moving cluster stars. The instability could also result from the perturbation of a stable system when it approaches a massive object (star, black hole, or molecular cloud). It is possible that some of the unstable systems are remnants of small clusters or stellar groups.  相似文献   

20.
A CCD BV R photometric study of the central region (15″ ≤ r ≤ 100″) of the globular cluster NGC 7006 based on color-magnitude diagrams is presented. We find for the main parameters of the cluster [Fe/H] = ?1.62, Y = 0.21, E B?V = 0.15 m , V HB = 18.84 m , M V HB =+0.56 m , R ⊙ = 37.1 kpc). Two previously unknown RR Lyr variables were discovered in the central region of the cluster. The morphological index of the horizontal branch for the entire region studied indicates that the red stellar population dominates, consistent with previous studies: HB mi = ?0.13. Such anomalously negative morphological indices are possessed by a whole group of Ool clusters with intermediate metallicities, which also display a characteristic distribution of stars along the horizontal branch. There is a radial dependence for the horizontal-branch morphology, with the color becoming primarily blue with approach toward the cluster center. One possible origin for this behavior could be the effect of inner dynamical processes on the spatial distribution of hot stars.  相似文献   

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