Kelvin-Helmholtz instability of composite plasma in an oblique magnetic field with resistivity

Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = K _g , = _g c ².Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (, ), (,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density _g to the central density _gc , _g / _gc ; pressureP to the _gc ,P/ _gc ; and the metric componente ^–, for three representative general relativistic (GR) isothermal configurations =0.1, 0.2, and 0.3. Figure 4 shows the solution curve (, ) for =0.1, 0.2, and 0.3 (=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4r ² P ^*(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of =0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c ² to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P _c , binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.Part of the work done at Azerbaijan State University, Baku, U.S.S.R., and Mosul University, Mosul, Iraq, 1985-1986     

Distribution of minima of the current size of the triple systems and their disruption

The dynamical evolution of triple systems has been studied by computer simulations. A function (t) has been defined, where p is the maximum distance of the components from their centre of inertia, and t is the time. The value of is used to indicate the current size of the triple system. The minima of have been followed during the course of evolution of the triples. A distribution of f(_min) has been obtained, which is described by the following statistical parameters: the mode is equal to 0.65d, the mean value _min= 0.750d, r.m.s. is 0.477d, the asymmetry is 0.218, the excess is 2.04 where d is the mean harmonic distance between the bodies in the equilibrium state of the triple system. As a rule, escapes from triples occur only after close three-body approaches.     

The effect of chemical abundance oscillations on the pulsational properties of A 5M ⊙ hydrogen-helium star

A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) _T and _T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) _T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.     

The asymptotic limit of the form-factors α and β product for celestial bodies

The applicability of the properties of central configurations proceeding from the many-body problem to study of gaseous sphere cloud evolution during its gravitational contraction is justified. It is shown that the product runs to a constant value in the asymptotic time limit of simultaneous collision of all the particles of the cloud where is a form-factor of the potential energy and is a form-factor of the moment of inertia.The spherical bodies as well as ellipsoids of rotation and general ellipsoids with a one-dimensional mass distribution (k),k[0, 1] are found to possess the property =const.

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. , - , , ., , - =const., , (k),k[0, 1].

     

Radial Flows in Supergranules

We determine the radial component of the supergranular flow velocity by examining the center-to-limb variation of the Doppler velocity signal. We acquire individual Doppler images obtained with the MDI instrument on the SOHO spacecraft and process them to remove the p-mode oscillation signal, the axisymmetric flows, the convective blueshift signal, and instrumental artifacts. The remaining Doppler signal contains only non-axisymmetric flow structures. The Doppler signal from the horizontal flows in these structures varies like sin, where is the heliocentric angle from disk center. The Doppler signal from radial flows varies like cos. We fit the center-to-limb variation of the mean squared velocity signal to a straight line in sin² over the central portion of the disk. The intercept of this line at disk center gives the amplitude of the radial component of the flow. The slope of the line gives the amplitude of the horizontal component. We find that the radial flows for typical supergranules have speeds about 10% that of their associated horizontal flows or about 30 m s^–1. The ratio of the radial to horizontal flow speed increases from 9% to about 18% as the size of the structure decreases from >60 Mm to 5 Mm. We use data simulations to check these results and find a ratio that increases from 5% to only about 12% over the same range of sizes. These smaller ratios are attributed to an underestimation of the horizontal flow speeds due to the fact that the transverse component of the horizontal flow is not detected by Doppler measurements.     

Electrical conductivity of neutron star cores in the presence of a magnetic field

General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities ₀, where ₀ = 2.8×10¹⁴ g cm^–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of ^–-hyperons at > _c , where _c 4₀. The electric resistivities along and acrossB, and , and the Hall resistivity _H are calculated and fitted by simple analytical formulae at _c and > _c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If _c , one has = [1 + (B/B ₀)²] for the normal neutrons, and for the superfluid neutrons, while _H = B/B _e for both cases. HereB _e 10⁹ T ₈ ² G,B ₀10¹¹ T ₈ ² G, andT ₈ is temperature in units of 10⁸ K. Accordingly for the normal neutrons atBB ₀, the transverse resistivity suffers an enhancement, _{1/4 1}. When 5₀ andB varies from 0 toBB _p 10¹³ T ₈ ² G, increases by a factor of about 10³–10⁴ and _H changes sign. WhenBB _p , remains constant for the superfluid neutrons, and _H B ² for the normal neutrons, while _H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.     

The maximum mass of a neutron star

We consider the possibility that gravitational energy may play a local as well as global role in the behavior of matter in strong gravitational fields. A particular idealized equation, suggested as representing uniform energy density in general relativity, is examined, and its stability with respect to oscillatory and convective perturbations shown to be consistent with general relativistic hydrodynamics, subject to a new physical effect predicted for the behavior of fluids moving in strong fields. We calculate from this idealized equation the mass of a non-rotating neutron star, obtaining a maximum surface redshift ofz=2.48 and a maximum core mass of 9.79 ₁₄ ^–1/2 M. This compares withz=2.00 and 11.4 ₁₄ ^–1/2 M for a Schwarzschild star (=const.) and 6.8 ₁₄ ^–1/2 M for a causal star (dP/d1).     

The jeans instability criterion for a compressible fluid including viscosity and heat conduction

For the region after the recombination era of the Universe the hydrodynamical density waves are analyzed including shear viscosity and heat conduction for =_c as well as for <_c(_c is the critical density of the Universe). Very near to the end of the recombination era (z=1200) we find the well-known Jeans instability. It is shown that the influence of the shear viscosity on the instabilities in negligible, however, a visible influence of the bulk viscosity is present.     

Neutron-phonon interaction in neutron stars: Phonon spectrum of Coulomb lattice

The phonon excitation spectrum of Coulomb lattice in the neutron star crusts is studied by solving Dyson's equation for phonons. It is shown that a strong renormalization of the phonon spectrum occurs at densities _s /4 for the crustal matter compositions with spherical nuclei, which imply relatively small nuclear mass numbers and charges. It is shown that, the lattice becomes unstable against density fluctuations above a critical density of the order of _s /3, where _s 2.6x10¹⁴ g cm^–3 is the nuclear saturation density. The neutron quasiparticle spectrum and the virtual mass of a nucleus are briefly discussed.     

Three-component fluid model of the universe of critical density

A three-component fluid model of the Universe during the recombination era is analysed for = _c ( _c is the critical density). In addition to the well-known instability of the Jeans mode at 10⁹ M , we find two more unstable modes at 10¹² M .     

On Low-Mass, Strange Quark Stars with a Crust

Low-mass strange stars with a crust are investigated within the framework of the bag model. The crust, which consists of degenerate electrons and atomic nuclei, has a limiting boundary density _cr , which is determined by the mass of the crust, and it cannot exceed the value _drip = 4.3·10¹¹ g/cm³, corresponding to the density at which neutrons drip from nuclei. For different values of _cr in the low-mass range (M 0.1 M) we calculate several series of configurations: we find the dependence of the stellar mass M on the central density _c for _cr = const, with 10⁹ g/cm³ _{cr drip} , and for each series we determine the parameters of the configuration for which the condition dM/d _c > 0 is violated. When the boundary density of the crust decreases to 10⁹ g/cm³, the minimum mass of a strange star decreases to M _min 10^-3 M, while the radius reaches 600 km.     

The Energy Equation in the Lower Solar Convection Zone

As a consequence of the Taylor–Proudman balance, a balance between the pressure, Coriolis and buoyancy forces in the radial and latitudinal momentum equations (that is expected to be amply satisfied in the lower solar convection zone), the superadiabatic gradient is determined by the rotation law and by an unspecified function of r, say, S(r), where r is the radial coordinate. If the rotation law and S(r) are known, then the solution of the energy equation, performed in this paper in the framework of the ML formalism, leads to a knowledge of the Reynolds stresses, convective fluxes, and meridional motions. The ML-formalism is an extension of the mixing length theory to rotating convection zones, and the calculations also involve the azimuthal momentum equation, from which an expression for the meridional motions in terms of the Reynolds stresses can be derived. The meridional motions are expanded as U _r(r,)=P ₂(cos)₂(r)/r ²+P ₄(cos)₄(r)/r ² +..., and a corresponding equation for U (r,). Here is the polar angle, is the density, and P ₂(cos), P ₄(cos) are Legendre polynomials. A good approximation to the meridional motion is obtained by setting ₄(r)=–H₂(r) with H–1.6, a constant. The value of ₂(r) is negative, i.e., the P ₂ flow rises at the equator and sinks at the poles. For the value of H obtained in the numerical calculations, the meridional motions have a narrow countercell at the poles, and the convective flux has a relative maximum at the poles, a minimum at mid latitudes and a larger maximum at the equator. Both results are in agreement with the observations.     

Models of Strange Stars with a Crust and Strange Dwarfs

Strange quark stars with a crust and strange dwarfs consisting of a compact strange quark core and an extended crust are investigated in terms of a bag model. The crust, which consists of atomic nuclei and degenerate electrons, has a limiting density of _cr=_drip=4.3·10¹¹ g/cm³. A series of configurations are calculated for two sets of bag model parameters and three different values of _cr (10⁹ g/cm³ _{cr drip}) to find the dependence of a star's mass M and radius R on the central density. Sequences of stars ranging from compact strange stars to extended strange dwarfs are constructed out of strange quark matter with a crust. The effect of the bag model parameters and limiting crust density _cr on the parameters of the strange stars and strange dwarfs is examined. The strange dwarfs are compared with ordinary white dwarfs and observational differences between the two are pointed out.     

Isotropic flat space cosmology in Jordan-Brans-Dicke theory

The process of re-escalation of the scalar field as R ³, the energy density as R ³, and the pressurep aspR ³P, lends itself to obtain a reduced equation that represents, for a wide variety of equations of state, the cosmological evolution of an homogeneous and isotropic, flat Universe. A particular solution to this equation is presented.     

Spectral analysis of cyclotron radiation in anisotropic plasmas

Following up our previous analysis of cyclotron radiation in anisotropic plasmas, we derived expression for the power received at a far field point per unit frequency range along the group velocity direction dP(, )/d. We then carry out a series of numerical analysis presenting the spectral features rather than directional features of cyclotron radiation. In particular, we analyse the power received per unit solid angle per unit frequency range d² P(, )/(d d). It is expected the analysis result presented here can be compared directly with observation for parameters pertaining to astrophysical plasmas in stellar and terrestrial atmospheres.     

Theorie de Weyl et principe de moindre action: Application a l'etude des mouvements

Sommaire Les lois du mouvement dans une variété riemannienneV ₄ peuvent être déduites d'un principe de moindre action. Nous établissons dans cet article l'équivalence des relations ds=0 et dL=-L _k d^k, où ds ²=L ² est une métrique riemannienne et d _k /dt une fonction homogène de degré 1 des variables dx ⁱ/dt qui définit un espace de Weyl. Ce théorème permet de ramener une théorie de jaugen à un principe de moindre action. Il peut être utilisé dans la théorie de la double métrique de Dirac, obtenue en choissant la théorie des grands nombres comme condition de jauge. Une fibration de l'espace physiqueV ₃ basée sur le théorème de Huyghens permet de déduire les propriétés dynamiques des particules des propriétés des photons dansV ₃, et constitue en ce sens une unification des propriétés dynamiques des particules.

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The laws of motion in a RiemannianV ₄ manifold can be deduced from the principle of least action. We state in this work the equivalence between the equations ds=0 and dL=-L _k d^k, where ds ² =L ² is the Riemannian metric and d _k /dt the homogeneous functions of first degree of the dx ⁱ/dt which define a Weylian space. This theorem can then reduce a gauge theory to a principle of least action. It can be used in the double metric theory of Dirac, obtained by means of the Large Number Hypothesis as a gauging condition. A fibration of the physical spaceV ₃ based on Huyghens' theorem allows the deduction of the dynamical properties of particles by means of the properties of photons inV ₃, and constitutes in this way an unification of the dynamical properties of particles.

     

Genericity of the non-periodic solutions of the central force problem

We study the classical problem of two-dimensional motion of a particle in the field of a central force proportional to a real power of the distancer. for negative energy and (0, 2), each energy levelI _h is foliated by the invariant toriI _hc of constant angular momentumc and, by Liouville-Arnold's theorem, the flow on eachI _hc is conjugated to a linear flow of rotation number _h (c).A well-known result asserts that if we require _h (c) to be rational for every value ofh andc, the, must be equal to one (Kepler's problem). In this paper we prove that for almost every (0, 2) _h (c) is a non-constant continuous function ofc, for everyh<0. In particular, we deduce that motion under central potentials is generically non-periodic.Partially supported by CIRIT under grant No. EE88/2.     

Hydromagnetic cylindrical shock in self-gravitating gas

Chisnell-Chester-Whitham method has been used to study the propagation of diverging hydromagnetic cylindrical shock through an infinitely electrically conducting self-gravitating gas having an initial density distribution ₀= r^-w where is the density at the axis of symmetry andw is a constant, simultaneously for the two cases, viz.: (i) when the shock is weak and (ii) when it is strong. The magnetic field is taken to be axial and initially of constant strength. Analytical relations for shock velocity and shock strength have been obtained. the expressions for the pressure, the density and the particle velocity immediately behind the shock have also been derived.     

A note on the equation of state of a scalar field

The energy momentum tensor of a scalar field is considered as being that of a perfect fluid with equation of statep=p(). In the extreme case that the field energy is purely kinetic,p=p, whereas if it is purely potential,p=–.     

Experimental verification of gravitational interaction of bodies immersed in fluids

This article deals with the experimental verification of the generalized Newton's gravitational law, formulated by Z. Horák. According to this law, the gravitational force between two resting homogeneous bodies immersed in resting homogeneous fluids is dependent on the densities ₁, ₂ of both the bodies and densities₁,₂ of both the fluids: furthermore,F=(1–₁/ ₁)(1–₂/ ₂)F=h ₁ h ₂ F, whereF is the force between the bodies in a vacuum andh ₁,h ₂ are the density factors. The aim of the experimental verification of the law was to determine the density factors by exploring the phenomenon that is influenced by the gravitational interaction of the bodies immersed in different fluids.The dynamic torsion-balance method was applied, during which the period of swinging of the torsion pendulum in the gravitational field of two cast iron spheres in the water.The swings of the pendulum suspended on a torsion filament in a vacuum chamber were measured in three regimes: (1) without the spheres, (2) with the spheres in the air, (3) with the spheres in the water. The motion of the pendulum was scanned by a laser ray, the period of the swing was measured electronically. The density factor determined by the dynamic torsion-balance method was 0.8562±0.0035, whereas the same factor determined by direct calculation from the densities was 0.8542±0.0003. Thus, with the relative error of 0.4%, the validity of Horák's gravitational law was proved.