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1.
This paper deals with the representation of relativistic equations of gas dynamics with due regard to the general relativity theory effects in the form accepted and widely applied in the special relativity theory. With this purpose, a strict formal definition of a non-inertial co-moving reference frame without rotation is carried out on the basis of a tetrad formalism by use of the Fermi—Walker rules of transport of 4-frame. The equations of physical kinetics, relativistic collapse, Einstein's equations, equations of relatiivistic radiation gas dynamics for ideal and dissipative gases, Taub's equations for a shock wave, which allow for radiation and electron-positron pairs, are obtained in this reference frame. On the basis of the local Lorentz transformation and the Ricci rotation coefficients, these equations are written in the laboratory reference frame, in order to illustrate the fact that the general relativity effects can be simply taken into account in the equations having a form accepted in the special relativity theory.  相似文献   

2.
Theoretical models of star formation from the collapse of molecular cloud cores have been evolving in complexity for many years. This work describes the evolution of models from the nonrotating, nonmagnetized singular isothermal sphere to rotating, magnetized singular isothermal toroids. Four members of the same family are studied–the four combinations of nonrotation/rotation and nonmagnetization/magnetization. It is found that although rotation alone can hinder collapse to a pointmass, addition of braking from a magnetic field can transport away much of the angular momentum upward in a low-velocity outflow during the collapse phase. For all magnetized cases, accretion proceeds at a constant rate similar to that of the isothermal sphere.  相似文献   

3.
Maclaurin's P-ellipsoid, which is an equilibrium figure in the post-Newtonian approximation of general relativity, is constructed in the neighbourhood of Maclaurin's classical ellipsoid. Its shape and rotation velocity are investigated. It is shown that in the case of a P-ellipsoid with the mass and the angular momentum of a basic ellipsoid the effects of general relativity reduce the rotation velocity and decrease its volume.  相似文献   

4.
In this paper, the equilibrium configurations of rapid rotating compact stars and some gravitational effects are studied within the general relativity by use of the Harrison-Wheeler equation of state and by the self-consistent field method. Numerical calculations show that the equilibrium configuration of a rotating star is a spheroid. For large spin velocities, say, ω > 3.0 × 102 sec−1 the eccentricity and mass increase very rapidly as the angular velocity increases, for the critical angular velocity of the rotating star, the eccentricity is about 0.7, the increase in mass is about 10–35%. The difference of the gravitational redshifts at the surface of the star caused by rotation, and the difference of the light bending when the beam moves in the direction of rotation or in the opposite direction are obvious.  相似文献   

5.
Joel E. Tohline 《Icarus》1985,61(1):10-21
The scalar virial equation can be used to elucidate many interesting properties of equilibrium gas clouds when the effects of surface pressure, rotation, self-gravity, and internal isothermal gas pressure are considered simultaneously. Details regarding the internal structure of rotating isothermal gas clouds are ignored in order to obtain an analytical expression describing global cloud properties. Excellent agreement is obtained between the simple analytical model and other previously published, more detailed models in physical regimes where other models have been constructed. For the first time, a physical connection is drawn between the surface-pressure-dominated equilibrium models of S. W. Stahler (1983, Astrophys. J.268, 155–184) and the rotation-dominated models of C. Hayashi, S. Narita, and S. M. Miyama (1982, Prog. Theor. Phys.68, 1949–1966). Stable axisymmetric models of any mass and angular momentum can be constructed. Using the analytic expression for virial equilibrium as a foundation, all rotating, isothermal collapse calculations can now be well understood. Limiting properties of isothermal clouds are outlined, and realistic “starting” models for cloud collapse are proposed.  相似文献   

6.
The non-isothermal magnetohydorstatic equilibrium is studied in this paper, on the basis of two-dimensional solutions of an isothermal case[9]. We present two models of temperature distribution and derive the two relevant partial differential equations of non-isothermal magnetohydrostatic equilibrium. Using the solution of the isothermal case as an approximation of the 1st degree and choosing appropriate boundary conditions, we obtain several solutions of the equations with an iterative method numerically, and obtain the equilibrium configurations and the distributions of temperature and magnetic energy. From these results, we find that the equilibrium configurations will change obviously as the temperature changes from the isothermal case slightly. Change of the temperature may play an important role in producing relatively violent solar activities through instability.  相似文献   

7.
Lens models appropriate for representing cusped galaxies and clusters are developed. The analogue of the odd-number theorem for cusped density distributions is given. Density cusps are classified into strong, isothermal or weak, according to their lensing properties. Strong cusps cause multiple imaging for any source position, whereas isothermal and weak cusps give rise to only one image for distant sources. Isothermal cusps always possess a pseudo-caustic. When the source crosses the pseudo-caustic, the number of images changes by unity.   Two families of cusped galaxy and cluster models are examined in detail. The double power-law family has an inner cusp, followed by a transition region and an outer envelope. One member of this family — the isothermal double power-law model — possesses an exceedingly scarce property, namely the lens equation is exactly solvable for any source position. This means that the magnifications, the time delay and the lensing cross-sections are all readily available. The model has a three-dimensional density that is cusped like r −2 at small radii and falls off like r −4 asymptotically. Thus, it provides a very useful representation of the lensing properties of a galaxy or cluster of finite total mass with a flat rotation curve. The second set of models studied is the single power-law family. These are single density cusps of infinite extent. The properties of the critical curves and caustics and the behaviour of the lenses in the presence of external shear are all discussed in some detail.  相似文献   

8.
Group-theoretical techniques are used for the analysis of non-radial oscillations of spherical stars, for the classification and the study of the splitting of the modes under the influence of rotation, tides and magnetic fields, as well as for ellipsoidal configurations. The general conclusions are compared with the analytical and numerical results which have up to now been worked out only for artificial models.  相似文献   

9.
In this paper, pulsating white dwarfs are treated via general relativity. Numerical integration of Einstein's equations was used to find equilibrium white dwarfs models and the fundamental periods of small oscillations about these equilibrium models. In these calculations account was taken of coulomb, Thomas-Fermi, and exchange interactions as well as ion zero point energies. It is shown that general relativity makes not just a quantitative difference in the results but a qualitative differences; pure C12 models which are stable in Newtonian mechanics can be unstable against collapse (at a central density of 3×1010 g/cm3) when general relativity is taken into account. The collapsing model may become a neutron star or may continue towards the Schwarzschild radius.More realistic white dwarf models with carbon burning products at the center, also were studied. For these models, the density at which the star becomes unstable against collapse due to electron capture (3×109 g/cm3) was found to be lower than the density at which general relativistic instability occurs.  相似文献   

10.
The aim of the present investigation has been to derive from the fundamental Cauchy's first law of continuum mechanics the explicit form of the Eulerian general equation which governs the three-axial generalized rotation about the centre of mass of a self-gravitating deformable finite material continuum, viscolinear (i.e., Newtonian) or not, consisting of compressible fluid of arbitrary viscosity, in an external field of force. The generalized rotation is a superposition of the so-called rigid-body (i.e., time dependent only) rotation of the continuum plus a nonrigidbody (i.e., position-time dependent) rotation of its configurations.In Section 2, which follows brief introductory remarks outlining the problem, we develop a mathematical theory which describes the whole phenomenon in terms of two rotation tensors corresponding, respectively, to the rigid-body and nonrigid-body rotation modes. In Section 3, we derive the differmation vectors of velocity and acceleration. The equations we have obtained are a very general version of Navier Stokes' equations, which were not given in previous investigations. In Section 4, we perform integration of the left-hand side of Cauchy's first law, cross-multiplied by the position vector, without any restriction. In Section 6, integration of the right-hand side of the same law, cross-multiplied by the position vector, is carried out, by taking account of actually simplifying assumptions stated in Section 5. All the integral terms occurring in both sides are expressed explicitly by quantities evaluated in terms of components of properly defined moments.Finally, in Section 7, the system of the general Eulerian equations is set up; and some easy modifications are given, which describe nicely physical models of special interest; while the concluding Section 8 contains a general discussion of the results.  相似文献   

11.
The aim of the present paper will be to utilize Poincaré's criteria to investigate secular stability of self-gravitating configurations, of arbitrary structure, in the state of rapid rotation. The potential energy, a knowledge of which is necessary for application of these criteria, will be determined by an extension of Clairaut's method; and its evaluation in terms of suitably chosen generalized coordinates carried out explicitly to quantities of fourth order in superficial oblateness, for configurations of arbitrary internal structure.The method employed can, moreover, clearly be extended to attain accuracy of any order — at the expense of mere manipulative work which lends itself to machine automation; and the angular velocity of axial rotation can be an arbitrary function of position as well as of the time. An application of our results to homogeneous configurations in rigig-body rotation will be undertaken to demonstrate that our method, when applied to a case for which a closed solution exists, leads to results which are consistent with it.  相似文献   

12.
The gravitational collapse mechanism of a non-magnetized isothermal rotating interstellar gas cloud is discussed analytically. The study predicts the formation of final flattened disk-like configurations in the central region of the infalling uniform gas cloud. The existence of critical times indicates the possibility that, beyond these times, discrepancies can arise in the numerical calculations. It seems therefore very likely that the ring-like structures, as suggested by earlier numerical calculations of hydrodynamic models, would be caused by pressure effects which arise through the introduction of higher order terms in the linearized theory.  相似文献   

13.
The corresponding field configurations of the solar isothermal atmosphere obtained from a series of non-constant shearing magnetic fields after considering both the gravity and gas pressure are examined and compared. When the shearing magnetic field increases, magnetic islands will appear, followed by shearing, quasi-three-dimensional field structures approaching the open state and with almost anti-parallel field lines. It is possible that this is related to the initial phase of a two ribbon flare.  相似文献   

14.
The evolution of halos consisting of weakly self-interacting dark matter particles is investigated using a new numerical Monte Carlo N-body method. The halos initially contain kinematically cold, dense r-1 power-law cores. For interaction cross sections sigma*=sigmawsi&solm0;mp>/=10-100 cm2 g-1, weak self-interaction leads to the formation of isothermal, constant-density cores within a Hubble time as a result of heat transfer into the cold inner regions. This core structure is in good agreement with the observations of dark matter rotation curves in dwarf galaxies. The isothermal core radii and core densities are a function of the halo scale radii and scale masses which depend on the cosmological model. Adopting the currently popular LambdaCDM model, the predicted core radii and core densities are in good agreement with the observations. For large interaction cross sections, massive dark halos with scale radii rs>/=1.4x104 cm2 g-1 (sigma*)-1 kpc could experience core collapse during their lifetime, leading to cores with singular isothermal density profiles.  相似文献   

15.
We consider global and gravitational lensing properties of the recently suggested Einstein clusters of weakly interacting massive particles (WIMPs) as galactic dark matter haloes. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can describe any galactic rotation curve by specifying the anisotropy. Due to this property, Einstein clusters may be considered as dark matter candidates. We analyse the stability of the Einstein clusters against both radial and non-radial pulsations, and we show that the Einstein clusters are dynamically stable. With the use of the Buchdahl type inequalities for anisotropic bodies, we derive upper limits on the velocity of the particles defining the cluster. These limits are consistent with those obtained from stability considerations. The study of light deflection shows that the gravitational lensing effect is slightly smaller for the Einstein clusters as compared to the singular isothermal density sphere model for dark matter. Therefore, lensing observations may discriminate, at least, in principle, between Einstein cluster and the other dark matter models.  相似文献   

16.
海潮模型的比较及海潮对地球自转变化的影响   总被引：2，自引：0，他引：2  
近年来,由于卫星测高工作的开展,提供了丰富准确的观测资料,产生出许多新的海潮模型。这些海潮模型的相互比较为研究海洋的精细结构、海潮的动力学、地球动力学提供了依据。另一方面,由现代空间技术和新方法来监测地球自转中的高频变化研究领域也有长足的进展。用这些技术可检测出地球自转中的周日和半日变化,从而激发地球自转的变化。一般来说,海潮影响地球自转的高频变化有两种不同的激发机制。地球的惯性张量的变化即质量项  相似文献   

17.
As shown by Chiéze, polytropic gas spheres imbedded in an ambient medium with a given pressure exhibit a relation between the mass and radius similar to isothermal gas spheres, providedn(polytropic index)>3 or <–1. Here, further investigation is made of the polytropic spheres. Not only the relation between radius and external pressure, but the relation between the central density ( c ) and the mass (M) is similar to isothermal spheres and neutron star models. Dynamical calculation shows that the stability of polytropic spheres is lost at the configuration which corresponds to the first peak in the c —M relation, as is the case for neutron star models in general relativity.  相似文献   

18.
The gravitational instability of an infinite homogenous rotating plasma through a porous medium in the presence of a uniform magnetic field with finite electrical and thermal conductivities has been studied. With the help of relevant linearized perturbation equations of the problem, a general dispersion relation is obtained, which is further reduced for the special cases of rotation, parallel and perpendicular to the megnetic field acting in the vertical direction. Longitudinal and transverse modes of propagation are discussed separately. It is found that the joint effect of various parameters is simply to modify the Jeans's condition of instability. The effect of finite electrical conductivity is to remove the effect of magnetic field where as the effect of thermal conductivity is to replace the adiabatic velocity of sound by the isothermal one. Rotation has its effect only along the magnetic field in the transverse mode of propagation for an inviscid plasma, thereby stabilizing the system. Porosity reduces the effect of both, the magnetic field and the rotation, in the transverse mode of propagation in both the cases of rotation. The effect of viscosity is to remove the rotational effects parallel to the magnetic field in the transverse mode of propagation.  相似文献   

19.
The electromagnetic properties of neutron stars (pulsars) are studied. It is shown that taking the presence of two angular rotation velocities of the components of neutron stars and the first corrections to the general theory of relativity into account in the equations of hydrodynamic equilibrium for the plasma and in Maxwell’s equations leads to the generation of toroidal magnetic fields in the depths of a neutron star. __________ Translated from Astrofizika, Vol. 49, No. 1, pp. 97–101 (February 2006).  相似文献   

20.
Quasi-toroidal oscillations in slowly rotating stars are examined within the framework of general relativity. Unlike the Newtonian case, the oscillation frequency to first order of the rotation rate is not a single value, even for uniform rotation. All the oscillation frequencies of the r -modes are purely neutral and form a continuous spectrum limited to a certain range. The allowed frequencies are determined by the resonance condition between the perturbation and the background mean flow. The resonant frequency varies with the radius according to the general relativistic dragging effect.  相似文献   

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