Detection of background gravitational radiation by Doppler tracking of spacecraft

Low-frequency gravitational radiation, with wavelengths reaching or exceeding interplanetary distances, and with a mean energy density of the order of the critical cosmological density _c , generates a frequency-shift of order/10^–15 h ₀(1/10⁸km)(/ _c )^1/2 in electromagnetic signals transponded by interplanetary spacecraft at a distancel from the Earth.     

A static theory of the stability of the equilibrium

A static relativistic theory of the stability of the equilibrium of an isentropic spherically-symmetric star is deduced from the properties of a functionu which is solution of a second-order differential equation, and which is related to the model by means of the formulau = m(v, c)/c, wherem is the mass-energy inside the coordinate volumev and c is the central mass-energy density.Work done in the Laboratorio Astrofisico di Frascati, Roma.     

Spatial density fluctuations in the radiation era of the Universe

It is shown that in the radiation era of the Universe spatial temperature fluctuations (T/T)<10^–5 in the cosmic plasma lead to huge changes of the density up to (/)10⁴. This effect results from the fact that the cosmic plasma in the radiation era can be considered as a general relativistic Boltzmann gas which is found in the very vincinity of equilibrium.     

Chromospheric downflow velocities as a diagnostic in solar flares

We explore the dynamics of chromospheric condensations driven by evaporation during the impulsive phase of solar flares. Specifically, we find that the maximum chromospheric downflow speed obeys the approximate relation _d = 0.4 (F/ _ch )^1/3, where F is that part of the flare energy flux driving chromospheric evaporation, and _ch is the mass density in the preflare chromosphere just below the preflare transition region. This implies that chromospheric downflows as measured by H asymmetries may be a powerful probe of flare energetics.     

Plane and cylindrical hydromagnetic shock waves

The Chisnell-Chester-Whitham method has been used to investigate the propagation of diverging plane and cylindrical shock waves through an ideal gas in presence of a magnetic field having only constant axial and variable azimuthal components, simultaneously for both weak and strong cases. Assuming an initial density distribution ₀=r ^–w , where is the density at the plane/axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strength have been obtained. The expressions for the pressure, the density, and the particle velocity immediately behind the shock have also been derived for both cases.     

Rapidly rotating polytropes in the post-Newtonian approximation to general relativity

The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order ⁴, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter = ²/2G _c and a relativity parameter, =p _c / _c C ² , wherep _c and _c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order ². The critical rotation parameterv _c , which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.     

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.     

A differential equation for the classical collapse problem

The classical gravitational collapse problem is analysed on the basis of an integral equation connecting the evolutionary time (defined as dt/d log ) with the density and the collapse function , or by an equivalent first-order non-linear differential equation. The general behaviour of solutions is discussed, and some particular cases are studied.     

The interrelationship between cosmic dust and the microwave background

Attention is given to the radiation of microwaves by charged dust in space. Presently-used particle distributions do not restrict the presence in space of large numbers of small (r<10^–6 cm) silicate grains, but it is shown that such densities (10^–25–10^–26 g cm^–3) of small grains would produce a microwave background with an energy density of the same order of magnitude as the energy density of the (presumed) cosmological 3 K background. Limits set by the isotropy of the latter are: (HI clouds)10^–26, (Galactic plane)10^–30, (Halo)10^–32, (Local Group)10^–34 g cm^–3. These limits imply that either there is a cutoff in particle distributions atr10^–6 cm, or that the density of silicate grains in space has been generally overestimated, or that cosmic rays have broken up a lot of grains so that they now form a population of grains of very small size (10^–7 cm) which are difficult to detect by conventional methods. One way to look for the latter population is by studying expected distortions of the 3 K spectrum to the short wavelength side of the portion hitherto observed (grains may have a size distribution able to give an approximate black-body curve for radiation from larger grains of 10^–6 cm size), and by testing the effective energy density of the 3 K field in other galaxies.     

Annihilation radiation from thermal electron-positron plasma on the ground Landau level: The case of low magnetic fields

The intensity and polarization of two-photon annihilation in a magnetic fuieldBB _cr =4.4×10¹³ G are studied in detail for a, one-dimensional thermal distribution of annihilating electrons and positrons on the ground Landau level. With the increase of temperatureT the total annihilation rate and energy losses decrease, being higher than for the isotropic thermal distributions at the sameT. The shapes of intensity spectra at sin =0 ( is the angle betweenB and wave-vector) are close to those in the isotropic case. The widths and blue-shifts of the spectra decrease with increasing sin and increase with increasingT. Logarthmic singularities arise in the spectra atE»mc ²/sin . Power-like parts are formed in the wings of the spectra forkTmc ² and not too small sin . The direction-integrated spectra reach their (finite) maxima, atE=mc ² for anyT. The radiation concentrates near the plane, perpendicular to the magnetic field forE close tomc ² and is beamed along the magnetic field forE far frommc ². Energy-integrated angular distributions are stretched alongB, the stronger the higherT. The rediation is linearly polarized in the plane formed by the magnetic field and weve-vector. Typical values of the polarization inside the cores of the annihilation spectra are (kT/mc ²) sin and [ln (kT/mc ²)]^–1 forkTmc ² andkT sin mc ², respectively. Annihilation radiation dominates over Bremsstrahlung in thee plasma atkT7mc ². The results are useful for interpretation of the annihilation radiation in the gamma-ray bursts. They permit to estimate temperature, gravitational potential, and emission measure of radiating regions and the beaming of the radiation.     

Soft X-ray observation of theϱ ophiuchus dark cloud region

Soft X-rays (0.1–0.8 keV) from the region including the Oph dark cloud were observed with the SAS-3 low-energy X-ray telescope. No X-ray absorption by the cloud was observed. This indicates that the diffuse component of soft X-rays in this region is mostly from the foreground of the Oph cloud which is located at a distance of 160–200 pc.     

Why are spicules absent over plages and long under coronal holes?

One-dimensional hydrodynamic simulations are performed in order to examine the influence of initial atmospheric structures on the dynamics of spicules. This is an extended version of our previous spicule theory: spicules are produced by the shock wave (MHD slow mode shock) which originates from a bright point appearance (sudden pressure increase) at the network in the photosphere or in the low chromosphere. Simulation results well reproduce the observational facts that spicules are absent over plages and long under coronal holes. The physical reason is that the growth of a shock wave during its propagation through the chromosphere is small in plage regions and large in coronal hole regions, since the growth of a shock is determined by the density ratio ( _{h 0}/ _c ) between the bright point and the corona. An empirical formula H _max ( _{h 0}/ _c )^0.46 is obtained, where H _max is the maximum height of spicules above the transition region. The cross-section of the vertical magnetic flux tube is assumed to be constant in the numerical simulations.     

Some fundamental elements of universe mechanics

An essential part in the mechanics under study is taking into consideration the effect of motions of the Universe objects upon that of an individual one surrounded by them including those infinitely far from it. Only macro-objects of the Universe are meant here.

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Zusammenfassung Ein wesentlicher Bestandteil der Mechanik unter unserer Betrachtung ist die Berechnung des Einflusses auf die Bewegung eines individuellen Objektes von Bewegungen der Universum Objekte die es umringen einschließlich jene Objekte, die unendlich entfernt sind. Nur Makroobjekte des Weltalles sind in der Absicht dabei.

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Coronal temperatures and temperature gradients from OSO-7 spectroheliograms

Temperatures and temperature gradients for the outer corona are obtained from brightness gradients of EUV lines that were measured with the spectroheliograph on OSO-7. Brightness gradients show considerable deviations from isothermal model calculations that include collisional excitation and photoexcitation. A negative temperature gradient that gives both positive and negative ion abundance gradients appears to be able to account for the discrepancy. For 284 of Fe xv, perhaps the strongest line from the outer corona, measurements during 1972 appear to be consistent with (i) a temperature near 2.3×10⁶K near the equator at = 1.3±0.1 solar radii from the solar center; (ii) (/T) dT/d values near -0.7 that extend from as low as = 1.2 to about = 1.8. Temperatures from strong lines of Fe xiv and Fe xvi indicate that variations of about ±0.2×10⁶K exist along lines of sight where emission is appreciable. There appears to be some agreement between these results and temperature measurements from ion abundances in the solar wind and Doppler width of 5303.     

εлектроны космических лучей радиогало галактики

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Johann Heinrich Lambert and the determination of orbits for planets and comets

Johann Heinrich Lambert, a Swiss-German scholar, was counted among the most famous men of his time. Being an autodidact and without formal university studies, he won access to the modern sciences, in particular to philosophy, mathematics, astronomy and physics; and indeed he was most successful in all these fields. In the area of mathematics, for example, he made contributions to the theory of irrational numbers (continued fractions), to the problem of parallel lines and non-Euclidian geometry, to trigonometry (group-theoretical formulation of Nepper's rule), the foundations of the perspective, he gave a proof for the irrationality of e and and moreover some remarkable indications for their transcendency, to mention only a few. In the field of astronomy, he made contributions not only to the foundations of photometry but also to the orbital determination of planets and comets, which culminated in Lambert's Theorem. This, as well as his Cosmologische Briefe (with which he made a contribution to the structure of the world parallel to the Kantian view) is the subject matter of the following report. Even in philosophy Lambert kept pace with Kant (Criterium veritatis, 1761 when he said: Wir wissen, dass Gestalt und Grösse vom Orte umabhängige Bestimmungen sind.).

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Zusammenfassung Johann Heinrich Lambert, ein deutsch-schweizer Wissenschaftler, gehörte zu den berühmtesten Männern seiner Zeit. Er hat als Autodidakt ohne Studium an einer Hochschule sich den Zugang zu den modernen Wissenschaften, insbesondere zue Philosophie, zur Mathematik, zu Astronomie und Physik geschaffen und auf diesen Gebieten Fortschrittliches geleistet. Auf dem Gebiete der Mathematik z.B. waren es seine Beiträge zur Theorie der Irrationalzahlen (Kettenbrüche), zum Problem der Parallellinien und der nichteuklidischen Geometrie, zur Trigonometrie (gruppentheoretischer Ansatz für die Neppersche Regel), die Begründung der Perspektive, Beweis der Irrationalität von e und mit Ansätzen zum Nachweis ihrer Transzendenz, um nur einiges herauszuheben. Auf dem Gebiete der Astronomie waren es neben seinen Grundlagen für die Photometrie seine Beiträge zur Bahnbestimmung von Planeten und Kometen, die er mit dem nach ihm benannten Lambertschen Theorem krönte. Darüber und über seine Cosmologischen Briefe, mit denen er einen Beitrag zur Struktur der welt parallel zu der von Kant gegeben hat, wird im folgenden ausführlich gehandelt. Auch in der Philosophie war er im Gleichschritt mit Kant (Criterium veritatis 1761 mit dem Ausspruch: Wir wissen, daß Gestalt und Größe vom Orte unabhängige Bestimmungen sind.).

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Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Linearly expanding universes in JBD-theory

The assumption of a linearly expanding universe for the JBD-cosmological equations generates a set of solutions for the barotropic equations of statep= (=const.). These solutions turn out to be valid for closed space-except in the casep= which is for open space. The gravitational constant which is inversely proportional to the scalar field increases with time if >–1/3 and decreases for <–1/3. No solution exists for =1/3. The Brans-Dicke parameter is negative if <–1/3.     

Сопоставление модели карлсона с моделью сплошной среды

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О колебаниях хвоста магнитосферы в приБлижении квазигидро динамики

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О природе всплесков γ-излучения

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