Isothermal neutron star cores

By considering the relativistic expression for isothermal NS cores,T·e ^/2 = constant, we have shown that some of the standard equations of state, when applied to NS cores, correspond to constancy of some adiabatic exponents. It has been shown that the equation of state,P=KE, corresponds to ₁ = to ₂ = ₃ 1 +K and the equation of state, dP/dE=K, corresponds to ₃ 1 +K. The conditions under which different equations of state represent isothermal cores have been obtained: For isothermal NS, the local temperatureT, can be expressed in terms of pressureP, energy densityE, and rest mass density . For example: (a)P =KE :T = constant × (E/); (b)P=KE :T = constant × (P/); (c) dP/dE =K :T ^K ; (d) = ₂ :T = constant × (P/E); and (e) = ₃ :T = constant × (P/)^1/2. Equation of state corresponding to = ₂ is obtained as:P=E/ln(K/E) and the equation corresponding to = ₃ comes out as:E=P ln(K/P). Core-envelope models can be developed for these two cases. When core equation corresponding to = ₂ or = ₃ is used in the core, we can ensure the continuity of dP/dE at the core-envelope boundary, along with the continuity ofP, E, , and . The parameters of isothermal NS cores corresponding to the cases = ₂ and = ₃, have been obtained. The maximum mass of these NS cores comes out to be 2.7 .     

Is a Power-Law Form of the Correlation Gamma Function Sufficient to State that a Distribution Has Fractal Properties?

This investigation indicates an ambiguity in interpreting the results of applying the apparatus of the correlation gamma function [(r) and ^*(r)] to analyze the spatial distribution of objects from some sample. The presence of a linear section in the dependences of log() on log(r) and of log(^*) on log(r) proves to be insufficient to state that the distribution has fractal properties (self-similarity). It is shown that a change in the geometrical boundaries of the sample may influence the form of the dependences of log() on log(r) and of log(^*) on log(r).     

Internal temperature of isothermal neutron star core matter

Two new equations of state obtained for matter constituting isothermal neutron star core by using isentropic nature of matter for the equalities =₂ and =₃ (where 's are usual adiabatic exponents) have been utilised to discuss the internal temperature of core. The temperature of matter has been obtained asT=T _a(P+E)/. Variation ofT/T _a(t) with energy density has been discussed for these new equations of state and some standard equations of state for nuclear matter.     

On the uniqueness of the determination of the coronal potential magnetic field from line-of-sight boundary conditions

We consider a simple model in which the coronal magnetic field B is assumed to be potential in the region between the solar surface _o and an exterior source-surface ₁ of arbitrary shape. We prove that the boundary value problem that determines B from the value B _lof its component on ₀ along either (orthoradial direction) or (fixed direction) has at most one solution. On the other hand, we show that a solution can exist only if B _lsatisfies some solubility conditions.     

Effects of mass transfer on the unsteady free convection flow past an accelerated vertical porous plate with variable suction

An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg^*(C –C )/U ₀ ³ ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U ₀) - v normal velocity component - v ₀ suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C _p specific heat at constant pressure - C _w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C _w -C )) - Gr Grashof number (g(T _w -T )/U ₀ ³ ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T _w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU ₀ ² /) - U ₀ reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U ₀) - v dimensionless velocity (v/U ₀) - v ₀ non-dimensionalv ₀ (v ₀ /U₀)=–at^–1/2 - y dimensionless ordinate (yU ₀/) - density of the fluid - coefficient of viscosity     

Correlation Properties of a Distribution of Objects from the PSCz Survey

The properties of a sample of IR galaxies from the Point Source Catalog z (PSCz) Survey were investigated using the correlation gamma function [(r) and ^*(r)]. The results with different volume-limited subsamples indicate that the regions of strong correlations (a power-law decrease in density with distance with an exponent ₁ 1) are limited to a scale of 10-15 Mpc. A break is present at this scale in the dependences of log() on log(r) and of log(^*) on log(r). Such a break is also observed for various other samples of galaxies and clusters (at different scales). After the break the density dependence changes to another regime, corresponding to a fully uniform distribution for bright galaxies in the northern Galactic hemisphere. For some subsamples of the southern and northern hemispheres the latter regime corresponds to some decrease in density with distance. Indications of significant differences between the distributions of objects in the southern and northern hemispheres are obtained. It is shown that the section of the gamma function after the break, even when its extent is small, is a significant indicator of actual correlation properties of the distributions. The results of the analysis are in good agreement, on the whole, with preceding studies of the PSCz survey.     

Core-envelope models for massive fluid spheres

The solution of equation of state corresponding to equality =₃ gives non-terminating solutions for isothermal neutron star cores. Hence, for this equality, core-envelope models have been developed by taking another equation of state, corresponding to the condition ₃, in the envelope. Various static, pulsational, and rotational parameters pertaining to neutron star models are calculated. These models are gravitationally bound and stable for radial perturbations and slow rotations.     

Expanding and shearing magneto-viscous fluid cosmological model in general relativity

The object of this paper is to investigate the behavior of a magnetic field in a viscous fluid cosmological model. It has been assumed that the expansion () is proportional to the eigenvalue ₁ of the shear tensor _i ^j and the coefficient of shearing viscosity is proportional to the scalar of expansion. The paper also discusses the behavior of the model when the magnetic field tends to zero and comments on some other physical properties.     

Multiple expansion of the tidal potential

The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O Tide raising object - (, , ) Spherical coordinates of the T.R.O. - (J, _E ) Earth spin axis orientation. _E is the longitude of the ascending node of Earth's equator on thexy-plane - (a ,I ,e , , ,M ) Elliptics elements of the T.R.O     

Cylindrical oscillations of force-free electromagnetic fields

This paper is devoted to Force-Free Electromagnetic Oscillations in a constant magnetic field. A correction is made in the derivation of the basic equation. The paper confirms the predicted spectrum of frequencies, namely _n = _o (n + 1)^1/2;n = 0, 1, 2, .... In addition it is suggested that hybrid frequency _n = ( _n ² + _H ² )^1/2 should be found in observational data.     

Discrete Alfvén waves in solar loop prominences

It is shown that a discrete Alfvén wave can explain the natural oscillations of solar loop prominences by considering the existence of a current flow. Discrete Alfvén waves are a new class of Alfvén waves which is described by the inclusion of the finite ion cyclotron frequency (/ _cl 0) and/or the equilibrium plasma current. In this paper we consider only the effect of the current since in solar prominences (/ _cl 0). We have modeled the solar prominences as a cylindrical plasma, surrounded by vacuum (corona), with L a where L and a are the plasma column, length, and radius, respectively. We have calculated the spectrum of the discrete Alfvén waves as function of the magnitude and shape of the plasma current.     

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.     

НутационнЫе демпферы спутиков С двойным вращением

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Nutational dampers of dual-spin satellites

The paper considers application of the small parameter methods (Artemjev, 1944; Volosov, 1962) in the linear theory of damping the nutating motion of dual-spin satellites. The external moments affecting the satellite are left out of consideration. The influence of the damper on the satellite motion is assumed to be small. As a special case the conditions of stability for the satellite stationary spinning and the optimal parameters ensuring a maximal rate of damping the nutating motion have been obtained.

     

Hydrogen and helium spectra in large magnetic fields

The energy levels and wave functions of hydrogen and helium atoms in the presence of large (10⁷G) magnetic fields are found by assuming that the eigenvalues and eigenvectors may be approximated by those of a truncated Hamiltonian matrix. In these atoms, fields of this size produce, in addition to the usual Paschen-Back effect, a quadratic Zeeman effect. This contributes an upward shift to the energy of all levels, which at sufficiently high fields dominates the Paschen-Back splitting.The behavior of a number of eigenvalues and wave functions as a function of magnetic field is presented. The effects of the field on the wavelengths and strengths of the components of H and the helium lines 4471, 4026 and 4120 as well as the forbidden 4025 are examined. In hydrogen the lines are split into components attributed to the now nondegenerate transitionsnlm _lnlm_l. In helium forbidden lines are excited, which may develop strengths larger than those of the allowed lines.     

The relationship between r.m.s. doppler velocities and temperature in the solar transition region

An attempt is made in this paper to determine the coefficient a in a power-law relationship of the form V ~T between the r.m.s. velocity fluctuation, V for raster images with 3 resolution and the temperature, T of line formation using SMM solar data. For T between 8000 and 10⁵ K, the data suggest a best fit with 3/4 < 1. It is argued, however, that unresolved fine structure tends to reduce the observed value of V and that higher resolution data may yield different values for . Skylab data have shown that the non-thermal line broadening velocity, , is proportional to T ^1/2. Also, for all temperatures less than 10⁵ K, V . This latter result, however, is again dependent on spatial resolution and may not be true in observations made with sufficient spatial resolution. The magnitudes of both V and indicate that bulk motions play important roles in the structure of the solar atmosphere as well as in its energy and momentum balance. It is important, therefore, to identify the true nature of such motions with better accuracy than is possible with currently available data.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Massive fluid spheres with isothermal cores

We can define some adiabatic exponents for neutron star cores. The equality of and ₃ leads to an equation of stateE=P ln(K/P) orP=K exp(–E/P). This equation has been solved alongwith equations for hydrostatic equilibrium for different physical conditions at the centre. The parameters of isothermal neutron star cores have been computed by taking surface densityE _a=2×10¹⁴ g cm^–3. ForP ₀=E ₀ the maximum mass and radius of neutron star core are 3.25M and 17.14 km, respectively.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

Higher-order stability of the restricted problem and the solar system

A generalization is expressed of the Poisson theorem referring to the invariance of the planetary semi-major axes using the restricted problem model. In particular, it is shown that first and second approximation in terms of a change in the initial states of planets describing closed motions in the solar system remain invariant in modulus after any number of revolutions. But third-order terms contain secular parts and, thus, they undergo a secular change in their orbital motion. Such change would be apparent after ^-2 Jovian years, where is a constant and is the maximum initial deviation of each planet from its reference orbit.     

(Super) cosmological solution for the Kasner model

In the theory of supergravity (N=1), the supersymmetric version of general relativity, and for the Kasner cosmological model (Bianchi type I) we find a non-trivial solution (for the metric and spinor-vector) under the most simple assumption =₁₁ + ₂₂; ₁₂+₂₁=0 and for a special choosed gaugeN=1,N ^j=0, ₀=0. This method could be also applied to other cosmological metrics and extended to enlarged Grassmann basis.O. Obregón was partially supported by the Alexander von Humboldt Stiftung.     

Absolute and relative amplitudes of variations in radius of classical cepheids

On the basis of observational data for the absolute R and relative R/R amplitudes of variations in radius of galactic classical cepheids (55 stars from Balona and Stobie (1979) and 30 stars from Sollazzoet al. (1981)), four kinds of empirical linear relations are obtained: log(P V)–logR, logP–logR, log(P V)–log(R/R), and logP–log(R/R);P, R, and V are the pulsation periods, the mean stellar radii, and the amplitudes of light variations, respectively. Three groups of stars are considered: short-period cepheids (SPC)-with logP1.1; long-period cepheids (LPC)-with logP>1.1; and s-cepheids (sC). Both the R values and the R/R values increase withP andP V, for a given group of variables. A comparison is performed with our results obtained from data in other sources (Kurochkin, 1966; Gieren, 1982; etc.). The investigated relations can be applied for determining R and R/R of galactic classical cepheids, by using their observedP and V. All studied galactic classical cepheids have R/R<0.35, R<10R for SPC and 10R <R60R for LPC. The sC have smaller R and R/R values than other classical cepheids, at the same periods (the difference is about 2 times for R and 1.4–2.8 times for R/R); the studied sC have R/R in the range 0.025–0.075 and R in the range 1–3R (only Y Oph has R8R ).