An Infra-Red model of the zodiacal emission

The Infra-Red Astronomical Satellite (IRAS) observations of the zodiacal dust emission are used to fit the dust grain composition and distribution in the ecliptical plane. We obtain a good fit to the data for a density distribution of black-body grains given by p = pr ^{0.66/log(1.7r/R)} for r < 0.87R and r < 3oR     

The determination of a complete sample of open clusters to compare with star clusters in other galaxies

In order to compare star cluster systems in galaxies, and consequently to obtain information on their different modalities of birth and evolution, a homogeneous and complete sample of galactic open clusters is obtained from Lynga's (1983)Catalogue of Open Clusters. This sample consists of 94 open clusters whose projected (onto the galactic plane) distance from the Sun and whose absoluteV-magnitude are smaller than 2 kpc and –4.5 mag, respectively. The completeness of the sample is based only on the usual hypothesis of a uniform projected distribution of the clusters in the solar neighbourhood. Some results concerning the distribution of relevant photometric and structural parameters are presented and discussed.     

Circular radiation by a monopole around neutron stars

Radiation by a monopole which revolves round a neutron star is investigated in detail. Using radiant probabilityW _p ^t (k), we solve the radiant kinetic equation and proliferative equation of a monopole having the distribution functionf _p, and obtain the solution of wave numberN _k ^t (r) and distribution functionf _p. From these solutions, we know when the monopole moves round the neutron star; the exponential radiation is yielded with change of the motive orbit radiusr. As radiusr increases, the radiation appears as a saturated effect.     

Radiative transfer in a cylinder. II. Special problems. Asymptotics

The method of computing the radiation field in an infinite circular cylinder proposed in Part I is now applied to the case of isotropic scattering with sources on the boundary and axis of the cylinder, as well as for a uniform distribution of sources inside the cylinder. For the simplest kernel we obtain exact solutions of the basic integral equation in explicit form. For scattering in a spectral line with complete frequency redistribution and a power absorption profile we develop an asymptotic theory for the case when the optical radius of the cylinder is large. We solve the asymptotic equations for the basic characteristics of the scattering in closed form for conservative scattering and find its asymptotics. We obtain estimates of the mean number of scatterings with a layered source, and also the mean and variance of the number of scatterings with a uniform source distribution.Translated fromAstrofizika, Vol. 37, No. 4, 1994.This work was carried out with the financial support of the Russian Basic Research Fund (grant 93-02-2957).     

Average photon path-length in isotropically scattering finite atmospheres

The determination of the average path-length of photons in a finite isotropically scattering plane-parallel homogeneous atmosphere is discussed. To solve this problem we have used the kernel approximation method which easily allows us to find the derivatives of the intensity with respect to optical depth, optical thickness and albedo of single scattering.In order to check the results we have used another approach by exploiting the set of integrodifferential equations of Chandrasekhar for theX- andY-functions. This approach allows us to find the average path length only at the boundaries of the atmosphere but on the other hand it gives also the dispersion of the path-length distribution function, thus generating the input parameters for determining the approximate path-length distribution function. It occurred that the set so obtained is stable and the results are highly accurate.As a by-product we obtain the first two derivatives of theX- andY-functions with respect to the albedo of single scattering and optical thickness, and the mixed derivative.     

Visual binary systems in the solar neighbourhood: The mass-ratio distribution

Nearby visual binaries, with both components on the Main Sequence, have been considered in order to obtain information about the distribution of their mass ratios. These systems have their primary components ranging from A0 to G9. The data have been corrected for selection effects and the differences V of the visual magnitudes have been transformed into mass-ratio values.The frequency distribution of the mass ratios appears to be bimodal, with a peak around unity and a maximum at about 0.25. It is suggested that this feature may be indicative of different mechanisms of formation for wide binaries.     

On coronal temperatures,temperature gradients and compositions

Average solar wind properties at 1 AU either alone or together with the electron density distribution are used to obtain or review some results that relate coronal temperatures, temperature gradients, and compositions. Measured values of the temperature (T) and the temperature gradient parameter ( = -d ln T/d ln r) are used to find compositions that satisfy the equations used to obtain the results. The total energy equation may be satisfied if the thermal conductivity is reduced by considerable depletions of H⁺ in the corona. The electron energy equation only gives information on coronal compositions that are coupled with d/d ln r. The hydrostatic approximation (momentum equation) for the electron density distribution also appears to require considerable depletions of H⁺ in the corona. Results from the integrated momentum equation for the solar wind support the hydrostatic results; together, they give some information on the minimum value of in the outer corona. Some changes in assumptions or values of parameters that may modify these interpretations are discussed.     

Nonlocal density wave theory for gravitational instability of protoplanetary disks without sharp boundaries

The stability of a self‐gravitating infinitesimally thin gaseous disk rotating around a central mass is studied. Our global linear analysis concerns marginal stability, i.e. it yields the critical temperature for the onset of instability for any given ratio of the disk mass to the central mass. Both axisymmetric and low‐m nonaxisymmetric excitations are analysed. When the fractional disk mass increases, the symmetry character of the instability changes from rings (m = 0) to one‐armed trailing spirals (m = 1). The distribution of the surface density along the spiral arms is not uniform, but describes a sequence of maxima that might be identified with forming planets. The number of the mass concentrations decreases with increasing fractional disk mass. We also obtain solutions in the form of global nonaxisymmetric vortices, which are, however, never excited.     

Correlation between the densities of X-ray sources and interstellar gas

The distribution of X-ray sources in our galaxy is obtained, assuming that the absolute X-ray luminosities of these sources are the same. The distribution is found to be in good correlation with the distribution of interstellar gas. The density of X-ray sources is nearly proportional to the square density of gas. This indicates that X-ray sources are comparatively young. The relation between the densities of X-ray sources and gas allows us to estimate the X-ray intensities of various objects such as Magellanic Clouds and Andromeda nebula, and also to obtain the average X-ray luminosity of spiral galaxies. The latter should increase as the age of a galaxy decreases, since the amount of gas decreases as the galaxy evolves. Under the assumptions that the gas density is inversely proportional to the age and that galaxies older thant ₀/30 are visible in X-rays, wheret ₀ is the present age of the universe, the contribution of X-ray sources in distant galaxies to the background component is calculated. The intensity and the spectrum of the background component of X-rays thus obtained are in fair agreement with observed ones in the energy range between 1 and 4 keV but significantly deviate from the latter at high energies.     

A new method for exact solution of transfer equations in finite media

In this paper we develop a new exact method combined with finite Laplace transform and theory of linear singular operators to obtain a solution of transport equation in finite plane-parallel steady-state scattering atmosphere both for angular distribution of radiation from the bounding faces of the atmosphere and for intensity of radiation at any depth of the atmosphere. The emergent intensity of radiation from the bounding faces are determined from simultaneous linear integral equations of the emergent intensity of radiation in terms ofX andY equations of Chandrasekhar. The intensity of radiation at any optical depth for a positive and negative direction parameter is derived by inversion of the Laplace transform in terms of intergrals of the emergent intensity of radiation. A new expression of theX andY equation is also derived for easy numerical computation. This is a new and exact method applicable to all problems in finite plane parallel steady scattering atmosphere.     

Time dependent monochromatic scattering of radiation in one dimensional media: Analytical and numerical solutions

In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic scattering for sources with an arbitrary spatial distribution and an arbitrary time variation of their power. The Lax-Wendroff method seems to be the most suitable. Because it is assumed that radiation delay is caused by the finite speed of light, the following difficulty arises when the numerical method is used: the region of variation of the variables (position τ and time t) is triangular (the inequality τ ≤ t). This difficulty is overcome by expanding the unknown functions in series in terms of small values of the time and position. By comparing the numerical and exact solutions for a point source with a given time dependence for its power and with pure scattering, the number of steps in the variables required to obtain a desired accuracy is estimated. This numerical method can be used to calculate the intensity and polarization of the radiation from sources in the early universe during epochs close to the recombination epoch. __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 109–123 (February 2008).     

Number-magnitude count for galaxies at the South Galactic Pole

COSMOS measures on a deep UK Schmidt Telescope Plate have been used to obtain the number-magnitude count for galaxies in a field of 14.6 square degrees near the South Galactic Pole. The results are in excellent agreement with data for the North Galactic Pole for galaxies fainter thanB=18.0, indicating no large-scale differences between north and south. A deficiency in numbers is observed for galaxies withB16.0. This is comparable to the deficiency atB17.5 for counts at the North Galactic Pole and supports the suggested asymmetry of the bright galaxy distribution between north and south galactic poles.     

Thermoelastic deformations of the Earth's lithosphere: A mathematical model

We examine the problem of the thermoelastic deformation of a spherical Earth with constant elastic parameters heated from within by the spontaneous decay of radiogenic elements.The problem consists of the simultaneous solution of the Navier-Stokes equation and the heat conduction equation. We reach an integrodifferential equation which we solve by means of the Laplace transform and the Green's function approach.We obtain analytic solutions for the temperature distribution and radial deformation as infinite series of functions of the radial distance and time, depending also on a sequence of eigenvalues. We provide particular solutions for the case when the two specific heats C _p and C _v are approximately equal. p ]We believe that our analytic results are applicable to the study of the oceanic lithosphere deformations. Our approach could be successfully applied to ascertain the deformation according to other regimes of internal heating.     

Numerical simulations of ther 1/4 law

We simulate the evolution of a system of points in a given potential. With a density distribution proportional to r^–n , and a logarithmic potential we obtain a stationary state following ther ^1/4 law of de Vaucouleurs. If we follow this simulation to the Galaxy and to M31, we findn=–4 for the Galaxy andn=–3 for M31.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Bayesian model-independent evaluation of expansion rates of the universe

Marginal likelihoods for the cosmic expansion rates are evaluated using the ‘Constitution’ data of 397 supernovas, thereby updating the results in some previous works. Even when beginning with a very strong prior probability that favors an accelerated expansion, we obtain a marginal likelihood for the deceleration parameter q ₀ peaked around zero in the spatially flat case. It is also found that the new data significantly constrains the cosmographic expansion rates, when compared to the previous analyses. These results may strongly depend on the Gaussian prior probability distribution chosen for the Hubble parameter represented by h, with h=0.68±0.06. This and similar priors for other expansion rates were deduced from previous data. Here again we perform the Bayesian model-independent analysis in which the scale factor is expanded into a Taylor series in time about the present epoch. Unlike such Taylor expansions in terms of redshift, this approach has no convergence problem.     

The luminosity-dependent evolution function of flat-spectrum radio sources at 5 GHz

The numerical method for obtaining the luminosity-dependent evolution function of radio sources is presented and applied to the flat spectrum radio sources selected at 5 GHz.The method constructed on the basis of the iterative one given by Robertson, which requires assuming a specific type of the searched function enables one to obtain the evolution function of sources with radio flux densityS _5.01 mJy.The influence of the shape of the local RLF, of the luminosity distributionN(P) and of the spectral index function on the resulting evolution function is investigated. The results presented show that the luminosity dependence of the evolution function of flat-spectrum radio sources is significant and should not be neglected. The obtained evolution function, which allows one to reproduce the source counts curve, the redshift distribution, and the spectral index distribution, may exhibit the redshift cut-off at z₀3.     

Bianchi Type-1 vacuum models in modified theory of general relativity

In this paper, the problem of spatially homogeneous and an isotropic Bianchi type-1 space time with perfect fluid distribution is considered in Barber's second theory of gravitation. To obtain determinate solutions, we have assumed the equation of statep= γρ, 0 ≤ γ ≤ 1. It is observed that the general fluid distribution degenerates isotropic vacuum model whenγ = 1 and Λ < 0. Further it is observed that the vacuum model obtained in case of γ = 0, ρ = 0 andΛ = 0, reduces to well known Kasner model in Einstein's theory. Some physical and geometrical aspects of the models together with singularities in the models are also discussed This revised version was published online in July 2006 with corrections to the Cover Date.     

An equation for the characteristic curve of a family of symmetric periodic orbits

Szebehely's equation for the inverse problem of Dynamics is used to obtain the equation of the characteristic curve of a familyf(x,y)=c of planar periodic orbits (crossing perpendicularly thex-axis) created by a certain potentialV(x,y). Analytic expressions for the characteristic curves are found both in sideral and synodic systems. Examples are offered for both cases. It is shown also that from a given characteristic curve, associated with a given potential, one can obtain an analytic expression for the slope of the orbit at any point.     

Automated Analysis of Light Curves of OGLE LMC Binaries: The Period distribution

We present a new algorithm, the Eclipsing Binary Automated Solver (EBAS) to analyse lightcurves of eclipsing binaries. To replace human visual assessment, we introduce a new ‘alarm’ goodness-of-fit statistic that takes into account correlation between neighbouring residuals. We apply the new algorithm to the whole sample of 2580 binaries found in the OGLE photometric survey of the LMC and derive the photometric elements for 1931 systems. To obtain the statistical properties of the short-period binaries of the LMC we construct a well defined subsample of 938 eclipsing binaries with main-sequence B-type primaries. Correcting for observational selection effects, we derive the distributions of the fractional radii of the two components and their sum, the brightness ratios and the periods of the short-period binaries. Somewhat surprisingly, the results are consistent with a flat distribution in log P between 2 and 10 days.     

Boltzmann-Fokker-Planck model for the electron distribution function in the Earth's ionosphere

Using Boltzmann-Fokker-Planck methods and the diffusion approximation, we derive coupled non-linear equations for the first two angular moments of the electron distribution function in the Earth's ionosphere. The theory includes a phenomenological treatment of photionization of the neutral species by an externally produced photon flux; electron-ion recombination; electronneutral particle attachment; elastic, excitation, deexcitation, and ionizing electron-neutral particle collisions; and elastic electron-electron and electron-ion collisions. At high and low energies, we obtain approximate analytic solutions for the steady-state electron distribution function. Under certain conditions we also obtain the standard continuous slowing-down formulae for the steady-state electron distribution function in the diffusion approximation.