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1.
The equilibria and periodic orbits around a dumbbell-shaped body   总被引：1，自引：0，他引：1  
This paper investigates the equilibria, their stability, and the periodic orbits in the vicinity of a rotating dumbbell-shaped body. First, the geometrical model of dumbbell-shaped body is established. The gravitational potential fields are obtained by the polyhedral method for several dumbbell-shaped bodies with various length–diameter ratios. Subsequently, the equilibrium points of these dumbbell-shaped bodies are computed and their stabilities are analyzed. Periodic orbits around equilibrium points are determined by the differential correction method. Finally, in order to understand further motion characteristic of dumbbell-shaped body, the effect of the rotating angular velocity of the dumbbell-shaped bodies is investigated. This study extends the research work of the orbital dynamics from simple shaped bodies to complex shaped bodies and the results can be applied to the dynamics of orbits around some asteroids.  相似文献   

2.
The formulation of the tensor virial equations is generalized to unrelaxed configurations, where virial equilibrium does not coincide with dynamical (or hydrostatic) equilibrium. Homeoidally striated, Jacobi ellipsoids, which generalize classical Jacobi ellipsoids, are studied in detail. Further investigation is devoted to the generation of sequences of virial equilibrium configurations where the anisotropy parameters are left unchanged, including both flattened and elongated, triaxial configurations, and the determination of the related bifurcation points. An application is made to dark matter haloes hosting giant galaxies (M ≈ 1012 m⊙), with regard to assigned initial and final configuration, following and generalizing to many respects a procedure conceived by Thuan & Gott (1975). The dependence of the limiting axis ratios, below which no configuration is allowed for the sequence under consideration, on the change in mass, total energy, and angular momentum, during the evolution, is illustrated in some representative situations. The dependence of the axis ratios, ε31 and ε21, on a parameter, related to the initial conditions of the density perturbation, is analysed in connection with a few special cases. The same is done for the rotation parameters. Within the range of the rotation parameter, λ, deduced from high‐resolution numerical simulations, the shape of dark matter haloes is mainly decided by the amount of anisotropy in residual velocity distribution. On the other hand, the contribution of rotation has only a minor effect on the meridional plane, and no effect on the equatorial plane, as bifurcation points occur for larger values of λ. To this respect, dark matter haloes are found to resemble giant elliptical galaxies. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
We present V -band surface photometry and major-axis kinematics of stars and ionized gas of three early-type spiral galaxies, namely NGC 772, 3898 and 7782. For each galaxy we present a self-consistent Jeans model for the stellar kinematics, adopting the light distribution of bulge and disc derived by means of a two-dimensional parametric photometric decomposition. This allows us to investigate the presence of non-circular gas motions, and derive the mass distribution of luminous and dark matter in these objects.
NGC 772 and 7782 have apparently normal kinematics with the ionized gas tracing the gravitational equilibrium circular speed. This is not true in the innermost region (| r |≲8 arcsec) of NGC 3898, where the ionized gas is rotating more slowly than the circular velocity predicted by dynamical modelling. This phenomenon is common in the bulge-dominated galaxies for which dynamical modelling enables us to make the direct comparison between the gas velocity and the circular speed, and it poses questions about the reliability of galaxy mass distributions derived by the direct decomposition of the observed ionized-gas rotation curve into the contributions of luminous and dark matter.  相似文献   

4.
The dynamical friction experienced by a body moving in a gaseous medium is different from the friction in the case of a collisionless stellar system. Here we consider the orbital evolution of a gravitational perturber inside a gaseous sphere using three-dimensional simulations, ignoring however self-gravity. The results are analysed in terms of a 'local' formula with the associated Coulomb logarithm taken as a free parameter. For forced circular orbits, the asymptotic value of the component of the drag force in the direction of the velocity is a slowly varying function of the Mach number in the range 1.0–1.6. The dynamical friction time-scale for free decay orbits is typically only half as long as in the case of a collisionless background, which is in agreement with E. C. Ostriker's recent analytic result. The orbital decay rate is rather insensitive to the past history of the perturber. It is shown that, similarly to the case of stellar systems, orbits are not subject to any significant circularization. However, the dynamical friction time-scales are found to increase with increasing orbital eccentricity for the Plummer model, whilst no strong dependence on the initial eccentricity is found for the isothermal sphere.  相似文献   

5.
In this paper, a model is developed for the dynamics of a system of two bodies whose material points are under the influence of a central gravitational force. One of the bodies is assumed to be rigid and spherically symmetric, while the other is assumed to be deformable. To develop a tractable model for the system, the deformable body is modeled using Cohen and Muncaster's theory of a pseudo-rigid body. The resulting model of the system has several of the features, such as angular momentum conservation, exhibited by more restrictive models. We also show how the self-gravitation of the deformable body can be accommodated using appropriate constitutive equations for a force tensor. This enables our model to subsume many existing models of ellipsoidal figures of equilibrium. After the model and its conservations have been discussed, attention is restricted to steady motions of the system. Several results, which generalize recent works on rigid satellites, are established for these motions. For a specific choice of constitutive equations for the pseudo-rigid body, we determine the steady motions with the aid of a numerical continuation method. These results can also be considered as generalizations of earlier works on Roche's ellipsoids of equilibrium.  相似文献   

6.
In this paper a unified theory of systematically rotating and peculiar motions is developed for homeoidally striated Jacobi ellipsoids, where both real and imaginary rotations are considered. The effect of positive or negative residual motion excess along the equatorial plane is considered to be equivalent either to an additional real or an imaginary rotation, respectively. The principle results consist of (i) the discovery that homeoidally striated Jacobi ellipsoids always admit an adjoint configuration i.e. a classical Jacobi ellipsoid of equal mass and axes; (ii) the establishment of further constraints on the amount of residual velocity anisotropy along the principal axes for triaxial configurations; (iii) the finding that bifurcation points from axisymmetric to triaxial configurations occur as in classical Jacobi ellipsoids, contrary to earlier findings. An interpretation of recent results from numerical simulations on stability is provided in the light of the model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

7.
We study the nature of non-axisymmetric dynamical instabilities in differentially rotating stars with both linear eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We especially investigate the following three types of instability; the one-armed spiral instability, the low   T /| W |  bar instability, and the high   T /| W |  bar instability, where T is the rotational kinetic energy and W is the gravitational potential energy. The nature of the dynamical instabilities is clarified by using a canonical angular momentum as a diagnostic. We find that the one-armed spiral and the low   T /| W |  bar instabilities occur around the corotation radius, and they grow through the inflow of canonical angular momentum around the corotation radius. The result is a clear contrast to that of a classical dynamical bar instability in high   T /| W |  . We also discuss the feature of gravitational waves generated from these three types of instability.  相似文献   

8.
Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion-induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high-density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.  相似文献   

9.
We calculate the structure of a wake generated by, and the dynamical friction force on, a gravitational perturber travelling through a gaseous medium of uniform density and constant background acceleration   g ext  , in the context of Modified Newtonian Dynamics (MOND). The wake is described as a linear superposition of two terms. The dominant part displays the same structure as the wake generated in the Newtonian gravity scaled up by a factor  μ−1( g ext/ a 0)  , where a 0 is the constant MOND acceleration and μ the interpolating function. The structure of the second term depends greatly on the angle between   g ext  and the velocity of the perturber. We evaluate the dynamical drag force numerically and compare our MOND results with the Newtonian case. We mention the relevance of our calculations to orbit evolution of globular clusters and satellites in a gaseous protogalaxy. Potential differences in the X-ray emission of gravitational galactic wakes in MOND and in Newtonian gravity with a dark halo are highlighted.  相似文献   

10.
Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and its dynamical evolution. Using the hitherto largest sample of lensing clusters drawn from the literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is excellent agreement between the weak lensing, X-ray and isothermal sphere model-determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2–4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters, as well as from assuming an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.  相似文献   

11.
We carry out a detailed orbit analysis of gravitational potentials selected at different times from an evolving self-consistent model galaxy consisting of a two-component disc (stars+gas) and a live halo. The results are compared with a pure stellar model, subject to nearly identical initial conditions, which are chosen so as to make the models develop a large-scale stellar bar. The bars are also subject to hose-pipe (buckling) instability which modifies the vertical structure of the disc. The diverging morphological evolution of both models is explained in terms of gas radial inflow, the resulting change in the gravitational potential at smaller radii, and the subsequent modification of the main families of orbits, both in and out of the disc plane.   We find that dynamical instabilities become milder in the presence of the gas component, and that the stability of planar and 3D stellar orbits is strongly affected by the related changes in the potential — both are destabilized, with the gas accumulation at the centre. This is reflected in the overall lower amplitude of the bar mode and in the substantial weakening of the bar, which appears to be a gradual process. The vertical buckling of the bar is much less pronounced and the characteristic peanut shape of the galactic bulge almost disappears when there is a substantial gas inflow towards the centre. Milder instability results in a smaller bulge, the basic parameters of which are in agreement with observations. We also find that the overall evolution in the model with a gas component is accelerated because of the larger central mass concentration and the resulting decrease in the characteristic dynamical time.  相似文献   

12.
The behavior of the orbits in a galaxy model composed of an harmonic core and a strong bar potential is studied. Numerical calculations show that a large number of orbits display chaotic motion. These orbits are low angular momentun orbits. The percentage of chaotic orbits increases as the angular velocity of the system increases or the strength of the harmonic term decreases. A new dynamical parameter, the S(c) spectrum, is introduced and used to detect the island motion and the evolution of the sticky regions. Comparison to previously obtained results reveals the leading role of the new spectrum. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

13.
We investigate the dynamical response, in terms of disc size and rotation velocity, to mass loss by supernovae in the evolution of spiral galaxies. A thin baryonic disc having the Kuzmin density profile embedded in a spherical dark matter halo having a density profile proposed by Navarro, Frenk & White is considered. For the purpose of comparison, we also consider the homogeneous and   r −1  profiles for dark matter in a truncated spherical halo. Assuming for simplicity that the dark matter distribution is not affected by mass-loss from discs and the change of baryonic disc matter distribution is homologous, we evaluate the effects of dynamical response in the resulting discs. We found that the dynamical response only for an adiabatic approximation of mass-loss can simultaneously account for the rotation velocity and disc size as observed particularly in dwarf spiral galaxies, thus reproducing the Tully–Fisher relation and the size versus magnitude relation over the full range of magnitude. Furthermore, we found that the mean specific angular momentum in discs after the mass-loss becomes larger than that before the mass-loss, suggesting that the mass-loss would most likely occur from the central disc region where the specific angular momentum is low.  相似文献   

14.
The aim of the present paper will be to derive an equation of dissipation of energy for a rotating body of arbitrary viscosity distorted by tides, which arise from the gravitational field of its companion in a close pair of such bodies.By a transformation of the fundamental equation of energy dissipation in terms of velocity of tidal deformation (Section 2), the dissipation function is constructed for a tidally-distorted body (Section 3). From this equation, the rate of dissipation of tidal energy is formulated for a nearly-spherical rotating body distorted by second harmonic longitudinal tides (Section 4); the coefficients of viscosity (or the bulk modulus) are treated as arbitrary functions of spatial coordinates. Finally (Section 5), expressions for the total energy dissipation within the orbital cycle are given for axial rotation of the distorted body, provided its angular velocity is constant (for example, with the Keplerian angular velocity).Research financed in part by the Division of Scientific Research and Development of Ministry of Sciences and Culture of Greece.  相似文献   

15.
It is shown that the radial velocity dispersion of the elongated HCGs (b/a ≤ 0.2) with smaller two‐dimensional galaxy‐galaxy median projected separation R is, on average, higher than those of the groups with larger R. It shows that galaxies in a group move preferentially along its elongation. Inspection of radial velocities of member galaxies in chain‐like and in roundish HCGs shows that galaxies in HCGs most probably rotate around the gravitational center of the corresponding group. Other two possible mechanisms: flying apart of galaxies from the group in opposite directions, and infall of field galaxies upon the group are excluded. It follows that HCGs are, probably, more stable formations, than it has been assumed. In this case the known inconsistencies between the results of the N‐body simulations and the observational facts are being excluded.  相似文献   

16.
Abstract— Splash‐form tektites are generally acknowledged to have the form of bodies of revolution. However, no detailed fluid dynamical investigation of their form and stability has yet been undertaken. Here, we review the dynamics and stability of spinning, translating fluid drops with a view to making inferences concerning the dynamic history of tektites. We conclude that, unless the differential speed between the molten tektite and ambient is substantially less than the terminal velocity, molten tektites can exist as equilibrium bodies of revolution only up to sizes of 3 mm. Larger tektites are necessarily non‐equilibrium forms and so indicate the importance of cooling and solidification during flight. An examination of the shapes of rotating, translating drops indicates that rotating silicate drops in air will assume the shapes of bodies of rotation if their rotational speed is 1% or more of their translational speed. This requirement of only a very small rotational component explains why most splash‐form tektites correspond to bodies of revolution. A laboratory model that consists of rolling or tumbling molten metallic drops reproduces all of the known forms of splashform tektites, including spheres, oblate ellipsoids, dumbbells, teardrops, and tori. The laboratory also highlights important differences between rolling drops and tumbling drops in flight. For example, toroidal drops are much more stable in the former than in the latter situation.  相似文献   

17.
We present a method for recovering the distribution functions of edge-on thin axisymmetric discs directly from their observable kinematic properties. The most generally observable properties of such a stellar system are the line-of-sight velocity distributions of the stars at different projected radii along the galaxy. If the gravitational potential is known, then the general two-integral distribution function can be reconstructed using the shapes of the high-velocity tails of these line-of-sight distributions. If the wrong gravitational potential is adopted, then a distribution function can still be constructed using this technique, but the low-velocity parts of the observed velocity distributions will not be reproduced by the derived dynamical model. Thus, the gravitational potential is also tightly constrained by the observed kinematics.  相似文献   

18.
A white dwarf rotating at a maximal angular velocity can take a form of a triaxial ellipsoid due to the rotation and to the presence of mountains on its surface. Such an object emits gravitational waves at a frequency of 2, where is the angular velocity of rotation, and the source of the radiated energy is the rotational kinetic energy. It is shown that the gravitational waves from rapidly rotating white dwarfs at an average distance of 50 pc from an terrestrial observer have an amplitude on the order of 10–24, so they can be detected by the new generation of detectors. Gravitational radiation from a pulsating white dwarf with a rough surface is also examined. It is shown that quasiradial pulsations of a white dwarf are long-lived; that is, once perturbed, a white dwarf will emit gravitational waves during all lifetime.Translated from Astrofizika, Vol. 48, No. 1, pp. 69–78 (February 2005).  相似文献   

19.
In this paper we give general relativistic expressions for the angular momentum and rotational kinetic energy of slowly rotating stars. These expressions contain contributions from the presure, gravitational red shift, and Doppler shift, and the motion of inertial frames. These contributions are not negligible, e.g., there are stable neutron star models for which the angular velocity of inertial frames at the center is about 70% the angular velocity of the star. These expressions are useful in the study of pulsars if pulsars are rotating neutron stars.  相似文献   

20.
We examine the chemical and dynamical structure in the solar neighbourhood of a model Galaxy that is the endpoint of a simulation of the chemical evolution of the Milky Way in the presence of radial mixing of stars and gas. Although the simulation's star formation rate declines monotonically from its unique peak and no merger or tidal event ever takes place, the model replicates all known properties of a thick disc, as well as matching special features of the local stellar population such as a metal-poor extension of the thin disc that has high rotational velocity. We divide the disc by chemistry and relate this dissection to observationally more convenient kinematic selection criteria. We conclude that the observed chemistry of the Galactic disc does not provide convincing evidence for a violent origin of the thick disc, as has been widely claimed.  相似文献   

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