On Low-Mass, Strange Quark Stars with a Crust

Low-mass strange stars with a crust are investigated within the framework of the bag model. The crust, which consists of degenerate electrons and atomic nuclei, has a limiting boundary density _cr , which is determined by the mass of the crust, and it cannot exceed the value _drip = 4.3·10¹¹ g/cm³, corresponding to the density at which neutrons drip from nuclei. For different values of _cr in the low-mass range (M 0.1 M) we calculate several series of configurations: we find the dependence of the stellar mass M on the central density _c for _cr = const, with 10⁹ g/cm³ _{cr drip} , and for each series we determine the parameters of the configuration for which the condition dM/d _c > 0 is violated. When the boundary density of the crust decreases to 10⁹ g/cm³, the minimum mass of a strange star decreases to M _min 10^-3 M, while the radius reaches 600 km.     

The λ 747 coronal line at the 1966 eclipse

Observations are presented of emission line resonance polarization in Fe xiii 10747 at the total solar eclipse of 12 November 1966. Useful data, with angular resolution 15, describe three quadrants of the corona from 1.08 R to a maximum of 1.6 R . The direction of the electric vector of observed polarization is perpendicular to the solar limb, to the limits of accuracy of measurement, in at least 74% of all cases. Departures in the other points are consistent with the magnetic depolarization expected from the non-radial fields of streamers. Polarizations observed range from near zero at the limb to 80 % and higher at 1.6 R . Averaged polarization is highest in non-streamer regions, where above 1.2 R it suggests pure radiative excitation of the 10747 line. Below 1.2 R , and in a dense streamer, the polarization is significantly depressed, indicating dominant collisional excitation of the line wherever the electron density exceeds 50 × 10⁶ cm^–3.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The velocity correlation function in cosmic-ray diffusion theory

The concept of velocity correlation functions is introduced and applied to the calculation of cosmic ray spatial diffusion coefficients. It is assumed that the pitch angle scattering coefficient is already known from some other theory, and is reasonably well-behaved. Previous results for the coefficient for diffusion parallel to the mean field are recovered when the velocity-changing mechanism is artificially restricted to pitch angle scattering. The velocity correlation method is then applied to the more general case where there are fluctuations in the local mean field. It is found that the parallel diffusion coefficient is reduced in proportion to the amplitude of the field fluctuations, and that the ratio of the perpendicular to parallel diffusion coefficients cannot be greater than B _x ² /B ₀ ² . It is shown in the appendix that the Liouville form of the scattering equation implies that the Fokker-Planck coefficients ²/t=2D and /t=D /, and that all higher-order coefficients are identically zero.     

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.     

Distribution of polarization and intensity of radiation across the stellar disk and numberical values of atmospheric characteristics governing this distribution

Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT _eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT _eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT _eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk.     

Effects of mass transfer on the unsteady free convection flow past an accelerated vertical porous plate with variable suction

An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg^*(C –C )/U ₀ ³ ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U ₀) - v normal velocity component - v ₀ suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C _p specific heat at constant pressure - C _w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C _w -C )) - Gr Grashof number (g(T _w -T )/U ₀ ³ ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T _w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU ₀ ² /) - U ₀ reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U ₀) - v dimensionless velocity (v/U ₀) - v ₀ non-dimensionalv ₀ (v ₀ /U₀)=–at^–1/2 - y dimensionless ordinate (yU ₀/) - density of the fluid - coefficient of viscosity     

Phenomenological theory of gravitational vacuum

An idea is developed that the vacuum in the gravitational field acquires properties of an elastic medium described by a definite tension _ik . The vacuum is stated to also participate in the formation of the space-time metric, together with the usual matter. So, the matter, vacuum and metric form a complex unity determined by the solution of the field equations. The vacuum may prove to play an essential role in the extremely strong fields existing in superdense celestial bodies. The tensor _ik is not to be identified with the pseudo-tensor of the energy-momentum of the gravitational field the idea of which is preserved.The problem of vacuum is investigated in the case of the central symmetry static field. A number of properties of the tensor _ik is found using the symmetry of the field and comparison with the post-Newton limit. The external and internal problems, as well as the procedure of joining the solutions on the surface of a celestial body, have been formulated. The stellar surface is determined in the usual way:P(r) = 0 whereP is the matter pressure. The theory includes three dimensionless parametersa=p/,b=p / (,p, p are the density of the vacuum energy and of its pressures in the radial and transverse directions) and determining the vacuum elastic properties. Generally speaking, they depend on the valueP/c² in the stellar centre where is the mass density. From general physical considerations it is shown that 0 1 + lim _P (l/q). The field equations are solved for the simple version of the theoryb=–a. There are solutions corresponding to superdense celestial bodies with masses considerably exceeding that of the Sun.     

Hollow beam distribution of energetic electrons and higher harmonics of electron cyclotron maser

The variations of the growth rates of ECM at first four harmonics in X-, Z-, and O-modes excited by a hollow beam distribution of weakly relativistic electrons with a parameter _p / _e are presented in this paper. The results show that the second harmonic of ECM in X-mode dominates the instability if < 1, and if 1.2 , 2 or 2.2 3 the third or fourth harmonic will dominate. The second and third harmonics of Z-mode waves grow faster only if 2 2.2 and 3 3.2, respectively, so it would not be a competition in most cases. It is suggested that the ECM emission at these harmonics in X-mode is a possible mechanism to produce solar spike emissions with high brightness temperature at shorter and longer decimetric wavelengths.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.On leave from the Department of Astronomy, Nanjing University, Nanjing, The People's Republic of China.     

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.     

High order symplectic integrators for perturbed Hamiltonian systems

A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(^p + ²²), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(^p +⁴²). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.     

Mercury: The Image of the Planet in the 210°–285° W Longitude Range Obtained by the Short-Exposure Method

For the purpose of obtaining images of the unknown portion of Mercury, we continued the previously started series of observations of this planet by the short exposure method. Several thousand electronic images of Mercury have been acquired on 1–2 May 2002 under good meteorological conditions at the high-altitude Skinakas Astrophysical Observatory of Iraklion University (Crete, Greece, 35°13 E, 24°54 N) during the evening elongation. The phase angle of Mercury was 95°–99° and the observed range of longitudes was 210°–285° W. Observations were carried out using Ritchy–Chrétien telescope (D = 1.29 m, F = 9.857 m) with the KS 19 filter cutting wavelengths shorter than about 700 nm. The planet's disk was seen, on average, at an angle of 7.75 arcsec. The image scale was equal to 47.8 m/arcsec. We used a CCD with a pixel size of 7.4 × 7.4 m in the regime of short exposures. By processing a great number of electronic images, we succeeded in obtaining a sufficiently distinct synthesized image of the unknown portion of Mercury's surface. The most prominent formation in this region is a giant basin (or cratered mare) centered at about 8° N, 280° W, which was given a working name Skinakas basin (after the name of the observatory where observations were made). By its size, the interior part of this basin exceeds the largest lunar Mare Imbrium. As opposed to Mare Imbrium, the Skinakas basin is presumably of impact origin. Its relief resembles that of Caloris Planitia but the size is much larger. A series of smaller formations are also seen on synthesized images. The resolution obtained on the surface of Mercury is about 100 km, which is close to the telescope diffraction limit. Also considered are the published theoretical estimations of the possible advantages offered by the short exposure method. Some results obtained by other research groups are discussed.     

B,V surface photometry of the UV continuum galaxy NGC 838

Surface photometry of the UV continuum galaxy NGC 838 has been carried out in theB, V system using photographic plates obtained with the 74 Kottamia telescope, Egypt. Isophotes, luminosity profiles, integrated photographic magnitudes, effective diameters and other photometric parameters are derived.The photoelectrically calibrated total apparent magnitudes areB _T =13.57 with maximum diameters 1.57×1.34 (at threshold _m =27.7 mag.//) andV _T =12.91 with maximum diameters 1.54×1.32 (at threshold _m =27.7 mag./). The integrated colour index(B–V) _T =0.66 and the effective surface brightness _e (B=19.0 mag./) and _e (V=19.7 mag./. The major axis is at position angle =85°±1°.The nucleus of NGC 838 is quite blue (integrated colour(B–V)=0.41 forr ^*<0.1) compared to normal galaxies while the colour becomes redder from the nucleus outwards. The UV excess, H emission and radio continuum emission previously observed from this galaxy by other investigators may be attributed to a recent burst of star formation in the nucleus of the galaxy of duration slightly greater than 2×10⁷ yr.     

A momentum distribution of high energy particles around Crab pulsar

We determine the momentum distribution of the relativistic particles near the Crab pulsar from the observed X- and -ray spectra (10³10⁹ eV), provided that the curvature radiation is responsible for it. The power law spectrum for the relativistic electrons,f() ^–5, reproduces a close fit to the observed high-energy photon spectrum. The theoretically determined upper limit to the momentum (due to radiation damping), _M 8×10⁶, corresponds to the upper cut-off energy of the -ray spectrum, 10⁹ eV. The lower limit to the momentum, _m 1.8×10⁵, is chosen such that flattening of the X-ray spectrum below 10 keV is simulated. The number density of these electrons is found to be much higher than the Goldreich-Julian density. We also discuss pulse shape and polarization of high-energy photons. The extremely high density of particles and the steep momentum spectrum are difficult to understand. This may imply that another, more efficient, mechanism is in operation.     

Can Brans-Dicke universes in five dimensions be interpreted as 4-dimensional general relativity cosmologies?

The 5-dimensional Jordan-Brans-Dicke cosmologies in vacuum are found for the Bianchi type I metric, their relation with general relativity cosmologies is studied. Two solutions are possible, both produce effective pressure and energy density in the 4-dimensional G.R.-universes. One is a power-law relation, with two cases, the first one is forp _eff=_eff and the other forp _eff=_eff(– 1 < < 1) has a behaviour as the open flat universe. The second solution is an exponential only valid forp _eff=–_eff. In all cases the three-space expansion reaches infinity ast and the fifth dimension can be made to decrease approaching zero. The scalar field can increase or decrease with time.     

Stability of and motion aboutL 4 at three-to-one commensurability

The stability ofL ₄ and the motion aboutL ₄ in the restricted problem of three bodies is investigated when there is three-to-one commensurability between the long and short periods of motion, that is, when the mass ratio has the value =0.013516.... The two time scale method is used (1) to show thatL ₄ is an unstable equilibrium point when =₃, (2) to determine for what initial conditions periodic orbits occur when ₃, (3) to determine the stability of the periodic orbits, and (4) to investigate the boundedness of the motions aboutL ₄ when ₃.     

Оболочки звездпри сверхкритической светимости

. , , .. . . , (, ) .     

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.     

Electrical conductivity of neutron star cores in the presence of a magnetic field

General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities ₀, where ₀ = 2.8×10¹⁴ g cm^–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of ^–-hyperons at > _c , where _c 4₀. The electric resistivities along and acrossB, and , and the Hall resistivity _H are calculated and fitted by simple analytical formulae at _c and > _c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If _c , one has = [1 + (B/B ₀)²] for the normal neutrons, and for the superfluid neutrons, while _H = B/B _e for both cases. HereB _e 10⁹ T ₈ ² G,B ₀10¹¹ T ₈ ² G, andT ₈ is temperature in units of 10⁸ K. Accordingly for the normal neutrons atBB ₀, the transverse resistivity suffers an enhancement, _{1/4 1}. When 5₀ andB varies from 0 toBB _p 10¹³ T ₈ ² G, increases by a factor of about 10³–10⁴ and _H changes sign. WhenBB _p , remains constant for the superfluid neutrons, and _H B ² for the normal neutrons, while _H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.     

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.     

On convergence of an asymmetrical body potential expansion in spherical harmonics

The gravity potential of an arbitrary bodyT is expanded in a series of spherical harmonics and rigorous evaluations of the general termV _n of the expansion are obtained. It is proved thatV _n decreases on the sphere envelopingT according to the power law if the body structure is smooth. For a body with analytic structure,V _n decreases in geometric progression. The exactness of these evaluations is proved for bodies having irregular and analytic structures. For the terrestrial planetsV _n =O (n ^–5/2).

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I I V _n IV _n I . . IV _n I . I. IV _n =O(n ^–5/2 )