A study of massive classical polytropes in general relativity

A detailed study of classical polytropes in general relativity has been presented for _O ((dP/dE)_O) 1.0 and _O((P/E _O)_O. The behaviour of various structural parameters with _O/_O, _O and _O are the values ofP/E and dP/dE at the centre) has been studied. The most important result of this study is the fact the qualitative behaviour of all the structural parameters depends only on the value of µ_O for the various assigned _O values. The maximum value of surface red shift occurs when µ_O=0.6 and for _O=1.0 it equals 0.618. These structures are gravitationally bound for µ_O0.8 and most so for µ_O=0.4. The maximum value of binding coefficient comes out to be 0.181 when _O=1.0. These structures have been used to model neutron stars. The maximum mass of neutron star based upon such a model comes out to be 2.55M (for µ_O=0.4 and _O=1.0) and maximum size comes out to be 15.0 km (for µ_O=0.2 and _O=1.0). It is also seen that the structures are pulsationally stable for µ0.6.     

Dissipative MHD solutions for resonant AlfvÉn waves in 1-dimensional magnetic flux tubes

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfvén waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfvén waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for _r , andP across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for _r , andP in terms of double integrals of Hankel functions of complex argument of order with compact analytical solutions that allow a straightforward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpendicular to the magnetic field lines which enables us to determine the dominant dynamics of resonant Alfvén waves in dissipative MHD.     

Covariance function analysis and the clustering of galaxies

Data on a statistic derived from the angular covariance function show that (contrary to the claim of Peebles that galaxies are distributed continuously with no distinct scales), superclusters and the maximum size of clusters are probably defined at scales of 15 and 2.0h ^–1 Mpc. This suggests some stepped-density profile like the idealized models of de Vaucouleurs and Wertz: consideration is therefore given to a semi-continuous hierarchy in which there are galaxies outside clusters, clusters outside superclusters etc. Theories of the origin of clustering by gravitational clumping and the escape of galaxies from clusters suggests the hypothesis that the average mass (m _g) of galaxies outside clusters is smaller than that of those inside (=fractionf of the total), a hypothesis supported by results on the continuity of the angular and spatial covariance functions. In a semi-continuous hierarchy, the overall packing fractionf _e and the fraction (1-f) of galaxies outside clusters both appear to increase as the distancer from a local origin increases, because a line-of-sight to greater depths intersects systems of the hierarchy of continually greater size (R _i). If the hypothesis is valid thatm _g inside clusters is slightly larger thanm _g outside, the apparent effect is to makem _g systematically distance-dependent from a local origin with and ₁0.3. No direct data on galaxy masses exist to refute such a small trend, but since the absolute magnitudes of galaxies are known to be correlated (very weakly) with their masses, a semi-continuous hierarchy has a location-dependent luminosity function, (M). Within uncertainties as to the steepness of (M) at the bright end, the model is consistent with optical number counts to a limiting photographic magnitudem _pg (isotropic slope,q=0.6; semicontinuous modelq=0.64; observation,q=0.67±0.03, standard error.) this removes the discrepancy between the determinations by de Vaucouleurs and Sandageet al. of the thinning factor (1.7). Predictions of the semi-continuous model are made which are at present observationally feasible to carry out. In particular, it is predicted thatq(20<|M|<22)/q(14<|M|<19)2(±0.2).     

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 .     

A study of the wavelength dependence of interstellar polarization using a scanning spectropolarimeter

A scanning spectropolarimeter has been constructed and used in a preliminary search for conspicuous features of the interstellar polarization curve between ^–1 = 1.58 ^–1 and 2.50 ^–1. The instrument was used at thef/4.5 prime focus of the 36 telescope of the Cambridge University Observatories. Scans were made on HD2905, HD21389, And and Tau with slitwidths of 50 Å and 100 Å.The commonly adopted method of correcting for instrumental polarisation by using observations of unpolarized stars has been applied. The normalized polarization curves corrected for instrumental polarization for HD2905 and HD21389 reveal a feature near ^–1 = 1.68 ^–1 which is most probably of insterstellar rather than instrumental origin.     

Radiation from a strongly-magnetized plasma: The case of predominant scattering

On the basis of diffusion approach for normal modes, solutions of the radiative transfer problem are obtained and analysed for an optically thick tenuous plasma with a strong magnetic field. The case is considered when the scattering processes without change of photon frequency are dominant. The radiative transfer coefficients as well as spectra, angular dependences and polarization of the outgoing radiation are investigated in detail for a cold plasma,kT _emc ², |–s _B|kT _e/mc ² )^1/2|cos|, whereT _e is the electron plasma temperature, _B=eB/mc the electron cyclotron frequency,s=1,2,... the number of cyclotron harmonic and the angle between the magnetic field and wave vector. The effects of electronpositron vacuum polarization are taken into account and shown to be very significant. Simple analytic solutions are obtained for various limiting cases (small and large vacuum polarization; high, low and close to the cyclotron resonance radiation frequencies; different orientations of the magnetic field, etc). The results obtained are necessary for analysing X-ray and gamma-ray radiation from strongly magnetized neutron stars.     

The significance of spatial curvature for energy output of remote quasars

There is a brightening effect of quasar outputs due to the positive curvature of space in the static Universe, if we use the right expression of distance as an arc³r=R , and not the corrected luminosity distance ofr=Rsin.     

A study of the contrast of sunspots from photometric images

The thermal contrast , and the umbra-penumbraA _u/A _p, were calculated for 63 sunspots of various sizes and morphologies. Contrary to the assumptions of the PSI model, andA _u/A _p were found to be quite variable. The values of ranged from 0.1807 to 0.4266;A _u/A _p ranged from 0.0089 to 0.4899. The values of andA _u/A _p correlated well (r = 0.6018;p<0.005) and the regression for andA _u/A _p was obtained: = (0.220 ± 0.016) + (0.340 ± O.06)A _u/A _p. The values of andA _u/A _p were then compared with complexity ratings, magnetic field strength, time, and . The quantities andA _u/A _p were found to be independent of the complexity, magnetic field strength, and time factors. The correlation between andA _u/A _p lead to the proposed division of into an umbral thermal contrast _u, and a penumbral thermal contrast _p. These values were calculated from the photometric data: _u = 0.57 ± 0.01 and _p = 0.26 ± 0.006.     

Apparent radii and other parameters for 416 B5 V-F5 V stars of the catalogue of the geneva observatory

Apparent radius, visual brightness, effective temperature and absolute radius for 416 B5 v-F5 v stars of the catalogue of the Geneva Observatory (Rufener, 1976) have been determined.Twenty-eight stars, anomalous in log versus (m _v)₀ diagrams, have been singled out. A good correlation for seven stars, in common with the list of Hanbury Brownet al. (1974), has been found. Similar parameters determined for 279 B5 v-F5 v stars of two preceding papers (Fracassiniet al., 1973, 1975) have allowed us to determine the averaged diagrams logq _v/q, logR/R and logT _e versus (B-V)₀ for 695 B5 v-F5 v stars.Moreover, in the present paper a good correlation logq _v/q versus logR/R and careful relation M _v=–7.40logR/R +3.31 for B5 v-F5 v stars have been determined. Plain correlations between logR/R and blanketing parameterm ₂ for some spectral types seem to point out that there arereal differences in the absolute radii of stars of thesame spectral type, in agreement with recent researches on the HR diagram (Houck and Fesen, 1978).Systematic differences between double (spectroscopic and visual) and single stars are found. In particular, the averaged relation m ₂ versus logR/R shows that A2 v-F5 v double stars may have a higher metallicity indexm ₂ and smaller absolute radii than single stars. Finally, the diagram logv sini versus logR/R confirms some properties of binary systems found by other researchers (Huang, 1966; Plavec, 1970; Levato, 1974; Kitamura and Kondo, 1978).Thesis for the degree in Applied Physics.     

Compact,variable sources on the Sun at 2 centimeter wavelength

Very Large Array (VLA) observations of compact transient sources on the Sun at 2 cm wavelength are presented. These sources have angular sizes of 5–25, brightness temperatures of T _B 1–3 × 10⁵ K, and lifetimes ranging between a few minutes to several hours. The emission originates in regions of diffuse plage and quiet Sun, where the photospheric magnetic fields are relatively weak (H 100 G). In some cases the 2 cm radiation may be explained as the thermal bremsstrahlung of a dense (N _e 10¹⁰ cm^-3) plasma in the transition region. For other sources, the relatively high circular polarization ( _c 40–50 %) suggests a nonthermal emission mechanism, such as the gyrosynchrotron radiation of mildly relativistic electron with a power-law spectrum.     

Spectral investigation of some Be stars for NRP variability

Spectroscopic observations of the Be stars Eri, Oph, 66 Oph, and Ori for the period 1982–1988 are reported. The NRP hypothesis was verified on the ground of rapid line profile variability, radial velocities, and equivalent widths. The star Eri is pulsating in bothl=2 andl=8 with period 0 _. ^d 7. Pulsation in modesl=2 andl=4 are observed in Hei profiles of Oph for May 1982. For radial velocities has been obtained a period 0 _. ^d 913. The H and H lines of 66 Oph for April–August 1983 are in emission state with two clearly expressed components with intensity variations. All the parameters measured have the same period of variation — 0 _. ^d 025. For Ori variations in line profiles for component Ab have been observed and a period of 0 _. ^d 463 found for the radial velocities.     

Some families of periodic oscillations in the restricted problem with small mass-ratios of three bodies

This paper reports on the numerical determination of families of periodic oscillations in the case =0.000 95 of the restricted problem. The families emanating out of the collinear Lagrangian pointsL ₁,L ₂,L ₃ are examined as well as some asymmetric periodic oscillations related to them. An effort is made to complete the global picture of simple-periodic symmetric oscillations in the present case of the problem (the S-J case). This is done by examining the orbits with initial conditions such that the infinitesimal body starts from a position on the ₁-axis (₀₂ = 0) with a negative initial velocity perpendicular to this axis . In a previous article this investigation has been carried out for negative values of ₀₁, where the position of the small primary defines ₁=0. Now we proceed to consider orbits with ₀₁>0. The phase portrait of asymmetric periodic orbits is also examined.     

Additional results for unstable stratified toroidal magnetic fields in stars

General conditions for adiabatic instability of weak axisymmetric toroidal magnetic fields are obtained. In particular all fields which haveH =0 and H ² />0 simultaneously are unstable. This includes all fields which exist near to the axis of symmetry and, indeed, any without an infinite current density anywhere. A detailed discussion is given of fields with an angular dependenceH ² |P (cos )|. These fields are dynamically unstable with respect to both axisymmetric and non-axisymmetric perturbations for all values of the azimuthal wave number |m|. The maximum growth rates are independent ofm and they are largest for the fields that are defined in the regions closest to the polar axis.     

Depolarization of solar bursts due to scattering by low-frequency waves

The possibility is explored that fundamental plasma emission in solar radio bursts of types I, II, and III is depolarized due to scattering off low-frequency waves. Three ways in which depolarization might occur are identified: (1) one or several large-angle scatters, (2) several small-angle scatters close to the plasma level, and (3) many small-angle scatters well above the plasma level. It is pointed out that the degree p of polarization (p = 1 initially) may be approximated by p() = cos after one large-angle scatter through an angle , and that for backscatter ( > /2) the sense of polarization changes (from o-mode to x-mode senses). Possibility (2) involves coupling between the o- and x-mode components through their longitudinal parts, and is explored in some detail. The wave vectors k required for the scatterings are identified, and it is suggested that ion-sound waves are suitable for possibility (1) and whistlers for possibility (2). The whistlers may be generated by the streaming electrons themselves.Large-angle scattering is favourable for depolarizing type I emission, as proposed by Wentzel, Zlobec, and Messerotti (1986). Scattering by whistlers near the plasma level is favourable for depolarizing type III bursts. Several predictions are made based on these possibilities.     

Photoionization models of QSO's intervening absorption clouds

A new sufficiently compact code LINESPEC is described which is designed to determine the kinetic (collisional+photo) ionization equilibrium in a slab of a hot (T10⁴K) rarefied gas, and to simulate synthetic absorption-line spectra formed due to passing continuous radiation (from a quasar) through the slab. Eighty-six resonant absorption lines of ions and atoms of H, He, C, N, O, Ne, Mg, Al, Si, S, Ca, Fe are included with wavelengths in the range 9125000 Å. the behaviour and observability of various lines are analysed as a function of intensity of the ionizing radiation and kinetic plasma temperature (for a power-law spectrum of ionizing photons,N _ph (E) E ^– with =1.5;E is photon energy). For the purely collisional ionization (N _ph =0), the spectrum contains various combinations of absorption lines of hydrogen and/or of atoms and ions of other elements, the relative intensities of the lines being strongly temperaturedependent. If the ionizing radiation is intense enough, the L line dominates. In a wide parameter range L may be the only line visible in the UV spectral range.     

Inertia coefficient considerations and the structure of Jovian planets

For Jupiter, an overall density model of the form= ₀(1–x ⁿ ), withn1/3 and , is consistent with information presently at hand; for Saturn, however, such a density law would lead to unacceptably high densities in the vicinity of the centre. The limiting cases of the previous law are shown to ben=+, corresponding to a homogeneous sphere, andn=–3, corresponding to a particular central particle model, investigated by a number of astronomers over the last hundred years. Forn0, the central density becomes +. Another possible representation, valid both for Jupiter and Saturn, is the density law= ₀(1–x) ^m ), with in the case of Jupiter, and in the case of Saturn. Graber's density law based on a maximum entropy principle leads to unacceptably high surface densities, both for Jupiter and Saturn. Finally, the paper investigates the problems involved in fitting two-layered parametrically simple density laws to theoretically derived much more elaborate models of the Jovian planets.     

Stability of the triangular libration points of the circular restricted problem in the presence of resonances

The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ₁ = 2₂ and ₁ = 3₂. The motion is unstable for all the values of parameters q and A when ₁ = 2₂ and the motion is unstable and stable depending upon the values of the parameters q and A when ₁ = 3₂. Here q is the radiation parameter and A is the oblateness parameter.     

On the origin of type III fundamental

A two-component scheme for the generation of type III fundamental radiation is proposed. The first component of the fundamental arises at a plasma level _{L t} because of the Rayleigh scattering of the plasma waves into electromagnetic radiation. The other component arises at _{L t} /2 because of the decay of the first component into plasma waves and the subsequent rescattering of the plasma waves into electromagnetic radiation _t 2( _t /2). By its properties (location, directivity, polarization) the second component is essentially the same as the second harmonic radiation produced by a stream of fast electrons at _L ( _t /2). This scheme is used to solve the main problems (localization and directivity of the source, polarization of type III fundamental) of the harmonic theory of type III solar bursts.     

Linear waves in a radiating and scattering grey medium

The problem on linear waves in a radiating and scattering grey medium is studied using Whitham's method. Analysis of the basic equations distinguishes two limiting cases: the one is theequilibrium case in which the energy exchange between the gas and radiation plays an essential role, and the other is theScattering case in which the effect of energy exchange is negligible. A new type ofradiation acoustic wave with the speed is found in the scattering case. The governing equations for linearized one-dimensional flow are reduced to one equation of radiative acoustics valid to order 1/c, and the criterion for the two limiting cases is derived from studying this equation. The harmonic solution is analytically studied to show that theeffective optical depth corresponding to the wavelength of perturbation gives the measure of the interaction between the gas and radiation. When _eff1, the sound speeda _g ² =P _g / and the propagating speed of radiative disturbancea _f ² =fc ² appear as the modified classical and radiation-induced modes respectively, wheref is the Eddington factor. When _eff1, the isentropic sound speeda _s ² =(P _g +P _r / appears in the equilibrium case, and the radiation acoustic speeda _A ² appears in the scattering case. The dispersion relation of the harmonic solution is numerically calculated. The result shows that the wave pattern depends critically on the ratio=P _g /(P _g +P _r ). When , the speeda _S anda _A arise from the modified classical mode, and when , they originate from the radiation-induced mode.