Nonradial oscillations of a neutron star in an inhomogeneous hydrodynamic model

An inhomogeneous model neutron star with a variable density profile of the type ₀(r)=_c[1–(2/3)r²/R²]exp(–r²/R²) is considered, where _c is the central density, R is the star's radius, and is the inhomogeneity parameter in the radial mass distribution. This parameterization adequately reproduces the results of numerical evolutionary calculations of the density profile and enables one to obtain in analytical form the parameters of hydrostatic equilibrium and the eigenmodes of nonradial oscillations of a nonrotating neutron star, modeled by a spherical mass of incompressible, inviscid liquid. It is shown that a characteristic manifestation of the star's inhomogeneity is the presence of a stable dipole f-mode, the lowest one in the spectrum of natural oscillations. The presence of this mode serves as a general and primary criterion that evidently distinguishes all inhomogeneous hydrodynamic models from the homogeneous Kelvin model, in which the quadrupole mode is the lowest stable mode. Estimates obtained for the periods of nonradial pulsations coincide with the periods of micropulses observed in the average pulse profiles of c-pulsars. This suggests that the detected variations in emission intensity in the range of micropulse duration (on the order of 10^–4 sec) are associated with nonradial stellar oscillations.Translated from Astrofizika, Vol. 39, No. 3, pp. 475–488, July–September, 1996.     

Unified Hamiltonian stability theory

We show that the spectral stability of Hamiltonian equilibria and periodic orbits may be analyzed by the same method. This is accomplished via the Cayley transform, =(+1)/(–1), which maps the unit circle onto the imaginary -axis. The advantages and disadvantages of the new method over previous techniques are elucidated.     

Oscillations of a polytrope with a toroidal magnetic field

The radial and the non-radial (l=2) modes of oscillation of a gaseous polytrope with a toroidal magnetic field are examined using a variational principle. It is found that the frequencies of oscillation of the radial mode and the Kelvin mode (l=2) decrease due to the presence of the magnetic field. The shift in the frequency of the Kelvin mode may be split up into two parts, viz. the shift in frequency due to the magnetic field on the unperturbed sphere [(1²)m, say] and the shift in frequency due to the distortion of the structure by the magnetic field [(1²)s, say]. In the first order calculations using one parameter trial function, it is found that (1²)m is indeed positive but is overweighed by a negative (1²)s. In the second order calculations using a trial function with two variational parameters, we find that the general behaviour of (1²)m and (1²)s is unchanged but that (1²)m becomes negative for polytropic indicesn1.5.In Appendix I we study the effect of a small rotation and toroidal magnetic field on the structure of a polytrope. It is found that the resulting configuration is a prolate spheroid, a sphere or an oblate spheroid according as respectively. Here denotes the magnetic energy andT the kinetic energy due to rotation andq is a constant which depends on the polytropic indexn. The values ofq are given in Table I.     

On the Freundlich red shift

The Freundlich red shift of wavelengths in the solar spectrum is discussed. Born's approach on the photon-photon interaction is used in conjunction with Melvin's recalculation of Freundlich's universal constant in order to derive the cross-section for scattering in the solar atmosphere. The new cross-section appears to be = 1.58 × 10^–18 cm², which is about one thousand times Born's estimate for the effective cross-section. However, a modified value of the constant is in a good agreement with the one obtained by Ter Haar by scattering process methods, which leads to 10^–18 cm² for the photon-photon interaction cross-section of the solar atmosphere. A new expression for Freundlich's red shift formula is obtained. Some numerical examples are given and some interesting aspects of Freundlich's parameters are discussed.     

New 115-1115-1115-1objects in dark nebulae. II.

Results of a search for new emission objects in the region of dark nebulae are presented. The observations were made in 1979 and 1985 at the 40 Schmidt telescope of the Byurakan Astrophysical Observatory. The spectra were obtained with a 4° objective prism (1100Å/mm near H) on Kodak 103aE, 103aF, IIaF, and IIIaF plates with the use of RG1 and RG2 filters. Of the 52 emission stars discovered, five show variability in the H line intensity.Translated fromAstrofizika, Vol. 38, No. 2, pp. 217–225, April–June, 1996.     

The relationship between r.m.s. doppler velocities and temperature in the solar transition region

An attempt is made in this paper to determine the coefficient a in a power-law relationship of the form V ~T between the r.m.s. velocity fluctuation, V for raster images with 3 resolution and the temperature, T of line formation using SMM solar data. For T between 8000 and 10⁵ K, the data suggest a best fit with 3/4 < 1. It is argued, however, that unresolved fine structure tends to reduce the observed value of V and that higher resolution data may yield different values for . Skylab data have shown that the non-thermal line broadening velocity, , is proportional to T ^1/2. Also, for all temperatures less than 10⁵ K, V . This latter result, however, is again dependent on spatial resolution and may not be true in observations made with sufficient spatial resolution. The magnitudes of both V and indicate that bulk motions play important roles in the structure of the solar atmosphere as well as in its energy and momentum balance. It is important, therefore, to identify the true nature of such motions with better accuracy than is possible with currently available data.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

New System of Coordinates for Tokamaks

A new system of coordinates for tokamak is presented here. They are described by the usual toroidal angle and coordinates in the meridian plane using the projection of the magnetic field lines and families of orthogonal lines. The number of families depends on the number of magnetic axis, and in this way the number of regions in the meridian plane are also defined. The differential operators are obtained using the curvatures _s and of each family. Grad–Safranov equation, poloidal field equations and Pfirsch–Schlüter transport are described in a general way using this kind of coordinates.     

Pulsar dispersion measures and the mean and mean-squared interstellar electron density

Theoretical distributions of pulsar dispersion measures (times sinb ^II) are computed for various assumed pulsar spatial distributions above (and below) the galactic plane, assuming a distribution for the ionized gas. The statistics on the twelve high-latitude pulsars lead to the conclusion that the pulsar distribution inz is at least as broad as the distribution of the ionized gas. The value derived for the local mean interstellar electron density in the galactic plane is 0.12 cm^–3 and is interpreted to be due to a uniform ionized intercloud medium.Interstellar absorption of radio waves at low frequencies and cosmic X-rays at low energies are considered with regard to irregularities in the distribution of ionized gas. It is shown that if the obervations are made with a wide angle receiver the effective absorption optical deph is –²/2 where is the mean value and is the dispersion in . This relation assumes is much larger than . Analysis of recent low-frequency radio measurements from a satellite-borne receiver, however, leads to the conclusion that effects of irregulatirities are large.     

Expanding and shearing magneto-viscous fluid cosmological model in general relativity

The object of this paper is to investigate the behavior of a magnetic field in a viscous fluid cosmological model. It has been assumed that the expansion () is proportional to the eigenvalue ₁ of the shear tensor _i ^j and the coefficient of shearing viscosity is proportional to the scalar of expansion. The paper also discusses the behavior of the model when the magnetic field tends to zero and comments on some other physical properties.     

The peculiarities of diffusion of the galactic cosmic rays at low energies

I give an interpretation of a result of Simpsonet al. (1988) on the variation with kinetic energyT _i of the mean pathlengthX _m (T _i ) of the galactic cosmic rays (CGRs) in the range 0.1T _i 10.0 GeV nucl^–1. I argue that the data onX _m (T _i ) may be interpreted in terms of a model of GCR diffusion on the one-dimensional Alfvén-wave turbulence, having a cutoff in the spectrum at frequencies _h , where _h is the proton gyrofrequency. The cutoff results in changing of the character of variation of the GCR diffusion coefficientD(T _i )T ^a in the rangeT _i 1 GeV nucl^–1 towards some more complicated variation at 0.1T _i 1.0 GeV nucl^–1 due to the peculiarities of the pitch-angle scattering at 90⁰.     

Representation of the Earth's gravitational potential

The paper represents the Earth's gravitational potentialV, outside a sphere bounding the Earth, by means of its difference V from the author's spheroidal potential. The difference V is in turn represented as arising from a surface density on the sphere bounding the Earth. Because of the slow decrease with ordern of the normalized coefficients in the spherical harmonic expansion ofV, the density anomalies from which the higher coefficients arise must occur in regions close to the Earth's surface. The surface density is thus an idealization of the product of the density anomaly and the crustal thicknessb. Values of are computed from potential coefficients obtained from two sources, Rapp and the Smithsonian Astrophysical Observatory. The two sources give qualitative agreement for the values of and for its contour map. The numerical values obtained for are compatible with the idea that the responsible density anomalies are reasonably small, i.e., less than 0.05 g/cm³, and occur in the crust alone.This paper was prepared under the sponsorship of the Electronics Research Center of the National Aeronautics and Space Administration through NASA Grant NGR 22-009-311.     

A note on σ-stability in hydromagnetics

The concept of -stability is reviewed and applied to the case of aligned magnetoatmospheric flow. A sufficient condition for -stability is derived, and the upper bound arising from this condition is investigated as a function of .     

Velocity dispersion profiles ofN-body simulations

The time evolution of the velocity dispersion as a function of radius, called v-profiles, of threeN-body simulations of Wielen are presented in units ofr/R _G (whereR _G is the gravitational or virial radius) and discussed as a function of mass sample. The evolution of the radial and tangential components of the velocity dispersion is discussed, and each v-profile is fitted to a simple power law in the halo (0.15r/R _G2.0). Several structural features appear at late time intervals: (a) an upturn in the radial component of v which occurs in a decreasing shell (closer to the core) in time, (b) the v-profile of the massive particles mimics that of the total sample, since equipartition of kinetic energy does not obtain, and (c) a local minimum atr0.3–0.5R _G appears in one model which coincides with the local minimum in the number density profiles and possibly with feature (a).The line-of-sight v-profile, called LS-profile, of each model as a function of time and mass sample are also presented and discussed. They contain the same structural features as the v-profiles. Projection factors at small radii are also discussed. The LS-profiles of the models can be compared with the observed velocity dispersion profiles of clusters of galaxies in Struble (1979a).     

Rosat X-ray light curves of early-type stars

We have investigated ROSAT X-ray data of OB stars to search for evidence of time variability in the X-ray emission from early-type stars. As an example for such studies we present a detailed variability analysis for our two program stars Ori and Ori which have been multiply observed with ROSAT. The long-term analysis of both stars now covers a time range of 2.5 years and includes six pointed PSPC observations, an additional pointed HRI observation of Ori and the ROSAT all-sky survey data of both stars. Over a long time range the X-ray light curves of Ori and Ori show no evidence for variability. In the case of Ori we detected a moderate increase in X-ray count rate during a period of 2 days which can be explained as a strong shock propagating in the wind of an O-type star.     

A model cosmology based on gravity-electromagnetism unification

In this article the GEM (Brandenburg, 1992; Brandenburg, 1988) theory is applied to the problem of the cosmos in which most of the matter is hydrogen, spacetime is flat, and a Cosmic Background Radiation CBR field exists. Using the two postulates of the GEM theory: 1. That gravity fields are equivalent to an array ofE ×B drifts or a spacially varying Poynting field, such that spacetime is determined by EM fields so that the stress tensor of ultrastrong fields is self-canceling; 2. That EM and gravity fields and protons and electrons are unified at the Planck scale of lengths and energies and split apart to form distinct fields and separate particles at the Mesoscale of normal particle rest energies and classical radii. A new derivation is made of the formula forG found previously:G =e ²/(m _p m _e ) exp(-2R ^1/2) = 6.668 × 10^–8 dynes cm² g^–2wherem _p andm _e are the proton and electron masses respectively,R =m _p /m _e and is the fine structure constant, shows that quantum processes may occur which make the vacuum unstable to appearance of hydrogen thus allowing matter creation and a steady state universe to occur. The value for the Hubble Time calculated from this model isT _o = (3/((2)(R ^1/2)⁴))^1/3(r _e /c)(e ²/Gm _p m _e )= 19 Gyr wherer _e =e ² / (m _e c ²)and follows the form first hypothesized by Dirac(1937). The CBR is traced to this process of matter creation and its temperature is calculated as beingT _CBR = ((3/4)Gm _e ² c/( ² _o ))^1/4 = 2.66K where is the Thomson cross section of the electron and _o is the Stefan-Boltzman constant.     

Pulsars and interstellar medium: Multiple regression analysis of related parameters

An empirical relation which relates the 408 MHz galactic continuum background temperature (408GCBT) to dispersion measures, position and radio-luminosity of 325 pulsars is obtained by means of multple stepwise regression analysis. This relation showns that pulsars may be considered as galactic probes for the distribution of 408GCBT and interstellar electron density (IED) in interstellar medium (ISM).Peculiar pulsars (O-C±2.5) point out galactic regions where the observedT ₄₀₈ are higher (or lower) andn _e lower (or higher) than the averaged ones.Normal pulsars (–2.5T ₄₀₈ andn _e are in agreement, on, the average.Standard pulsars (O-C±0.05) show galactic regions where observed and computedT ₄₀₈ andn _e are in good agreement. Recent models of pulsar disk systems, suggested by Michel and Dessler (1981) could justify the conclusions drawn for peculiar pulsars having O-C>2.5.     

The formation of a ring galaxy during a head-on collision between a disk and a spherical galaxy

The tidal force effects of a spherical galaxy passing head-on through a disk galaxy have been studied at various regions of the disk galaxy and for various orientations of the disk galaxy with respect to the direction of relative motion of the two galaxies. The density distribution of the disk galaxy is taken to be, (r)=_ce^–4r/R , where _c is the central density andR is the radius of the disk. The density distribution of the spherical galaxy is taken to be that of a oolytrope of indexn=4. It is found that as a result of the collision, through the central parts and the outer parts of the disk galaxy remain intact, the region in between these two regions disrupts. Thus a ring galaxy with a nucleus embedded in the ring-i.e., a ring galaxy of the RN-type, is formed.     

The configuration of a thin,rotating self-similar disk in general relativity

Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density and an angular velocity . Self-similarity as a statement of the absence of scales implies that and can be written as=c ²/4Gr, =c/r, and demands that and be pure numbers.     

Measurements of radial velocities of α and: A spotted HgMn star?

Measurements of radial velocities from the SiII 6347A and 6371Alines and the HeI 6678A line based on observations of 1989–1994 are examined. The variability of the line shapes over the 96.6-day orbital period is analyzed. Evidence for a second component is found from lines in the spectrum of And which correspond to the silicon lines 6347 and 6371A. The preliminary value for the rotational velocity of the secondary component is 100–120 km/sec. Analysis of the variability of the radial velocities of the HeI 6678A line during the night has given the rotational period of the star of P_rot=I^d.012344 and indicates an inhomogeneous distribution either of the helium abundance or of the physical conditions over the surface. Thus, we have the first evidence for the existence of spots on the surface of an HgMn star.Translated fromAstrofizika, Vol. 39, No. 3, pp. 375–384, July–September, 1996.     

On the Power in the Legendre Modes of the Solar Radial Magnetic Field

The power in the different modes of an expansion of the solar radial magnetic field at the surface in terms of Legendre polynomials,P , is calculated with the help of a solar dynamo model studied earlier. The model is of the Babcock–Leighton type, i.e., the surface eruptions of the toroidal magnetic field – through the tilt angle, , formed by the magnetic axis of a bipolar magnetic region with the east-west line – are the sources for the poloidal field. In this paper it is assumed that the tilt angle is subject to fluctuations of the form, = ()+ <> where <> is the average value and () is a random normal fluctuation with standard deviation which is taken from Howard's observations of the distribution of tilt angles. For numerical considerations, negative values of were not allowed. If this occurred, was recalculated. The numerical integrations were started with a toroidal magnetic field antisymmetric across the equator, large enough to generate eruptions, and a negligible poloidal field. The fluctuations in the tilt angle destroy the antisymmetry as time increases. The power of the antisymmetric modes across the equator (i.e., odd values of ) is concentrated in frequencies, _p, corresponding to the cycle period. The maximum power lies in the =3 mode with considerable power in the =5 mode, in broad agreement with Stenflo's results who finds a maximum power at =5. For the symmetric modes, there is considerable power in frequencies larger than _p, again in broad agreement with Stenflo's power spectrum.