The inverse planetary problem: a numerical treatment

The so-called inverse planetary problem can be stated as follows: given the distances from the centre, masses, and radii of (say) three planets of a planetary system, find the optimum polytropic index, mass, and radius of their star, and also other quantities of interest, which depend either explicitly or implicitly on the foregoing ones (e.g., central and mean density, central and mean pressure, central and mean temperature, etc.). It is hereafter tacitly assumed that the system is opaque with respect to observations concerning periods of planetary otbits; hence, we cannot have any relevant estimates due to the well-known period laws. In the present paper, the inverse planetary problem is treated numerically on the basis of the so-called global polytropic model, developed recently by the first author.     

Thermal conduction and modeling of static stellar coronal loops

We have modeled stellar coronal loops in static conditions for a wide range of loop length, plasma pressure at the base of the loop and stellar surface gravity, so as to describe physical conditions that can occur in coronae of stars ranging from low mass dwarfs to giants as well as on a significant fraction of the Main-Sequence stars.Three alternative formulations of heat conduction have been used in the energy balance equation, depending on the ratio ₀/L _Tbetween electron mean free path and temperature scale height: Spitzer's formulation for ₀/L _Tless than 2 × 10^–3, the Luciani, Mora, and Virmont non-local formulation for ₀/L _Tbetween 2 × 10^–3 and 6.67 × 10^–3 and the limited free-streaming formulation for ₀/L _Tlarger than 6.67 × 10^–3.We report the characteristics of all loop models studied, and present examples to illustrate how the temperature and density stratification can be drastically altered by the different conductivity regimes. Significant differences are evident in the differential emission measure distribution vs temperature, an important observable quantity. We also show how physical conditions of coronal plasma, and in particular thermal conduction, change with stellar surface gravity.We have found that, for fixed loop length and stellar gravity, a minimum of loop-top plasma temperature occurs, corresponding to the highest value of base plasma pressure for which the limited free-streaming conduction occurs. This value of temperature satisfies the appropriate scalingT 10^–9 L g, in cgs units.     

Quasi-periodical structures in the galaxy populations: mass and luminosity functions for the cluster galaxies

A search and estimation of the statistical significance of the quasi-periodical structures (QPS) has been carried out: for the luminosity function of the galaxies in a few rich clusters; for the integrated mass function of galaxies in the superclusters identified via = 21 cm observations. Some statistically significant QPS have been revealed. The periods for these structures are in agreement between each other, at this basis the hypothesis has been proposed that an effect of the QPS at the level of galaxies has some universal character. Frequency doubling has been discovered for these QPS.     

Radiation pressure effects in the oscillations of compressible rotating homogeneous spheroids

Earlier models of compressible, rotating, and homogeneous ellipsoids with gas pressure are generalized to include the presence of radiation pressure. Under the assumptions of a linear velocity field of the fluid and a bounded ellipsoidal surface, the dynamical behaviour of these models can be described by ordinary differential equations. These equations are used to study the finite oscillations of massive radiative models with masses 10M and 30M in which the effects of radiation pressure are expected to be important.Models with two different degrees of equilibrium are chosen: an equilibrium (i.e., dynamically stable) model with an initial asymmetric inward velocity, and a nonequilibrium model with a nonequilibrium central temperature and which falls inwards from rest. For each of these two degrees of equilibrium, two initial configurations are considered: rotating spheroidal and nonrotating spherical models.From the numerical integration of the differential equations for these models, we obtain the time evolution of their principal semi-diametersa ₁ anda ₃, and of their central temperatures, which are graphically displayed by making plots of the trajectories in the (a ₁,a ₃) phase space, and of botha ₁ and the total central pressureP _c against time.It is found that in all the equilibrium radiative models (in which radiation pressure is taken into account), the periods of the oscillations of botha ₁ andP _c are longer than those of the corresponding nonradiative models, while the reverse is true for the nonequilibrium radiative models. The envelopes of thea ₁ oscillations of the equilibrium radiative models also have much longer periods; this result also holds for the nonequilibrium models whenever the envelope is well defined. Further, as compared to the nonradiative models, almost all the radiative models collapse to smaller volumes before rebouncing, with the more massive model undergoing a larger collapse and attaining a correspondingly larger peakP _c.When the mass is increased, the dynamical behavior of the radiative model generally becomes more nonperiodic. The ratio of the central radiation pressure to the central gas pressure, which is small for low mass models, increases with mass, and at the center of the more massive model, the radiation pressure can be comparable in magnitude to the gas pressure. In all the radiative models, the average periods as well as the average amplitudes of both thea ₁ andP _c oscillations also increase with mass.When either rotation or radiation pressure effects or both are included in the equilibrium nonradiative model, the period of the envelope of thea ₁ oscillations is increased. The presence of rotation in the equilibrium radiative model, however, decreases this period.Some astrophysical implications of this work are briefly discussed.     

Spectrophotometric studies of two Be stars,α Leo and 17 Tau

The present work deals with spectrophotometric studies of two Be stars ( Leo and 17 Tau) using 74 telescope at Kottamia observatory.The results obtained revealed the presence of variations in the general shape and the equivalent width of the profiles of hydrogen lines in the spectrum of both stars within short period interval.     

The effect of Antarctic O3 decline on night airglow intensity of Na5893Å, O5577Å, OH emissions and its correlation with total solar flare numbers

The paper presents the effect of O₃ depletion on different night airglow emission lines. Calculations based on chemical kinetics show that the airglow intensity of Na5893Å, O5577Å and OH band emissions will also be affected due to the depletion of O₃ concentration. Intensity of Na5893Å is calculated theoretically for Halley Bay (76° S,27° W), British Antarctic Survey Station, during the period 1973 to 1984. It is concluded from the covariation of different emission lines that O5577Å and OH emissions also follow the same trend of variation. A study has been made to find the correlation between the depletion of O₃ concentration and total solar flare numbers. Important results are as follows:

Chemical abundance behavior of type I planetary nebulae

In this work 13 Planetary Nebulae have been classified as Type I according to Peimbert's criteria (Peimbert, 1978). These objects have been added to a previous sample (Maciel and Faúndez-Abans, 1985) and diagrams of O/H versus N/H, S/H, Ne/H and Ar/H, as well as N/H versus S/H, Ne/H and Ar/H have been drawn. All of them exhibit a tendency for linear correlation; moreover, the behavior of O and N versus Ar and S are very similar, with approximately the same slope. When the excitation class parameter was included in the diagrams, no clear tendency can be discerned, for any class.     

Solution of a transfer equation by a Modified Spherical Harmonic Method in a thin anisotropically scattering atmosphere

Wan, Wilson and Sen (1986) have examined the scope of Modified Spherical Harmonic Method in a plane medium scattering anisotropically. They have used the phase functionp(µ, µ) = 1 +aµµ. In this paper, the Transfer Equation has been solved by the Modified Spherical Harmonic Method using the phase functionp(µ, µ) = 1 + ₁ P ₁(µ)P ₁(µ) + ₂)P ₂(µ)P ₂(µ) and a few sets of numerical solution have been predicted for three different cases.     

Effect of temperature gradient on the wave propagation in a self-gravitating medium and its role in the central region of our Galaxy

The wave propagation in a finitely conducting, self-gravitating, non-relativistic hydromagnetic medium with temperature gradient and a heat-energy transport into it has been considered. Firstly, a General Dispersion Relation (G.D.R.) has been derived. The interest has been kept limited for the study of one dimensional wave propagation in a typical medium where magnetic field and it's gradient, density gradient, temperature gradient are all along the direction of wave propagation. The D.R. of such a medium follows from G.D.R. In particular, the effect of temperature gradient on the wave propagation has been studied. Analytical expressions for the wave parameters have been derived under different conditions. It has been found that the longitudinal waves could be sufficiently energetic for being unstable by the temperature gradient. Further, the modified Jeans' criterion (depending on temperature gradient), a criterion important for stability, has also been obtained.On assuming the gas medium in the central region ( 10 pc) of our Galaxy to behave like hydromagnetic fluid, and the direction of wave propagation (z-direction) as the direction perpendicular to the Galactic plane, few numerical estimations for the wave parameters (like wave lengths, phase velocity, etc.) have been made (as application of the above theoretical discussions). It has been found that the phase velocity of longitudinal waves at 1 pc level is at least 170 kms^–1 while at the 10 pc level the longitudinal waves of length less than a parsec may propagate smoothly through the medium. It has been suggested that (i) in the central region ( 10 pc) of our Galaxy the temperature gradient could be one of the major causes of the mass-outflow along the direction perpendicular to the Galactic plane (ii) outside the central region ( 10 pc) of our Galaxy, there may be long term consequences of such mass-outflow like Halo formation.     

Adsorption of fluoride on goethite surfaces-implications on dental epidemiology

Fluoride ion interaction with synthetically prepared goethite has been investigated over a range of pH values (4–9) and F^– concentrations (10^–3–10^–5 M). The amount of F^– retained by goethite suspensions was found to be a function of pH, media ionic strength, F^– concentration, and goethite concentration. The lowest ionic strength (0.001 M KNO₃) gave the highest adsorption medium. Uptake was minimal at pH >7 and increased with decreasing pH. Thermodynamic properties for fluoride adsorption at 298 K and 323 K were investigated. The isosteric heat of adsorption (H _r) was calculated and the heterogeneity and homogeneity of the surface examined for goethite. In view of the importance of fluoride in dental health, the interaction of fluoride on goethite in the physical environment has important implications on dental epidemiology.