General-relativistic hierarchical cosmology: An exact model

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.     

Spatial density fluctuations in the radiation era of the Universe

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.     

Detection of background gravitational radiation by Doppler tracking of spacecraft

Low-frequency gravitational radiation, with wavelengths reaching or exceeding interplanetary distances, and with a mean energy density of the order of the critical cosmological density _c , generates a frequency-shift of order/10^–15 h ₀(1/10⁸km)(/ _c )^1/2 in electromagnetic signals transponded by interplanetary spacecraft at a distancel from the Earth.     

A differential equation for the classical collapse problem

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.     

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.     

A relation in families of periodic solutions

We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form T/A=–/E, whereT is the period,A is the angular momentum, is the angle through which the system has rotated after one period, andE is the energy.     

Linearly expanding universes in JBD-theory

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.     

On the interplanetary cosmic-ray scintillations

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.     

Phase relation between the poloidal and toroidal solar-cycle general magnetic fields and location of the origin of the surface magnetic fields

The phase relation of the poloidal and toroidal components of the solar-cycle general magnetic fields, which propagate along isorotation surfaces as dynamo waves, is investigated to infer the structure of the differential rotation and the direction of the regeneration action of the dynamo processes responsible for the solar cycle. It is shown that, from the phase relation alone, (i) the sign of the radial gradient of the differential rotation (/r) can be determined in the case that the radial gradient dominates the differential rotation, and (ii) the direction of the regeneration action can be determined in the case that the latitudinal gradient (/) dominates the differential rotation. Examining the observed poloidal and toroidal fields, it is concluded that (i) the / should dominate the differential rotation, and (ii) the determined sign of the regeneration factor (positive [negative] in the northern [southern] hemisphere) describing the direction of the regeneration action requires that the surface magnetic fields should originate from the upper part of the convection zone according to the model of the solar cycle driven by the dynamo action of the global convection.     

Comparison between stability limits for satellite motion

Numerical and analytical comparisons are made between three methods of obtaining stability information on satellite motion using the model of the restricted problem of three bodies. Kuiper's (1961) and Szebehely's (1978) approximate results are compared with computer solutions obtained by successive iterations. The three methods show close agreement regarding the maximum values of the orbital radii for stability. The lowest result and therefore the most conservative estimate is obtained by the simplest formula, _max=(/81)^1/3 where is the ratio of the satellite's orbital radius to the distance between the primaries with massesm ₁>m ₂ and is the mass-ratio given bym ₂/(m ₁+m ₂).     

Космическое черенковское излучение

, . N/E, E _r, (E _r)=1. , (, ) . .     

The interrelationship between cosmic dust and the microwave background

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.     

The latitude of filament bands at the sunspot minimum and the activity level in the two following 11-year solar cycles

The zonal structure of the distribution of filaments is considered. The mean latitudes of two filament bands are calculated in each solar hemisphere at the minima of the sunspot cycle in the period 1924–1986: middle latitude _{2, m} and low latitude _{1, m} . It is shown that the mean latitude of the filament band _{2, m} at the minimum -m of the cycle correlates, with = 0.94, with the maximum - M sunspot area S(M) and maximum Wolf number W(M) in the succeeding solar cycle M. It is shown that the mean latitude of the low-latitude filament band _{1, m} is linearly dependent on the mean latitude filament band _{2, m + 1} at the succeeding minimum. We found a correlation of the latitude of the low-latitude filament band _{1, m} with the maximum sunspot area in the M + 1 cycle. This enables us to predict the power of two succeeding 11-year solar cycles on the basis of the latitude of filament bands at the minimum of activity, 1985–1986: W(22) - 205 ± 10, W(23) - 210 ± 10. The importance of the relationships found for theory and applied aspects is emphasized. An attempt is made to interpret the relationships physically.     

Plane and cylindrical hydromagnetic shock waves

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.     

Central holes in disks of spiral galaxies

On the basis of the solutions obtained in the previous paper, the changes in the scenario of the standard model of the Big Bang are found. The chaos degree (constrainst on fluctuation spectra) is obtained, which could be still preserved by the initially completely chaotic Universe at the time of light elements nucleosynthesist _es. The time boundaries of hadron and lepton eras and the time the electron neutrinos and neutrons become frozen in reactions of weak interaction may be shifted up to 1.4 times. The corresponding temperatures may shift off from the standard ones 0.88 times if the mean-square level of fluctuations is close to unity. If the density of the energy of fluctuations concentrated in the short-wave region of the spectrum is less than 1.5 ^– , the nucleosynthesis leads to a helium abundance coinciding with the observe one. If at the timet _es the maximum of the spectral density of the energy is in the long-wave region, that is _max ct _es the level of the chaos during the period of nucleosynthesis is restricted to 1.76 (where |C _K |² d³ K,C _K is Fourier component of the amplitude of metric fluctuations). In particular, the protogalactic vortical disturbances with a wide spectrum 4 × 10^{3 -1}( = K/K, = /_crit) are compatible with the observed helium abundance.     

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¦ .     

Coronal temperatures and temperature gradients from OSO-7 spectroheliograms

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.     

The effect of luminosity-redshift correlation on the analysis of the angular size-redshift relation for radio galaxies

The variation of radio luminosity with redshift and its effect on the analysis of the angular size-redshift ( –z) relation for a bright radio source sample (s ₁₇₈ 10Jy) has been investigated. By assuming a power law dependence of luminosity on redshift of the formP (1 +z), it was found that 4.4 (with correlation coefficientr 0.99) for at leastz 0.3. Correction for such a strongP – (1 +z) correlation when considering the –z data for the sample led to a steeper –z slope. This could be explained by assuming linear size evolution of the formD (1 +z)^–n withn = 2.8 – 3.3 consistent with both theoretical results and those obtained for more homogeneous source samples.     

Annihilation radiation from thermal electron-positron plasma on the ground Landau level: The case of low magnetic fields

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.