The boundary conditions for relativistic polytropic fluid spheres

The differential equations governing relativistic polytropic fluid spheres have been integrated numerically for polytropic indexn = 0.0 (0.1) 4.9 and relativity parameter = 0.0 (0.1) 0.9, and the resulting boundary conditions for and other related quantities are presented in this paper.     

Models of galactic mass distribution

Three groups of galactic mass models, each consisting of nine inhomogeneous spheroids of two kinds are described, according to three adopted values of the total density near the Sun: 0.10, 0.15 and 0.20 M pc^–3. Approximately 20% of the total mass of each model is in the halo, constructed to adequately fit recent RR Lyrae star observations. It is shown that the maxima found in the RR Lyrae star densities towards the galactic axis (Plaut, 1970) should not be interpreted as being associated with the galactic nucleus, but as the result of the greater decrease in density with increasingz over the increase in density as the galactic axis is approached. Even at the low galactic latitude of 5° (l=0°), this effect causes a 0.5 kpc correction to the distance to the galactic centre. A basic model for kpc, km s^–1, M pc^–3 is first constructed, mainly to satisfy structural conditions near the sun and in the halo. An attempt to optimize the basic model is made by scaling it so as to retain constant density and angular velocity near the sun, and to best fit kinematic data, including the recent re-examination of the 21-cm data of Simonson and Mader (1972). No unknown matter is required in the models, in accordance with the results of Weistrop (1972b), and, as pointed out earlier (Innanen, 1966b) the faintM-stars must be in a highly flattened spheroid. The optimizing indicates that an adequate fit to kinematics can be achieved for km s^–1. More detailed results are tabulated for a representative model for which . Two new galactic density functions are discussed in the Appendix.     

The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions , where is the Lie derivative of the Killing vector _j , permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.     

An approximate solution for the polytropen=3

In general, the Lane-Emden equation for an arbitrary polytropic indexn does not admit of an analytic solution. Simple approximation to the numerical results can, however, be found; and, in particular, affords a hitherto unreported good approximation to then=3 model. This term is accurate to within 10% of the tabulated values over 78% of the polytropic interior.     

Simulations of cosmic-ray particle diffusion

The diffusion of charged particles in a stochastic magnetic field (strengthB) which is superimposed on a uniform magnetic fieldB ₀ k is studied. A slab model of the stochastic magnetic field is used. Many particles were released into different realizations of the magnetic field and their subsequent displacements z in the direction of the uniform magnetic field numerically computed. The particle trajectories were calculated over periods of many particle scattering times. The ensemble average was then used to find the parallel diffusion coefficient . The simulations were performed for several types of stochastic magnetic fields and for a wide range of particle gyro-radius and the parameterB/B ₀. The calculations have shown that the theory of charged particle diffusion is a good approximation even when the stochastic magnetic field is of the same strength as the uniform magnetic field.     

Tidal effects in the earth–moon system and the earth's rotation

Analytical expressions for tidal torques induced by a tide‐arising planet which perturbs rotation of a nonrigid body are derived. Corresponding expressions both for secular and periodic perturbations of the Euler's angles are given for the case of the earth's rotation. Centennial secular rates of the nutation angle θ and of the earth's angular velocity ω, as well as the centennial logarithmic decrement ν of the Chandler wobble are evaluated:  mas, . In the Universal Time (UT) a large out‐of‐phase (sine) dissipative term with the period 18.6 years and the amplitude 2.3 ms is found. Corrections to nutation coefficients, which presumably have not been taken into account in IAU theory, are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-singular de Sitter universe inR+R 2−2Λ gravity

For the theory described by the action and taking the FRW flat space metric we find an exact non-singular de Sitter model universe exp(t ²), with . It is also proved that the standard general relativity de Sitter cosmology , >0 is also a model of this higher derivative theory of gravity. If the metric is conformally flatS could describe a consistent quantum theory and its classical solutions would correspond to cosmological models in this theory.This work was supported in part by CONACYT grand P228CCOX891723, and DGICSA SEP grant C90-03-0347.     

Sound and thermal waves propagation in a hydrogen plasma heated by an external radiation field

The thermal equilibrium of a hydrogen plasma heated and ionized by an external radiation field, diluted by a factorW _* and defined by an effective temperatureT _*, is studied. In addition, the problem of propagation of acoustic and thermal waves in the above plasma model is also analysed. It is found that an external radiation field has stabilizing effects against wave amplification. From the dispersion relation obtained, the phase velocity for sound and thermal waves and their respective scale-length of damping (or anti-damping) is calculated as a function of the frequency for representative values of the plasma temperature and the external radiation fieldT _*.     

Meridional flow in thick accretion disks

We have studied the effect of the flow in the accretion disk. The specific angular momentum of the disk is assumed to be constant and the polytropic relation is used. We have solved the structure of the disk and the flow patterns of the irrotational perfect fluid.As far as the obtained results are concerned, the flow does not affect the shape of the configuration in the bulk of the disk, although the flow velocity reaches even a half of the sound velocity at the inner edge of the disk. Therefore, in order to study accretion disk models with the moderate mass accretion rate—i.e.,

Static spherical configurations of cold matter in the Einstein-Cartan theory of gravitation

We investigate static, spherical configurations of cold catalized matter in the Einstein-Cartan theory of gravitation. Assuming that density of spin is proportional to the number density of baryonsn and using an equation of state of a degenerate, relativistic Fermi gas, we numerically integrated the relativistic equation of equilibrium. We have also studied the stability of those configurations. Configurations with central number densityn _c such that where is the effective pressure, are very similar to general relativistic configurations with the same central density. In the Einstein-Cartan theory there exists another disjoint family of equilibrium configurations for which but . Those configurations have very small masses 10^–6 g and raddi 10^–34 cm and are unstable.Supported in part by Research Grant MR-I-7.     

Radio frequency emission in electron beam-plasma and beam-beam interaction

A linear excitation of electromagnetic modes at frequencies , in a plasma through which two electron beams are contra-streaming along the magnetic field is investigated. This may be a source of the observed emissions at auroral latitudes.     

On the influence of gradients in the angular velocity on the solar meridional motions

If fluctuations in the density are neglected, the large-scale, axisymmetric azimuthal momentum equation for the solar convection zone (SCZ) contains only the velocity correlations and where u are the turbulent convective velocities and the brackets denote a large-scale average. The angular velocity, , and meridional motions are expanded in Legendre polynomials and in these expansions only the two leading terms are retained (for example, where is the polar angle). Per hemisphere, the meridional circulation is, in consequence, the superposition of two flows, characterized by one, and two cells in latitude respectively. Two equations can be derived from the azimuthal momentum equation. The first one expresses the conservation of angular momentum and essentially determines the stream function of the one-cell flow in terms of : the convective motions feed angular momentum to the inner regions of the SCZ and in the steady state a meridional flow must be present to remove this angular momentum. The second equation contains also the integral indicative of a transport of angular momentum towards the equator.With the help of a formalism developed earlier we evaluate, for solid body rotation, the velocity correlations and for several values of an arbitrary parameter, D, left unspecified by the theory. The most striking result of these calculations is the increase of with D. Next we calculate the turbulent viscosity coefficients defined by whereC _ro ⁰ and C _o ⁰ are the velocity correlations for solid body rotation. In these calculations it was assumed that ₂ was a linear function of r. The arbitrary parameter D was chosen so that the meridional flow vanishes at the surface for the rotation laws specified below. The coefficients v _ro ⁱ and v _0o ⁱ that allow for the calculation of C _ro and C _0o for any specified rotation law (with the proviso that ₂ be linear) are the turbulent viscosity coefficients. These coefficients comply well with intuitive expectations: v _ro ¹ and –v _0o ³ are the largest in each group, and v _0o ³ is negative.The equations for the meridional flow were first solved with ₀ and ₂ two linear functions of r ( ₀ ¹ = – 2 × 10 ^–12 cm ^–1) and ( ₂ ¹ = – 6 × 10 ¹² cm ^–1). The corresponding angular velocity increases slightly inwards at the poles and decreases at the equator in broad agreement with heliosismic observations. The computed meridional motions are far too large ( 150m s^–1). Reasonable values for the meridional motions can only be obtained if _o (and in consequence ), increase sharply with depth below the surface. The calculated meridional motion at the surface consists of a weak equatorward flow for gq < 29° and of a stronger poleward flow for > 29°.In the Sun, the Taylor-Proudman balance (the Coriolis force is balanced by the pressure gradient), must be altered to include the buoyancy force. The consequences of this modification are far reaching: is not required, now, to be constant along cylinders. Instead, the latitudinal dependence of the superadiabatic gradient is determined by the rotation law. For the above rotation laws, the corresponding latitudinal variations of the convective flux are of the order of 7% in the lower SCZ.     

Dark matter particles and the flat rotation curves of spiral galaxies

It is shown that a gas of massive bosonic particles (m 60 eV), e.g. Higgs particles, surrounding disk galaxies is able to generate the flat rotation curves of spiral galaxies without internal difficulties with physical principles. We have analyzed 36 galaxies and find good agreement with the empirical data.     

[CII] Emission and Star Formation in Late-Type Galaxies

A linear correlation between the ratio of the[CII( $^{\text{2}}$ P A linear correlation between the ratio of the[CII( P → P )] line intensity to the [ CO(J:1 →0)] line emission, I /I and the equivalent width (EW) is found, over the range 2–71 ? in EW, for a sample of 21late-Type= galaxies. The latter is comprised of an optically selected sample of 12 normal Virgo Cluster spiral galaxies with [CII] detections obtained by us with ISOLWS, plus nine late-Type= galaxies with higher star formation rates (SFRs), for which [CII] data and, especially, EW data are available in the literature. As a result we infer I /I to be a reliable tracer of the current mass-normalized global SFR for non-starburst spiral galaxies. Moreover, the ratio of the [CII] line to the total far-infrared (FIR) continuum intensity, I /I , is found to decrease from ∼0.5% to ∼0.1% with decreasing SFR which we propose is due to a `[CII]-quiet' component of I from dust heated by the general interstellar radiation field (ISRF). The more `quiescent' galaxies in the sample have values of I /I different from those observed in `compact' Galactic interstellar regions. Their [CII]-emission is interpreted to be dominated by diffuse regions of the interstellar medium (ISM). For normal `star-forming' galaxies the diffuse component of the [CII] emission is estimated to account for at least 50% of the total. This revised version was published online in July 2006 with corrections to the Cover Date.     

The motion of the line of apsides of ζ phoenicis

An estimate of the period of the rotation of the line of apsides of the double-star system Phe is obtained by representing the density function as a product of a normal Gaussian distribution and an associated Legendre polynomial .The asymptotic behaviour of this function coincides with the results obtained by Zeldovichet al. (1981).The period of motion of the line of apsides of Phe (about 63 years) obtained in this way comes close to the period determined by an empirical formula for of Batten (1973).     

Effect of anisotropy and viscous dissipation on turbulence production

The paper is concerned with turbulent flow of incompressible, spatially homogeneous viscous fluid. A model for turbulence energy equation is obtained, ignoring the pressure redistribution term in dynamical equations for the Reynolds stresses. The mechanism of dissipation on turbulence production is discussed and shown that the turbulence kinetic energy decays upto a constant value as time becomes infinitely large, i.e., for isotropy, dissipation inhibits the production process and if > initially then dissipation causes reduction in anisotropy.     

Completely Integrable Systems Connected with Lie Algebras

In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems. A new class of integrable systems may be devised using the following sequence: , where A is a Lie algebra is a Lie–Poisson structure on R ₃, C is a Casimir for is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket , which is a key element in using the Lie algebra A to constructing this sequence. New examples of Lie algebras and their related integrable Hamiltonian systems are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

The light curved in the CM field

In this paper we introduce the CM field in Sections 2 and 3 based on the paper by Wang and Peng (1985), and calculate the light curved in the CM field in Section 4. The result shows thatP makes _CM larger than _C at , and smaller at . Under a special circumstance which source, CM lens, and observer are in the same line, if we get | ₀₌₀ , and | _=/2 , we can determine theP(M) andQ(M) of the CM lens,M is the mass of the CM lens.     

Fourier analysis of the light curves of eclipsing variable stars

The aim of the present paper is to find the eclipse perturbations, in the frequency-domain, of close eclipsing systems exhibiting partial eclipses.After a brief introduction, in Section 2 we shall deal with the evaluation of thea _n ^(l) integrals for partial eclipses and give them in terms ofa ₀ ⁰ ,a ₀ ⁰ (of the associated -functions) and integrals; while Section 3 gives the eclipse perturbations arising from the tidal and rotational distortion of the two components. The are given for uniformly bright discs (h=1) as well as for linear and quadratic limb-darkening (h=2 and 3, respectively).Finally, Section 4 gives a brief discussion of the results and the way in which they can be applied to practical cases.     

The compton effect in the chromosphere,II

The red shift and central intensity are given for eleven spectral lines having an observed reduced equivalent widthV ranging fromV=15 toV=200. The computations have been repeated for eight values of the scattering thickness of the chromosphere, from to . A theoretical interpretation of measurements in the Sun is also given.