Characteristics of electron and high-energy proton flares

High-energy proton (E _p > 55 MeV) and electron (E _e > 50 keV) events were observed by University of Iowa experiments on the satellites Explorer 33 and 35. The solar X-ray (2–12 Å) flares associated with the energetic proton events were found to have in general higher peak fluxes, considerably longer decay times (t) and smaller rise to decay time ratios (r) than the X-ray flares associated with the electron events. The most common decay times and rise to decay time ratios are: 80 t 100 min, 0.1 r 0.2 for the proton X-ray flares and t 20 min, 0.3 r 0.7 for the electron ones.     

Approximate expressions for Gyrosynchrotron radiation in Transverse Propagation

Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity _–/BNand absorptivity _– B/Nfor e-mode, effective temperature T _effand frequency of peak brightness _p. The expressions are designed for the range 2 to 7 of electron energy spectral index and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=/_B). Their statistical error is, respectively, ±18% and ±29% for _–/BNand _– B/Nfor 10/_B100, ±128% and and ±170% for 2/_B10.     

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.     

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 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.     

Theory of the Trojan asteroids,IV

In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies ₁ and ₂. In terms of thecritical masses m_j(₂), or the associatedcritical energies _j ² (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |₂– _j ² |<_j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 0²1, lying in: and (2) despite the clustering of _j ² (m) atj=, the family () includes, for ²=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL ₃.In a similar manner, the family () can be extended to the horseshoe branch 1<_{2 2} ² .     

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.     

Possible effects of anisotropy ofG on celestial orbits

Will (1971) has discussed a possible anisotropy in the gravitational constantG. Suppose that the attractive gravitational force between two particles of massesm ₁ andm ₂ is given by the usual expressionF=–Gm ₁ m ₂ r/r ³, wherer is the separation vector. Ifc is the velocity of light in vacuo and if 1 _r r/r, he expresses the anisotropy byG=G [1+(v·1 r/c)²], whereG is a constant,v is identified practically as the velocity of the Sun around the galaxy, and 1. Will's suggestion is to look for such an effect in the laboratory.The purpose of the present paper is to look for such an effect in the solar system, wherem ₁ andm ₂ become the masses of the Sun and a planet or of the Earth and the Moon. For simplicity I consider only those planets whose orbits are close to the ecliptic, so that the angle betweenv and the plane of the ecliptic is about 59°.With the above force, the resulting two-body problem is completely solvable. The results are these. If =1, there is an increase in mean motion of 7 parts in 10⁸, a periodic fluctuation in true longitude with period half that of the orbit and amplitude ranging possibly from 0.01 to 0.02, and periodic fluctuations in the radius vector, with period also one half that for the orbit. The amplitudes are: 2.7 km for Mercury, 5.1 km for Venus, 7.0 km for Mars, 18 m for the Moon about the Earth, and 28 cm for a close artificial satellite with inclination 23°. The more conservative estimate <0.0115 would reduce these values by the factor 70.     

Circular Polarization of Starlight

Of the 7500 stars cited in the Catalog of starlight polarization, those which satisfy the condition P _obs % and A _V 0^m.5 are selected. It is presumed that the selected stars (n=216) have circularly polarized light.     

The distribution law of stellarp-modes

We show that the overall densityg() of asymptotic acoustic frequencies of a star obeys a Weyl lawg() ^D–1, whereD is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed,D is equal to the actual dimensionality of the star,D=3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameterD=4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range > _i 2× fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval _i << _f , _f being a very high frequency critically depending on the surface sound velocity, while the full asymptotic law, withD=3, holds for > _f .     

Spectral analyses of solar photospheric fluctuations

Residual intensity fluctuation measurements within the wings of the 5183.6 Mgi b₁ line, obtained from two, high-resolution, high-dispersion, Sacramento Peak Observatory spectrograms, have been subtracted from intensity fluctuations in the adjacent continuum in order to isolate fluctuations associated exclusively with line formation. The useable spectral range for studying these lineformation fluctuations is restricted to wavelengths between 1040 and 7170 km because the subtraction increases the relative importance of noise and large-scale photographic variations across the spectrograms could not be completely removed. Power and cross-power (coherence and phase) spectra proved to be valuable diagnostic tools in isolating line-formation fluctuations.Over this spectral range, the line-formation fluctuations are characterized by flat power spectra as compared to those for continuum fluctuations, appreciable fluctuation rms relative to that for continuum fluctuations, and the necessity to multiply the wing fluctuations by a factor 0.95 _min 1.00 to most effectively isolate these fluctuations (Figures 3 and 4). That continuum fluctuations are modified in shape but otherwise not drastically changed in the line wings explains the flat spectrum. The relative rms's vary from 0.34 in the inner wing to 0.22 in the outer. The range of possible values for _min results from uncertainties in the photographic density-residual intensity calibration.     

Coronal magnetic-field model with non-spherical source surface

Previous global models of coronal magnetic fields have used a geometrical construction based on a spherical source surface because of requirements for computational speed. As a result they have had difficulty accounting for (a) the tendency of full magnetohydrodynamic (MHD) models to predict non-radial plasma flow out to r 10r and (b) the appreciable magnitude, 3, of B _r , (the radial component of B) consistently observed at r 1 AU. We present a new modelling technique based on a non-spherical source surface, which is taken to be an isogauss of the underlying potential field generated by currents in or below the photosphere. This modification of the source surface significantly improves the agreement between the geometrical construction and the MHD solution while retaining most of the computational ease provided by a spherical source surface. A detailed comparison between the present source-surface model and the MHD solution is made for the internal dipole case. The resulting B field agrees well in magnitude and direction with the coronal B field derived from the full MHD equations. It shows evidence of the slightly equatorward meridional plasma flow that is characteristic of the MHD solution. Moreover, the B field obtained by using our non-spherical source surface agrees well with that observed by spacecraft in the vicinity of the Earth's orbit. Applied to a solar dipole field with a moment of 1 G-r ³ , the present model predicts that B _r at r 1 AU lies in the range of 1–2 and is remarkably insensitive to heliomagnetic latitude. Our method should be applicable also to more general (i.e., more realistic) configurations of the solar magnetic field. Isogauss surfaces for two representative solar rotations, as calculated from expansions of observed photospheric magnetic-field data, are found to show large and significant deviations from sphericity.     

The parameters of planetary nebulae and their central stars derived from observations

On the basis of data on planetary nebula (PN) central star temperatures obtained by measurements in the ultraviolet (UV) range, the empirical calibration dependence between the number of Lyman photons emitted by a central starS and PN diameterD, is constructed. The temperatures of 118 PN central stars are estimated with this dependence. It is shown that the central star masses are distributed in a wide interval from 0.5 to 1.2M . About 60% of all stars have masses <0.6M , about 25% have masses >0.6M and the remainder have masses 0.6M . The averaged empirical tracks of evolution of low-mass (<0.6M ) and massive (>0.6M ) central stars differing considerably from each other are constructed. It is shown that the majority of central stars may possess hot chromospheres (T>2×10⁵ K) which spread for several tens of radii of the central star. The PN originates as a result of ionization of the matter ejected by a red giant at the superwind stage. The cause for this ionization is the UV radiation of the PN central star.     

The centre-to-limb variation of the moon's brightness at 2 and 6cm wavelength

A map of the Moon at 2 cm wavelength is presented. The angular ( 1arc) and temperature resolution (< 0.1 K) is sufficient to study systematic details of the brightness distribution. In particular, the centre-to-limb variation is considered. An estimate of the dielectric constant is possible (1.4 2.5). The existence of a temperature gradient in the lunar surface layers is used to derive the depth of penetration of electromagnetic waves (L _e ), which isL _e 8 m for 2 cm wavelength. The parameters derived from the 2 cm map are found to be compatible with those obtained from a former observation at 6 cm wavelength.     

Early cosmological models in Lyra's geometry

A spatially homogeneous and isotropic Robertson-Walker model withzero-curvature of the universe is studied within the frame-work of Lyra'smanifold. The gauge-function in Lyra's manifold is taken to betime-dependent. Exact solutions of Einstein equations are obtained for twodifferent early phases of the universe viz. Inflationary phase andradiation-dominated phase by using `gamma-law' equation of statep = ( - 1) . The -index, describing the material content,varies continuously with cosmic time so that in the course of itsevolution, the universe goes through a transition from an inflationaryphase to a radiation-dominated phase. The physical properties of themodels are also discussed.     

Lois exponentielles de distance pour les systèmes de satellites

Résumé Une formulation exponentielle de la loi empirique de Titus-Bode a été proposée par Basano et Hugues. Ces auteurs introduisent l'hypothèse de trois planètes manquantes ou trous. Toutes les planètes obéissent à la relation a _n = ⁿ qui donne les demi-grands axes a des planètes pour des valeurs entières de n.Nous proposons une nouvelle méthode qui permet de retrouver la relation de Basano et Hugues pour le système solaire. Nous appliquons cette méthode aux systèmes de satellites de Jupiter, Saturne et Uranus en introduisant des trous pour combler les lacunes dans les séquences de satellites. Nous en tirons trois relations exponentielles de distance, analogues à la relation de Basano et Hugues. Nous constatons que les coefficients sont semblables pour les systèmes solaire, jovien et uranien alors que le coefficient du système de Saturne vaut approximativement la racine carrée des trois autres .Nous expliquons cet espacement exponentiel grâce à un modèle simple d'une nébuleuse gazeuse initiale soumise à de petites perturbations qui engendrent des oscillations dans la distribution de densité. Les minima de la densité perturbée sont donnés par les zéros des fonctions de Bessel décrivant la propagation de la perturbation. Les positions des maxima correspondent aux sites d'accrétion.Tous les trous introduits dans les parties intérieures des systèmes de satellites sont comblés par les anneaux et petits satellites. Dans le système d'Uranus, il reste deux trous vacants qui pourraient être occupés par des petits satellites non encore découverts.

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Exponential distance laws for satellite systems

A revised Titius-Bode law for the Solar system was proposed by Basano and Hugues, by introducing three missing planets. This law can be written a _n = ⁿ (with = 0.2853 AU and = 1.5226), which gives the distances a _n of the nth planet for successive integers n.We propose a new method to find this Basano-Hugues law for the Solar system. Based upon the comparison of the ratios of successive distances, this method can be applied to the satellite systems of the three giants planets Jupiter, Saturn and Uranus by introducing missing satellites to fill the gaps in satellites sequences. We find three exponential distance relations, similar to that of Basano-Hugues. We note that the coefficients for the Solar, Jovian and Uranian systems are almost equal while the Saturnian system's coefficient is nearly the square root of that of the three others.We explain that exponential spacing by a simple model of an initial gaseous nebula subject to small perturbations generating oscillations in the density distribution. The minima of the perturbed density are given by the zeros of Bessel functions describing the perturbation propagation. The maxima positions correspond to accretion sites.All the empty places in the inside parts of satellite systems are occupied by rings and small satellites. In the Uranian system, there are two empty places which could be filled by new undiscovered small satellites.

     

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.     

The blanketing in the rocket ultraviolet from 225.2 to 319.6 nm

The blanketing effect for the solar disc center and its value near the limb (cos = 0.23) are obtained for the rocket ultraviolet region using the Harvard center and limb spectra. The value of for the disc center appears to be 0.67 (on average) relative to the quasicontinuum. The essential decrease of towards the limb is also revealed.     

Horizontal-branch star models

Evolutionary tracks of 0.9M , 0.7M and 0.6M models for Population II stars have been computed in the post-red giant phase. The stars are initially composed of a helium core containing a mass fraction equal to 0.9 and of a hydrogen-rich envelope. They represent hypothetical remnants of stars after substantial mass loss in previous evolutionary phases or/and at the helium flash.u 0,9M , 0,7M 0,6M . , 90% , . , .Riassunto È stata calcolata per modelli di stelle di 0,9M , 0,7M e 0,6M di Popolazione II l'evoluzione successiva allo stadio di gigante rossa. Inizialmente i modelli constano di un nucleo di elio contenente il 90% della massa totale e di un inviluppo idrogenico. Essi possono interpretarsi come i resti di stelle che abbiano perso una frazione di massa considerevole in fasi evolutive precedenti, o all'innesco violento dell'elio al centro.