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.     

Пе⌕вичный адрон: Происхождение звезд галактик и астрономицеской вселенной

, J=(m/m _p)^1+1/n , n=2 , n=3 , . , . , , . - wc m _P, G c . -.     

On gravitational orbits and the virial theorem

We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)–E _kin/E _pot.R is calculated as a function of the eccentricity (e) and of the energy (E). Whent, independently ofe andE, R1/2 for closed orbits (this clearly illustrates the fulfillment of the virial theorem in classical mechanics); whereasR1, at any time, for open orbits.     

Структура и эволюция Сверхмассивных вращающихся магнитных политроп

. - . . , . - . - , , , -. ., , .

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The structure of rotating magnetic polytropes is considered in Roche approximation. Investigation of the influence of poloidal as well as toroidal magnetic fields on the conditions of the beginning of matter outflow due to rotational instability is carried out. The influence of the turbulent convection and twisting of magnetic force-lines on the time of smoothing of differential rotation is considered. The estimate of the magneto-turbulence energy generated by differential rotation is presented. Both maximum possible energy output and duration of the quasi-statical evolution phase up to the appearance of hydrodynamic instability due to the effects of general relativity are calculated for supermassive magnetic polytropes of index three with uniform or differential rotation. The radius-mass relation is obtained for supermassive differentially-rotating magnetic polytropes referring to the longest part of the quasi-statistical evolution stage; some consequences are pointed out, including the period-luminosity relation.The evolution of the considered models of supermassive rotating magnetic polytropes with different character of rotation and different geometry of a magnetic field is discussed.The results obtained are summarized in the last section.

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English translation will appear in the next issue ofAstrophys. Space Sci.

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Receipt delayed by postal strike in Great Britain     

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     

CH3CN J = 8 − 7 and CS J = 3 − 2 emission in orion KL

The data of the line series CH₃CN 8(K) – 7(K) K = 0 – 7 and line CS J = 3 – 2 were taken simultaneously. At beam size of 16 the emissions of CH₃CN and CS have a common center position located near IRc2 with deviations -8 and 5. The observed data show that in Orion KL core the integrated intensities of the two species have double peaks separated by a space of 14. The 2-dimension Gaussian fitting plots (FWHM) are ellipses ofD _maj = 26 andD _min = 22 for CH₃CN 8(K) – 7(K) K = 3 – 6 andD_maj = 39 D_min = 31 for CS J = 3 – 2 at a distance about 450 pc. Towards the multiple line emission region of CH₃CN 8(K) – 7(K) K = 3 – 6, using a simplified very large velocity gradient model to solve the statistical equilibrium and radiative transfer equations, we find to fit the observed results, the optimum physical parameters and kinetic temperatureT _k 120 K, densityn(H _a) 1.2 × 10⁵ cm^–3, velocity gradientV _gr 92 km s^–1 pc^–1 and the local abundance of CH₃CNF _ab 3 × 10^–8. However towards the region of single line emission of CS J = 3 – 2 we have to use LTE and the optical thin approximation on the assumption ofT _k= 120 K to obtain the lower limits of column density and then, an averaged abundance of CS of 6 × 10^–8.     

Оь излучении звезд типа Т Тельца в далеком ельтрафиоле те

, oqn ANS (1500–3300 Å) , I , 3–15 . , <2000 Å nepexo , 1.5 MB . ₀ , . .     

Индуцированное комптоновское рассеяние изотропного излучения релятивистскими электронами

, kT _b mc ² . . , , . E ^–5, - E ², mc ²(kT /mc ²)^1/7. , (>2.10⁵ cm ^–3) . , -, , .     

High velocity neutron stars and γ-ray bursts

The observations of the BATSE instrument on the Compton Gamma-Ray Observatory show that the spatial distribution of -ray burst sources is isotropic but radially non-uniform. As is well known, the spectral features, the time histories and the X-ray tails present in some -ray bursts suggest that they may arise from galactic neutron stars. But, low velocity neutron stars born in the Galactic disk would concentrate toward the galactic plane and center, and could not fit the BATSE results. However, the high velocity neutron stars with velocity 1000 km s^–1 may escape from the Galactic gravitational field and form a nearly isotropic distribution. Here we calculate the three statistical values of V/V _max, sin² b and cos as functions of the intensitiesC _max/C _min and find that they could be fitted by the distribution of high velocity neutron stars under the assumption that the high velocity neutron stars should turn on as -ray burst sources only after some time (perhaps after they have ceased to be radio pulsars). Our calculation shows that the statistical value of cos is more sensitive than sin² b to the angular distribution of high velocity neutron stars, i.e. the deviation of cos from 0 is more readily detected than the deviation of sin² b from 1/3, so we expect that with the increasing sensitivity of instrument and the more exact value of cos , it is possible to determine whether this high velocity neutron star model is correct. Some results are discussed in the text.     

Secular perturbations in general planetary theory

Based on a general planetary theory, the secular perturbations in the motion of the eight major planets (excluding Pluto) have been derived in polynomial form. The results are presented in the tables. The linear terms of second order with respect to the planetary masses and the nonlinear terms of first order up to the fifth (and partly seventh) degree with respect to eccentricities and inclinations were taken into account in the right-hand members of the secular system. Calculations were carried out by computer with the use of a system that performed analytic operations on power series with complex coefficients.

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qA ( ). . ( ) . .

     

Stability of and motion aboutL 4 at three-to-one commensurability

The stability ofL ₄ and the motion aboutL ₄ in the restricted problem of three bodies is investigated when there is three-to-one commensurability between the long and short periods of motion, that is, when the mass ratio has the value =0.013516.... The two time scale method is used (1) to show thatL ₄ is an unstable equilibrium point when =₃, (2) to determine for what initial conditions periodic orbits occur when ₃, (3) to determine the stability of the periodic orbits, and (4) to investigate the boundedness of the motions aboutL ₄ when ₃.     

Linearized limb-darkening coefficients for use in analysis of eclipsing binary light curves

Linear limb-darkening coefficientsu required in the analysis of eclipsing binary curves, are tabulated for a wide range of effective temperature (50 000° to 4000°), wavelength (0.2 2.2 ), and gravitiesg (2.0logg5.0). The computation is based on the comprehensive range of model atmospheres of Carbon and Gingerich (1969).The results are compared with the theoretical values of Hosokawa (1957), Kopal (1959) and Grygaret al. (1972), and examined in relation to empirically determined values ofu from analyses of eclipsing binary light curves. An improved agreement between theory and observation for the calculated limb-darkening coefficients of the present work is noted.     

On the pulsation amplitude of cepheid variables

On the basis of more abundant data a relation logPV/logR for cepheid variables (Fernie, 1965) is constructed. A linear relation between logP V and logR for classical cepheids is found, which perhaps has a break at R=10R . On the logR/logP diagram thes-cepheids (Efremov, 1968) show a distinct sequence. Alls-cepheids present a relative variation of the radii R/R0.075. The existence of non-s-cepheids with R/R0.075 raises a point about the evolutionary place of these stars (see Efremov, 1968). One could suppose that cepheids with logP>1.1 pulsate in the first overtone.     

NGC7538 Irs1 N: Modeling a Circumstellar Maser Disk

We present an edge-on Keplerian disk model to explain the main component of the 12.2 and 6.7 GHz methanol maser emission detected toward NGC7538-IRS1N. The brightness distribution and spectrum of the line of bright masers are successfully modeled with high amplification of background radio continuum emission along velocity coherent paths through a maser disk. The bend seen in the position–velocity diagram is a characteristic signature of differentially rotating disks. For a central mass of 30M, suggested by other observations, our model fixes the masing disk to have inner and outer radii of 270 and 750 AU.     

A static theory of the stability of the equilibrium

A static relativistic theory of the stability of the equilibrium of an isentropic spherically-symmetric star is deduced from the properties of a functionu which is solution of a second-order differential equation, and which is related to the model by means of the formulau = m(v, c)/c, wherem is the mass-energy inside the coordinate volumev and c is the central mass-energy density.Work done in the Laboratorio Astrofisico di Frascati, Roma.     

The scattering of light by dielectric particles

We consider homogeneous particles with a frequency-dependent index of refractionn =n +in = 1 +(), ()1, in an outer electromagnetic field. From general considerations we derive an expression for the total scattering cross-section of these particles. We calculate the efficiency factor for the sphere, the infinite circular cylinder, and for an ellipsoidal particle with the main axesa=1,b=2,c=1. In contrast with the ray approximation, the present method can be used to calculate the polarization of the scattered light from ellipsoids.     

On the reconstruction of the nonlinear force-free coronal magnetic field from boundary data

Using a simple model in which the corona is represented by the half-space domain = {z > 0} and the photosphere by the boundary plane = {z = 0}, we discuss some important aspects of the general problem of the reconstruction of the magnetic field B in a small isolated coronal region from the values of the vector B¦ measured by a magnetograph over its whole basis. Assuming B to be force-free in : (i) we derive a series of relations which must be necessarily satisfied by the boundary field B¦ , and then by the magnetograph data if the force-free assumption is actually correct; (ii) we show how to extract directly from the measured B¦ some useful informations about the energy of B in and the topological structure of its field lines; (iii) we present a critical discussion of the two methods which have been proposed so far for computing effectively B in from B¦ .     

The ‘naked’ singularity in the scalar-tensor gravitation theory

The complete analysis of possible types of non-relativistic and ultra-relativistic motions in the field of the naked singularity of the STGT is given. The problem of the infall of a monochromatic radiation emitter on the naked singularity is studied. In spite of the absence of a freezing effect in the STGT, the naked singularity is not observable, for the brightness of the falling emitter decreases much faster than in the GTR. Atrr _g , the trajectory of particles and light are quite similar to that of the GTR, and due to this fact the naked singularity is observationally indistinguishable from a black hole.     

Optically thick accretion onto black holes

Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn ₀=10⁸ cm^–3 andT ₀=10⁴ K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×10³³ erg s^–1, which primarily arises from the optical surface (1) ofT10⁴ K. The accretion flow is characterized by 1 and (v/c)10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at 1. The radiative equilibrium is strictly realized at (v/c)10.     

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.