General-relativistic hierarchical cosmology: An exact model

An exact solution of Einstein's equation is stated in which the density (), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having R ^–2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law ( R ^–, approximately, with =a number, 02). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy.     

Expanding and superdense astrophysical systems in general relativistic hierarchical cosmology

A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( _i+1/ _i [r _i /r _i+1] is approximately equal to the exponentN in a continuous density law (=aR ^–N) provided (r _i /r _i+1)^3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c ² R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s^–1 Mpc^–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c ² R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R ^N ,N2); (j) for the Galaxy, theory predictsp _G7×10^–12 dyn cm^–2, observation givesp _G5×10^–12 dyn cm^–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 10¹² g s^–1, compared to 10¹¹ g s^–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×10⁹ years for the Sun and 10¹⁰ years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN _B of baryons; (o)N _B10⁵⁷N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L _max10⁵⁹ erg s^–1); (r) larger bodies have longer time-scales of energy radiation atL _max (10^–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR ^–N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.     

The abelian higgs sunspot endowed with a local conformal symmetry

We show that the requirement of alocal conformal symmetry of the Abelian Higgs sunspot leads, at least formally, to a complex-valued electromagnetic potential, whose imaginary part is a conformal compensating potential. It is shown that there exists a fundamental difference between conformal and ordinary electromagnetic fields; whereas the ordinary total magnetic flux of a spot is quantized its conformal analogue has to vanish if the Higgs field is to be single-valued. We further stress that such a complex-valued Abelian Higgs field configuration mimics quite well, under certain conditions (all the salient features of) the classical Abelian Higgs sunspot.     

Graphisches Konstruktionsschema zur Bestimmung der Bewegungsparameter eines drallstabilisierten Flugkörpers mit Nutationsdämpfung unter dem Einflusz von Lagekorrekturimpulsen

Zusammenfassung Es wird gezeigt, daß die unter der Einwirkung einer Momentenimpulsserie entstehende Bewegung eines rotierenden Flugkörpers mit Nutationsdämpfung sich vollständig einem regelmäßigen Polygon entnehmen läßt, das durch das Trägheitsmomentenverhältnis, den Integralwert eines Einzelimpulses, den Drall und eine die Dämpfung charakterisierende KonstanteK ₀ bestimmt ist.Die Bewegung setzt sich aus logarithmischen Spiralen zusammen, derenn-ten Anfangsradius man erhält, indem man den Teilungspunkt des im VerhältnisK ₀:1 geteilten (n–1)-ten Radius mit der (n+1)-ten Polygonecke verbindet.Es wird bewiesen, daß das Konstruktionsnetz zu einem im äußeren Polygon liegenden ähnlichen inneren Polygon konvergiert, das gegenüber ersterem gedreht ist.Einfache Beziehungen zur Bewegungsbestimmung mit dem Polygonschema werden für Pulsfrequenzen angegeben, die ganzzahlige Vielfache oder Bruchteile der Spinfrequenz sind.

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It is shown that the motion of a spinning body with nutation damping due to a series of torque pulses can be completely derived from a regular polygon determined by the ratio of inertias, the integral of one pulse, the momentum and a constantK ₀ characterizing damping.The motion is composed of spirals thenth initial radius of which is obtained by connecting the dividing point of the (n–1)th radius with the (n+1)th polygon corner. Each dividing point divides the respective radius in the ratioK ₀:1. The net of construction lines converges into an inner polygon turned against the outer one and having the same shape.Simple rules are shown for the application of the scheme on pulse frequencies which are multiples or fractions of spin frequency.

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Symbole 1-2-3 Achsen des flugkörperfesten Koordinatensystems - a,b,c Hilfsgrößen zur Bestimmung der Iterationsgrößen - E _i i-te Polygonecke - H Drall des Flugkörpers - K _i Verhältnis deri-ten Drehzeigerlängen zu Beginn und am Ende eines Impulses - M Iterationsmatrix - Integralwert des Momentenimpulses - P ₀ Äußeres Polygon - P ₁ Spitze des Drehzeigersr _00e - P Drehpunkt des Drehzeigersr ₀₀ - P Konvergierendes Polygon - P _i Teilungspunkt des [i–1]-ten Zeigers - r _0i Drehzeiger aufgrund desi-ten Impulses allein - r _0ia Zeigerr _0i in Anfangslage - r _0ie Zeigerr _0i in Endlage - r _i i-ter Summenzeiger - r _ia Zeigerr _i in Anfangslage - r _ie Zeigerr _i in Endlage - T Dauer einer Flugkörperumdrehung - t,t, Zeitargumente - x-y-z Achsen eines raumfesten Koordinatensystems - x _i ,y _i Iterationskoordinaten - _n Phase desn-ten Radius gegenüber der anliegenden Polygonseite - Drehung des inneren Polygons gegenüber dem äußeren - Abklingkonstante - Phasenänderung des Drehzeigers innerhalb einer Flugkörperumdrehung - ₀ Anteil der über 2 hinausgehenden Phasenänderung des Drehzeigers - ₃ Trägheitsmoment um die Spinachse - ₁₂ Trägheitsmoment um die Querachsen - Zahl der Ecken des Konstruktionspolygons - _1,2 Eigenwerte der Iterationsmatrix - Zahl der vollen Umläufe des Konstruktionspolygons - Fortbewegungsachse des Drallvektors - ₀ Ausgangsphasenwinkel - _i Phasenlage desi-ten Summenzeigers - _x, _y Drehwinkel nach Einzelimpuls fürt - , Funktionen der Iterationsgrößen - , Drehwinkel umx-bzw.y-Achse - Drehgeschwindigkeit der Spinachse um den Drallvektor - Fiktive Größen bei Pulsfrequenzen kleiner als Spinfrequenz - Fiktive Größen bei Pulsfrequenzen größer als Spinfrequenz     

Search for relativistic companions in ‘non-X-ray’ binary systems

Consideration is given to a search for relativistic objects in massive close binary systems without strong X-ray emission (L _x <10³⁴ erg s^–1). It is pointed out that, according to the present-day theory on the evolution of massive close binaries, the number of neutron stars and black holes in non-X-ray binary systems must be 100 times the number of the known X-ray binaries comprising OB supergiant stars; that is why, in studying non-X-ray binary systems, the chances are to detect about a hundred of black holes in the Galaxy.Criteria are formulated for the relativistic nature of companions in the binary systems, such as high spatial velocity values and height Z over the galactic plane for OB stars (runaway stars) and for Wolf-Rayet stars. As reported by Tutukov and Yungelson (1973), as well as by van den Heuvel (1976), the presence of ring-type nebulae can serve as another indication of a relativistic nature of companions in the case of Wolf-Rayet stars.Data are collected on Wolf-Rayet stars with low-mass companions (Table I), which can be relativistic objects accreting within a strong stellar wind from Wolf-Rayet stars. Presented are new findings in respect of spectral examination of the runaway OB-stars (Table II), bringing together data on eight OB stars which can represent binary systems with relativistic companions (Table III).A list of 28 OB-stars (Table IV) which offer a good chance for finding relativistic companions is given.     

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.     

A novel methodology for radiative transfer in a planetary atmosphere

A novel methodology for evaluating the field of anisotropically scattered radiation within a homogeneous slab atmosphere of arbitrary optical thickness is provided. It departs from the traditional radiative transfer approach in first considering that the atmosphere is illuminated by an isotropic light source. From the solution of this problem, it subsequently proceeds to that for the more conventional case of monodirectional illumination. The azimuthal dependence of the field is separated in the usual manner by an harmonic expansion, leaving a problem in four dimensions (=optical depth, ₀=thickness, , =directions of incidence and scattering) which, as is well known, is numerically extremely inconvenient. Two auxiliary radiative transfer formulations of increasing dimensionality are considered: (i) a transfer equation for the newly introduced functionb ^m(,,₀) with Sobolev's function ^m(,₀) playing the role of a source-function. Because the incident direction does not intervene, ^m is simply expressed as a single integral term involvingb ^m. For bottom illumination, an analogous equation holds for the other new functionh ^m(,,₀). However, simple reciprocity relations link the two functions so that it is only necessary to considerb ^m; (ii) a transfer equation for the other new functiona ^m(,,,₀) with a source-function provided by Sobolev's functionD ^m(,,₀). For bottom illumination, another functionf ^m(,,,₀) is introduced; by a similar argument using reciprocity relations,f ^m is reduced toa ^m rendering necessary only the consideration ofa ^m. However, a fundamental decomposition formula is obtained which shows thata ^m is expressible algebraically in terms of functions of a single angular variable. The functions ^m andD ^m are shown to be the values in the horizontal plane ofb ^m anda ^m, respectively. The other auxiliary functionsX ^m andY ^m are also expressed algebraically in terms ofb ^m. These results enable one to proceed to the final step of evaluating the radiation field for monodirectional illumination. The above reductions toalgebraic relations involving only the functionb ^m appear to be more advantageous than Sobolev's (1972) recent approach; they also circumvent some basic numerical difficulties in it. We believe the present approach may likewise prove to be superior to most (if not all) other methods of solution known heretofore.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory under Contract No. NAS-7-100 sponsored by the National Aeronautics and Space Administration.     

Close Binary System Go Cygnus: Standard Ubv Observations and Light Curve Analysis

Standard UBV light curves of eclipsing binary star GO CYGNUS havebeen presented. These light curves indicate a Lyrae typevariations with circular orbit. The Light curve analysis have beencarried out on three colours U, B and V. The results obtained fromthese analysis represent an occultation solution with r r =1.24.     

The solar minimum temperature determined by the CO (A 1Π-X 1Σ)

The synthetic Voigt profile of the following transitions (v=0,v=0), (v=0,v=1), (v=1,v=1), (v=1,v=0) have been computed for different concentrations and temperatures of CO and compaed to the measured intensities of the UV sunspot spectrum by a high resolution spectrograph. From this comparison the solar minimum temperature has been determined.     

The spatial distribution and birth-rate of pulsars

The distribution of pulsars in the wide range of observed luminosities has been obtained. It is shown that the function of luminosity (FL) within 3×10²⁶L2×10³⁰ erg s^–1 conforms to the power law dN/dL–c ₁ L ^–, where =1.76±0.06. ForL3×10²⁶ erg s^–1, FL changes its inclination and may be approximated as , where ₁ = 0.7±0.2. On the basis of statistical selection, including all pulsars withL>3×10²⁸ erg s^–1, the distribution of pulsars has been investigated as a function of the distance to the centreR and galactic planeZ.The obtained laws of the radial andZ-distribution of pulsars and galactic supernova remnants and also the radial distribution of types I and II supernovae in the models Sb and Sc support the hypothesis of their origin from the objects of the flat subsystem of Population I. Since there are some arguments in favour of a possible connection between supernovae I and the objects of the intermediate component of the Galaxy, one cannot exclude the possibility of supernovae explosions at the end of the evolution of stars with masses of 1.5–2M . It is also shown that pulsars and supernovae are evidently objects that are connected genetically, and, within the limits of statistical error, they have a similar birth-rate.The empirical law of the evolution of a pulsar's luminosity as a function of its true age has been obtained, according to whichL=c ₂ t ^–, wherec ₂=(3.69±3.4)×10³⁵, =1.32±0.11.     

PO — Prospects in interstellar medium

Proton transfer and condensation reactions followed by dissociative electron recombination and charge transfer processes may yield a significant concentration of PO in interstellar clouds. Relevant terrestrial PO lines in the ultraviolet, infrared and microwave regions are listed in order to aid the detection of PO in interstellar clouds. Within the framework of Klein-Dunham potential, spontaneous emission rates and oscillator strengths of strong (v=0 sequence) beta bands of the PO molecule are estimated. For SgrB2 source, under optically thin case, each of the two strongest²_1/2,J=2.5–1.5 rotational transitions (108.998 GHz and 109.206 GHz) of PO would have antenna temperature less than 125 mk for beam efficiency0.6 and =0.7D (electric dipole moment of PO in thev=0 level of theX ² state). For Orion molecular cloud, PO (4, 4.5, 5-3, 3.5, 4) (e, f) lines are excitable at 196.305 and 196.500 GHz and each line would have antenna temperature less than 110 mK.This work was partially supported by Fapesp and CNPq, Brazil, under contract numbers 80/1659-0 and 30.4076/77-FA01, respectively.     

Blind operation of optical astronomical interferometers options and predicted performance

Maximum sensitivity for optical interferometers is achieved only when the optical pathlengths between the different arms can be equalized without using interference fringes on the research object itself. This is called blind operation of the interferometer. In this paper I examine different options to achieve this, focussing on the application to the Very Large Telescope Interferometer (VLTI). It is proposed that blind operation should be done using a so-called coherence autoguider, working on an unresolved star of magnitude V=11 to 13 within the isoplanatic patch for coherencing, which has a diameter of about 1 degree. Estimates of limiting magnitudes for the VLTI are also derived.     

О колебаниях хвоста магнитосферы в приБлижении квазигидро динамики

-- () ., , , , , . , , . , .     

A search for discrete gamma-ray sources of energy greater than 2×1012 eV

The results of the observations to search gamma-ray sources with the energy greater than 2×10¹² eV, which were made in Crimean Astrophysical Observatory during the years 1969–73 are presented. A technique of the detection of the EAS Cerenkov flashes was used.The quality of the data obtained is analysed. The criteria for the selection of the data free from meteorological variations are considered.It was shown that two objects, namely, Cyg X-3 and Cas -1, may be the sources of high-energy gamma quanta. It is probable that the object with the coordinates =05^h15^m, =+1° is the source of gamma-rays as well. An unidentified object Cas -1 is variable: gamma-ray flux was observed twice — in Sepember–October 1971 and in December 1972. It is possible that the flux from Cyg X-3 has a period of 4.8 hr.

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I I , I I , - >2.10¹² . I . I , I I, I ., - -1 Cyg -3- -I . , =0515 ·=+1° -.I -1 I: I J I- - 1971 1972 . Cyg -3, , - T=4.8 .

     

Structure and evolution of solar radio bursts at 26.4 MHz

Two dimensional source brightness distributions at 26.4 MHz for solar bursts of spectral type II, III, IV, and V are derived from observations with a multiple-baseline, time-sharing interferometer system. It was designed explicitly to study the large angle (40 halo) component of low frequency solar bursts first reported by Weiss and Sheridan (1962). Thirty-two bursts occurring in the interval of June–August, 1975, were fit with a circular gaussian core and an elliptical gaussian halo component. Half-power halo diameters (E-W×N-S) averaged 30×28 for type III bursts and 42×27, 28×37, 30×25 for type V, II and IV bursts respectively. Typical core sizes fell in the range of 10±4 giving 31 halo to core size ratio. All burst types were found to have some large angle structure: the specific intensity was 10% compared to the core but the total power in each component was comparable. Two processes for producing the core-halo structure of type III bursts are compared: scattering and refraction of a point source and refraction from many sources over an extended region. It is concluded that the core can be explained by either model but the halo is more consistent with emission from an extended source region of 40° in longitude.     

Об устойчивости лагранжевых решений пространственной эллиптической задачи трех тел

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Stability of the librational triangular points of the three-dimensional elliptic restricted three-body problem is studied. The problem is solved in the non-linear statement at the small values of eccentricity.For all values ofe, , besides ones which correspond to the resonances of the third and the fourth order the librational points are stable taking into account the terms up to the fourth order in the normal form of the Hamiltonian function of the perturbed motion.At sufficiently smalle and the non-stability in sense of Liapunov has been proved. The approximate equations of the boundary of the stability area in the planee, has been obtained. The cause of the non-stability is an equality of the rotational period of the principal attracting masses in the elliptic orbit and the period of oscillation of indefinitely small mass along the direction perpendicular to the plane of their motion.

     

Stability of the libration points of a rotating triaxial ellipsoid

The problem of stability of the equilibrium points (the libration points) in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid is investigated in the strict sense.In the plane of parameters, depending on the form and dynamical characteristics of the ellipsoids, the regions of stability and instability of the libration points are obtained.It is shown that the libration points of the ellipsoids, the form and dynamical characteristics of which are close to the planets of the solar system, are stable.

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( ) . , , . , , , .

     

Doubly averaged effect of the Moon and Sun on a high altitude Earth satellite orbit

Infinite series expansions are obtained for the doubly averaged effects of the Moon and Sun on a high altitude Earth satellite, and the results used to interpret numerically integrated examples. New in this paper are: (1) both sublunar and translunar satellites are considered; (2) analytic expansions include all powers in the satellite and perturbing body semi-major axes; (3) the fact that retrograde orbits have more benign eccentricity behavior than direct orbits should be exploited for high altitude satellite systems; and (4) near circular orbits can be maintained with small expenditures of fuel in the face of an exponential driving force one forI _ab, whereI _b=180°–I _a andI _a is somewhat less than 39.2° for sublunar orbits and somewhat greater than 39.2° for translunar orbits.Nomenclature a semi-major axis - A _lk coefficient defined in Equation (11) - B _lk coefficient defined in Equation (24) - C _km coefficient defined in Equation (25) - D, E, F coefficients in Equations (38), (39) - e eccentricity - H _k expression defined in Equation (34) - expression defined in Equation (35) - I inclination of satellite orbit on lunar (or solar) ring plane - J ₂ coefficient of second harmonic of Earth's gravitational potential (1082.637×10^–6 R _E ² ) - K _k, L_k, M_k expressions in Section 4 - expressions in Section 4 - p=a(1–e ²) semi-latus rectum - P _l Legendre polynomial of degreel - q argument of Legendre polynomial - radial distance of satellite - R _E Earth equatorial radius (6378.16 km) - R, S, W perturbing accelerations in the radial, tangential and orbit normal directions - syn synchronous orbit radius (42 164.2 km=6.6107R _E) - t time - T satellite orbital period - T orbital period of perturbing body (Moon) - T _e period of long periodic oscillations ine for |I|<I _a - T _s synodic period - U gravitational potential of lunar (or solar) ring - x, y, z Cartesian coordinates of a satellite with (x, y) being the ring plane - coefficient defined in Equation (20) - average change in orbital element over one orbit (=a, e, I, , ) - ₁,₂₃ unit vectors in thex, y, z coordinate directions - _r , _s , _w unit vectors in the radial, tangential and orbit normal directions - =+ angle along the orbital plane from the ascending node on the ring plane to the true position of the satellite - angle around the ring - gravitational constant times mass of Earth (3.986 013×10⁵ km s^–2) - gravitational constant times mass of Moon (or Sun) - _m gravitational constant times mass of Moon (/81.301) - _s gravitational constant time mass of Sun (332 946 ) - ratio of the circumference of a circle to its diameter - radius of lunar (or solar) ring - _m radius of lunar ring (60.2665R _E) - _s radius of solar ring (23455R _E) - true anomaly - argument of perigee - ₀ initial value of - _i critical value of in quadranti(i=1, 2, 3, 4) - longitude of ascending node on ring plane This work was sponsored by the Department of the Air Force.     

Lower hybrid wave model for aurora

In the framework of non-linear fluid theory we use a lower hybrid (LH) wave of the form as a pump which interacts with the small fluctuations with the low-frequency vibrations _i or =0, where _i , is the hydrogen ion-cyclotron (HIC) gyrofrequency. The ponderomotive force generated by the beating of the high-frequency pump wave ₀ and the sideband LH waves (±₀) produces a non-linear coupling between the high- and low-frequency motions of electrons and ions. Under certain conditions the HIC waves and the zero-frequency waves both become parametrically unstable and start to grow. These excited waves then heat the ions by stochastic acceleration in the transverse direction, thus explaining the formation of ion comics along the auroral field lines. Electrons would be heated in the parallel direction directly by the pump field as well as by low-frequency waves. Thus a single mechanism can explain the existence of ion-cyclotron waves, zero-frequency waves, ion conics, and energetic electrons along the auroral field lines.     

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.