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.     

Approximate expressions for Gyrosynchrotron radiation in Transverse Propagation

Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity _–/BNand absorptivity _– B/Nfor e-mode, effective temperature T _effand frequency of peak brightness _p. The expressions are designed for the range 2 to 7 of electron energy spectral index and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=/_B). Their statistical error is, respectively, ±18% and ±29% for _–/BNand _– B/Nfor 10/_B100, ±128% and and ±170% for 2/_B10.     

A Razin-Tsytovich effect for bremsstrahlung

It is shown that bremsstrahlung from electrons with Lorentz factor 1 is suppressed for >_p in a plasma with plasma frequency _p compared with emission in vacuo. For _p the ratio of the power emitted per unit frequency in the plasma to that in vacuo varies as ².This suppression effect is analogous to the suppression of synchrotron radiation in a plasma (Razin-Tsytovich effect). It is argued that such suppression is a characteristic property of emission by relativistic particles in a plasma.     

Circular Polarization of Starlight

Of the 7500 stars cited in the Catalog of starlight polarization, those which satisfy the condition P _obs % and A _V 0^m.5 are selected. It is presumed that the selected stars (n=216) have circularly polarized light.     

Models of clusters of point masses with large central redshifts

Conclusions In the Newtonian case we have obtained an isotropic self-consistent distribution of gravitationally interacting point masses which satisfies the transport equation without collisions, and the gravitational equation for an arbitrary powerfunction density distribution =r^–s, s<3.For =r^–2 the analogous self-consistent solution was obtained for the anisotropic distribution function both in Newtonian and GTR cases.The GTR solutions with =r^–2 have central redshifts which increase without limit in accordance with the law 1+zr^–1/ as we approach the center. In the isotropic case, they appear to be stable when the mean velocities are much less than the velocity of light u<0.2c, >21.The hydrodynamic GTR solution was found for a perfect gas at constant temperature (but variable T=T(g₀₀)^1/2) which also has z for r0.We should like to thank K. Thorne, L. Hazin, and M. Podurets for valuable discussions. K. Thorne was particularly helpful in supplying unpublished results on circular orbits obtained by American authors.Astrofizika, Vol. 5, No. 2, pp. 223–234, 1969     

Early cosmological models in Lyra's geometry

A spatially homogeneous and isotropic Robertson-Walker model withzero-curvature of the universe is studied within the frame-work of Lyra'smanifold. The gauge-function in Lyra's manifold is taken to betime-dependent. Exact solutions of Einstein equations are obtained for twodifferent early phases of the universe viz. Inflationary phase andradiation-dominated phase by using `gamma-law' equation of statep = ( - 1) . The -index, describing the material content,varies continuously with cosmic time so that in the course of itsevolution, the universe goes through a transition from an inflationaryphase to a radiation-dominated phase. The physical properties of themodels are also discussed.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

Neutron-phonon interaction in neutron stars: Phonon spectrum of Coulomb lattice

The phonon excitation spectrum of Coulomb lattice in the neutron star crusts is studied by solving Dyson's equation for phonons. It is shown that a strong renormalization of the phonon spectrum occurs at densities _s /4 for the crustal matter compositions with spherical nuclei, which imply relatively small nuclear mass numbers and charges. It is shown that, the lattice becomes unstable against density fluctuations above a critical density of the order of _s /3, where _s 2.6x10¹⁴ g cm^–3 is the nuclear saturation density. The neutron quasiparticle spectrum and the virtual mass of a nucleus are briefly discussed.     

The proton-proton reaction and related reactions in an intense magnetic field

The reaction rates for the proton-proton reaction and the related electron capture reaction in a strongly magnetized relativistic electron gas of arbitrary degree of degeneracy are computed. The proton-proton reaction rates are unaffected by the presence of the magnetic field for field strengths up to the critical valueH _q =m ² c ³/e=4.414×10¹³G. For fields greater thanH _q , the proton-proton reaction rates are enhanced linearly with (=H/H _q ).The PeP reaction is investigated in detail for a wide range of temperatures, densities and magnetic field strengths that are of interest. The main results are as follows: In the non-degenerate regime the reaction rates are significantly reduced for high temperatures (T ₉5) and low fields (1). For instance, _pep(H)=0.04 _pep(O) at =10^–3,T ₉=10. For relatively high fields (>1) and low temperatures (T ₉2), the reaction rates are enhanced approximately linearly with . In the complete degenerate regime the reaction rates are reduced up to one-third of the field-free value for moderate densities (₆/_e10). At high densities (₆/_e10) the reaction rates are unaffected by the magnetic field.     

Three-component fluid model of the universe of critical density

A three-component fluid model of the Universe during the recombination era is analysed for = _c ( _c is the critical density). In addition to the well-known instability of the Jeans mode at 10⁹ M , we find two more unstable modes at 10¹² M .     

Kelvin-Helmholtz instability of composite plasma in an oblique magnetic field with resistivity

Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = K _g , = _g c ².Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (, ), (,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density _g to the central density _gc , _g / _gc ; pressureP to the _gc ,P/ _gc ; and the metric componente ^–, for three representative general relativistic (GR) isothermal configurations =0.1, 0.2, and 0.3. Figure 4 shows the solution curve (, ) for =0.1, 0.2, and 0.3 (=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4r ² P ^*(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of =0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c ² to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P _c , binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.Part of the work done at Azerbaijan State University, Baku, U.S.S.R., and Mosul University, Mosul, Iraq, 1985-1986     

The jeans instability criterion for a compressible fluid including viscosity and heat conduction

For the region after the recombination era of the Universe the hydrodynamical density waves are analyzed including shear viscosity and heat conduction for =_c as well as for <_c(_c is the critical density of the Universe). Very near to the end of the recombination era (z=1200) we find the well-known Jeans instability. It is shown that the influence of the shear viscosity on the instabilities in negligible, however, a visible influence of the bulk viscosity is present.     

The blanketing in the rocket ultraviolet from 225.2 to 319.6 nm

The blanketing effect for the solar disc center and its value near the limb (cos = 0.23) are obtained for the rocket ultraviolet region using the Harvard center and limb spectra. The value of for the disc center appears to be 0.67 (on average) relative to the quasicontinuum. The essential decrease of towards the limb is also revealed.     

Some applications of Jacobi dynamics to the stellar evolution

The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR _eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR _eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR _eff one obtains the amounts of actionA _c(M), the effective densities _eff(M)=(M)³(M), the densities of action and of energy (or mean presures in the stellar interior)a _c(M),e _c(M), and the potential energiesE _p(M).The amounts of action areA _cM ^k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density _eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M ^–1.81, (M)M^0.6.The cases for the M stars (e _c(M)M ^–1) and for the A and earlier stars (betweena _c(M)=constant and _eff(M)M ^–1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M M25M .With all this, one can build dynamical HR diagrams withA _c(M), E_p(M), _eff M ^–p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA _c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE _p(M)M ^–p according to the stellar models used here and the observed frequency function (MM _–q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE _p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA _c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.     

Analysis of extreme-ultraviolet spectroheliograms of solar prominences

The optical depth at the head of the Lyman continuum, _H, is determined at a number of positions in three hedgerow prominences using spectroheliograms (5 × 5 resolution) of C III 977, LC 896, and O IV 554 observed with the Harvard experiment on Skylab. At heights greater than 10 above the limb the maximum value of _H is 30 to 50, which occurs at the central part of the prominences. For one of the prominences the determination of _H is found to be consistent with data from spectroheliograms of Mg X 625. The degree of ionization of hydrogen is estimated from the intensity of LC 896 at _H 1. In the central part of a model prominence N _P/N _HI1.9 for a reasonable range of the electron densities, where N _P and N _HI are the proton density and the neutral hydrogen density, respectively.     

Cosmological Primeval Perturbation Spectra in Mildly Non-Linear Regime

The linear equation (2.14) describing the dynamical evolution of density perturbation in an expanding universe is not able to determine the form of power-spectrum |_k|², i.e. the energy distribution with respect to wave numbers k. However, in the case of weak turbulence, we may construct the kinetic equation for the wave modes of an oscillating universe with k > k_J (the Jean wavenumber). For the growing modes with long-wavelength in the range k < k_J after recombination, the perturbations are of vortex-like and their relative amplitudes are large (but we still study the case frac < 1); owing to the non-linear interactions, the system of the perturbations will finally towards a statistical equilibrium. In cases of both above, we obtain the primeval spectra in the form of | <>_k | ² k⁰, which are fitting to the self-similar clustering picture.     

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).     

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.     

Galactic4He and heavy elements enrichment by stellar nucleosynthesis

The contribution to the galactic abundance of He and heavy elements by stellar nucleosynthesis is calculated as a function of time, keeping account of present knowledge about stellar and galactic evolution. A model is used which distinguishes the phase of the contracting halo from the subsequent history of the disc. Various uncertainties involved both in stellar and in galactic evolutionary theory are discussed. The amount of⁴He produced by stars of different masses and ejected in interstellar medium is fairly well known from stellar theory, while we have assumed its primordial abundance as a free parameter, ranging from 0 up to 0.4. We find that stellar activity provides a significant contribution to the cosmic⁴He, though not sufficient to explain the observed abundance. The best agreement with observational data (Y 0.26 andY _now0.28) is obtained starting with a primordial abundanceY =(0.20–0.23), which is consisten with the Big-Bang theory predictions and with recent observational estimates. The contribution to the abundance of heavy elements depends on the last stellar stages and on the final explosion mechanism, which are only now beginning to be understood. Nevertheless, in the framework of present theories, we individuate a stellar evolutionary scheme reproducing the observedZ abundances for Populationi and Populationii stars, with the correctly estimated Y/Z value. In this scheme, only stars belonging to two narrow mass ranges (10m/m 15 andm/m 80) are allowed to eject metal-enriched matter, possibly with the solar (C+O)/(Si+Fe) ratio.