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1.
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.  相似文献   

2.
An exact solution of Einstein's equation is stated in which the density (), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having R –2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law ( R –, approximately, with =a number, 02). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy.  相似文献   

3.
The classical gravitational collapse problem is analysed on the basis of an integral equation connecting the evolutionary time (defined as dt/d log ) with the density and the collapse function , or by an equivalent first-order non-linear differential equation. The general behaviour of solutions is discussed, and some particular cases are studied.  相似文献   

4.
The equation for the two-particles cosmic-ray distribution function is derived by means of the Boltzmann kinetic equation averaging. This equation is valid for arbitrary ratio of regular and random parts of the magnetic field. For small energy particles the guiding-center approximation is used. On the basis of the derived equation the dependence between power spectra of cosmic-ray intensity and random magnetic field is obtained. If power spectra are degree functions for high energy particles ( 10 GeV nucleon–1), then the spectral exponent of magnetic field lies between and –2, where is the spectral exponent of cosmic-ray power spectra. The experimental data concerning moderate energy particles are in accordance with =, which demonstrates that the magnetic fluctuations are isotropic or cosmic-ray space gradient is small near the Earth orbit.  相似文献   

5.
The assumption of a linearly expanding universe for the JBD-cosmological equations generates a set of solutions for the barotropic equations of statep= (=const.). These solutions turn out to be valid for closed space-except in the casep= which is for open space. The gravitational constant which is inversely proportional to the scalar field increases with time if >–1/3 and decreases for <–1/3. No solution exists for =1/3. The Brans-Dicke parameter is negative if <–1/3.  相似文献   

6.
While Euclidean models with uniform matter density have a number of radio sources of flux density greater thanF at frequencyv that varies asN(>F, v)1 F –3/2, hierarchical models with = 0 r –2 haveN(>F,)F –1/2 (Section 1). Since the observed dependency isN(>F,)F –1.8, severe density and/or luminosity evolution must be present in a workable hierarchical cosmology (Section 2). The same argument applies (Section 3) to the number of sources of apparent luminosity greater thanl,N(>l) and (Section 4) to the number of sources within redshift distancez from the local origin. To give agreement with empirical data demandsq o=+1 and large first and second derivatives with respect to time of the number source density (Section 5). The adoption ofq o=+1 allows one to show (Section 6) that a Lemaitre-type hierarchical Universe with a long coasting or waiting time can give agreement with observations of the numbers of QSO's etc. if the age of the Universe is more than 1013 yr. The dependence of the effective Hubble parameter onk(t), (t) andR (Section 7) leads one to suggest that ak=0, =0 hierarchy with 0 might be the simplest acceptable form of model Universe. Section 8 (Conclusion) points out that further data on source count anisotropies should allow the component levels of the hierarchy to be delineated.  相似文献   

7.
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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.

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

Receipt delayed by postal strike in Great Britain  相似文献   

8.
A simple reticle with parallel equally spaced lines to transmit light in an autometric gyro is shown to give a signal which can be used for very accurate angular precession measurements. Frequency analysis of the signal is chosen over time domain analysis and/or over a specially designed reticle.Gyro precession will induce a change in the interference structure of the spectrum in addition to dilating the overall frequency distribution. The expected output spectrum has been analytically determined, exhibiting the dependence on spot and reticle line cross sections and line spacing so that they can be precisely determined from the output data.The spectrum structure is extremely sensitive to precession. Computer simulations indicate that accuracy will be limited by reticle line spacing variations to ±4×10–9 rad. This would allow a Lense-Thirring precession measurement accurate to ±20% in 30 days (accuracy being limited by physical effects common to all such experiments) or a ±1% de Sitter precession measurement in four days.Nomenclature a n() Fourier coefficients ofI() - a n r () rapidly varying part ofa n() - a m x ,b m x Fourier coefficients ofI(x) - a (),b () Fourier sine and cosine transforms of x(x) - angle between star and gyro spin axis - 0 initial alignment angle - f focal length of optical system - I transmitted light intensity, signal function - l reticle line width - r distance from light spot center - R light-circle radius - = reduced light-circle radius - 0 reduced reticle center-spin center offset - s reticle line space - T(x) reticle transmission function - angle of gyro rotation - w g gyro angular velocity This work was supported by the M.I.T. Center for Space Research under NASA Grant NGL-22-009-019.  相似文献   

9.
It is shown that in the radiation era of the Universe spatial temperature fluctuations (T/T)<10–5 in the cosmic plasma lead to huge changes of the density up to (/)104. This effect results from the fact that the cosmic plasma in the radiation era can be considered as a general relativistic Boltzmann gas which is found in the very vincinity of equilibrium.  相似文献   

10.
The intensity and polarization of two-photon annihilation in a magnetic fuieldBB cr =4.4×1013 G are studied in detail for a, one-dimensional thermal distribution of annihilating electrons and positrons on the ground Landau level. With the increase of temperatureT the total annihilation rate and energy losses decrease, being higher than for the isotropic thermal distributions at the sameT. The shapes of intensity spectra at sin =0 ( is the angle betweenB and wave-vector) are close to those in the isotropic case. The widths and blue-shifts of the spectra decrease with increasing sin and increase with increasingT. Logarthmic singularities arise in the spectra atE»mc 2/sin . Power-like parts are formed in the wings of the spectra forkTmc 2 and not too small sin . The direction-integrated spectra reach their (finite) maxima, atE=mc 2 for anyT. The radiation concentrates near the plane, perpendicular to the magnetic field forE close tomc 2 and is beamed along the magnetic field forE far frommc 2. Energy-integrated angular distributions are stretched alongB, the stronger the higherT. The rediation is linearly polarized in the plane formed by the magnetic field and weve-vector. Typical values of the polarization inside the cores of the annihilation spectra are (kT/mc 2) sin and [ln (kT/mc 2)]–1 forkTmc 2 andkT sin mc 2, respectively. Annihilation radiation dominates over Bremsstrahlung in thee plasma atkT7mc 2. The results are useful for interpretation of the annihilation radiation in the gamma-ray bursts. They permit to estimate temperature, gravitational potential, and emission measure of radiating regions and the beaming of the radiation.  相似文献   

11.
The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order 4, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter = 2/2G c and a relativity parameter, =p c / c C 2 , wherep c and c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order 2. The critical rotation parameterv c , which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.  相似文献   

12.
The paper represents the Earth's gravitational potentialV, outside a sphere bounding the Earth, by means of its difference V from the author's spheroidal potential. The difference V is in turn represented as arising from a surface density on the sphere bounding the Earth. Because of the slow decrease with ordern of the normalized coefficients in the spherical harmonic expansion ofV, the density anomalies from which the higher coefficients arise must occur in regions close to the Earth's surface. The surface density is thus an idealization of the product of the density anomaly and the crustal thicknessb. Values of are computed from potential coefficients obtained from two sources, Rapp and the Smithsonian Astrophysical Observatory. The two sources give qualitative agreement for the values of and for its contour map. The numerical values obtained for are compatible with the idea that the responsible density anomalies are reasonably small, i.e., less than 0.05 g/cm3, and occur in the crust alone.This paper was prepared under the sponsorship of the Electronics Research Center of the National Aeronautics and Space Administration through NASA Grant NGR 22-009-311.  相似文献   

13.
The Chisnell-Chester-Whitham method has been used to investigate the propagation of diverging plane and cylindrical shock waves through an ideal gas in presence of a magnetic field having only constant axial and variable azimuthal components, simultaneously for both weak and strong cases. Assuming an initial density distribution 0=r –w , where is the density at the plane/axis of symmetry andw is a constant, the analytical expressions 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 for both cases.  相似文献   

14.
Temperatures and temperature gradients for the outer corona are obtained from brightness gradients of EUV lines that were measured with the spectroheliograph on OSO-7. Brightness gradients show considerable deviations from isothermal model calculations that include collisional excitation and photoexcitation. A negative temperature gradient that gives both positive and negative ion abundance gradients appears to be able to account for the discrepancy. For 284 of Fe xv, perhaps the strongest line from the outer corona, measurements during 1972 appear to be consistent with (i) a temperature near 2.3×106K near the equator at = 1.3±0.1 solar radii from the solar center; (ii) (/T) dT/d values near -0.7 that extend from as low as = 1.2 to about = 1.8. Temperatures from strong lines of Fe xiv and Fe xvi indicate that variations of about ±0.2×106K exist along lines of sight where emission is appreciable. There appears to be some agreement between these results and temperature measurements from ion abundances in the solar wind and Doppler width of 5303.  相似文献   

15.
Heating of the primaeval plasma prior to the epoch of recombination results in distortions in the Rayleigh-Jeans region of the microwave relic radiation spectrum (1–60 cm, or more exactly =2.5–7/8 cm). The present observational data allow limits to be set to such energy injection from which follow upper limits to (a) the amount of antimatter in the universe; (b) the parameters of primaeval turbulence; and (c) the adiabatic fluctuation spectrum for small masses (M<1011 M ).If the heating takes place prior to the epocht=101012/5 sec (and in particular at the annihilation of electron-positron pairs atT108–1010 K,t<300 sec), no observable distortions are expected in the relic radiation spectrum. Here =/crit is the dimensionless average density of matter in the universe.Translated from the Russian by D. F. Smith.  相似文献   

16.
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.  相似文献   

17.
Attention is given to the radiation of microwaves by charged dust in space. Presently-used particle distributions do not restrict the presence in space of large numbers of small (r<10–6 cm) silicate grains, but it is shown that such densities (10–25–10–26 g cm–3) of small grains would produce a microwave background with an energy density of the same order of magnitude as the energy density of the (presumed) cosmological 3 K background. Limits set by the isotropy of the latter are: (HI clouds)10–26, (Galactic plane)10–30, (Halo)10–32, (Local Group)10–34 g cm–3. These limits imply that either there is a cutoff in particle distributions atr10–6 cm, or that the density of silicate grains in space has been generally overestimated, or that cosmic rays have broken up a lot of grains so that they now form a population of grains of very small size (10–7 cm) which are difficult to detect by conventional methods. One way to look for the latter population is by studying expected distortions of the 3 K spectrum to the short wavelength side of the portion hitherto observed (grains may have a size distribution able to give an approximate black-body curve for radiation from larger grains of 10–6 cm size), and by testing the effective energy density of the 3 K field in other galaxies.  相似文献   

18.
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.  相似文献   

19.
This work contains a transformation of Hill-Brown differential equations for the coordinates of the satellite to a type which can be integrated in a literal form using an analytical programming language. The differential equation for the parallax of the satellite is also established. Its use facilitates the computation of Hill's periodic intermediary orbit of the satellite and provides a good check for the expansion of the coordinates and frequencies. The knowledge of the expansion of the parallax facilitates the formation of differential equations for terms with a given characteristic. These differential equations are put into a form which favors the solution by means of iteration on the computer. As in the classical theory we obtain the expansions of the coordinates and of the parallax in the form of trigonometric series in four arguments and in powers of the constants of integration. We expand the differential operators into series in squares of the constants of integration. Only the terms of order zero in these expansions are employed in the integration of the differential equations. The remaining terms are responsible for producing the cross-effects between the perturbations of different order. By applying the averaging operator to the right sides of the differential equations we deduce the expansion of the frequencies in powers of squares of the constants of integration.Basic Notations f the gravitational constant - E the mass of the planet - M the mass of the satellite - t dynamical time - x, y, z planetocentric coordinates of the satellite - u x+y–1 - s x–y–1 - the planetocentric distance of the satellite - w 1/ - 0 the variational part of - w 0 the variational part ofw, - n the mean daily sidereal motion of the satellite - a the mean semi-major axis of the satellite defined by means of the Kepler relation:a 3 n 2=f(E+M) - a the mean semi-major axis defined as the constant factor attached to the variational solution - e the constant of the eccentricity of the satellite - the sine of one half the orbital inclination of the satellite relative to the orbit of the sun - c(n–n) the anomalistic frequency of the satellite - c 0 the part ofc independent frome,e, and - g(n–n) the draconitic frequency of the satellite, - g 0 the part ofg independent frome,e, and - exp (n–n)t–1 - D d/d - e the eccentricity of the solar planetocentric orbit - a the semi-major axis of the solar orbit - n the mean daily motion of the sun in its orbit around the planet - m n/(n–n) - a/a-the parallactic factor - the disturbing function  相似文献   

20.
The possibility that the diffuse interstellar lines and bands are but structure in the continuous extinction by dust grains is considered in detail. The lines are assumed to arise from impurities in the grains. Profiles of the strongest diffuse features are computed for a wide variety of host grain types and sizes, including size distributions of particles, and spheroidal and coated spherical grains.New observational profiles, of which 4430, 4765 and 4885 have been derived from automated spectrophotometry of electronographic spectra, are also presented; and comparison is made between theory and observation. The most useful tool of comparison is found to be the ratio of maximum apparent emission in the violet wing to maximum apparent absorption, . This ratio increases with size of the host particle, and with both real and imaginary parts of its refractive index; but is independent of the observed variations in strength and width of a particular line. The ratio is larger for 4430 than for the other lines.Taking into account current opinion as to the composition of interstellar dust, the observations may be explained by the presence of impurities in either silicate grains with effective radii of about 120 nm, or possibly graphite grains about 50 nm in radius coated with a thin dielectric condensate. None of the observed profiles are at variance with the hypothesis that all the lines arise from the same impurities in the same type of grains. The concentration of such impurities needed to reproduce the observed line profiles and strengths is only about one in 104 atoms in the grain.  相似文献   

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