On Geovenelli's approximate form of j(τ)

The accuracy of the approximate replacement of the frequency meanj() of the total intensityJ () byJ _c+a{J ₀()–J _c} by Geovenelli, whereJ _c is the total intensity at the continuum,J ₀() is that at the line center anda is independent of depth, is studied. Numerical calculations for strong solar lines show very high values of the residual intensities. A slight change in the approximation is then suggested to get a result quite consistent with observational and existing calculated data.     

A strong limitation on the rapidity of flux-pile-up reconnection

The reconnection rate which can be achieved in the steady-state flux-pile-up regime is severely limited by the gas pressure of the plasma. Using the family of solutions obtained previously by Priest and Forbes, we show that the Alfvén Mach number of the plasma flowing towards the reconnection site cannot exceed _e/(8 ln R _me), where _e and R _me are the plasma and magnetic Reynolds numbers at large distance. This limit corresponds to a very weak flux-pile-up, and it is a factor of _e slower than the maximum Petschek rate. Thus the maximum flux-pile-up reconnection rate in the corona is at least two orders of magnitude smaller than the rate implied by flare observations.     

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.     

Fourier analysis of the light curves of eclipsing variables-XXV: Error analysis in the frequency-domain

The aim of the present paper has been two-fold. In the first part (Sections 1–2), closed algebraic formulae will be set up furnishing the momentsA of the light curves of arbitrary index , and, due to arbitrary type of eclipses, in terms of the coefficientsa of Fourier cosine series obtained by least-squares fit to the given data; and the uncertainty of the momentsA deduced from that of thea 's.In the second part (Sections 3–4) we shall establish the explicit forms of the lincar functions r _1,2, (cosi) and L ₁ for the variation of the respective elements expressible likewise in terms of the Fourier coefficientsa . The probable errors of these elements can then be identified with those of the respective linear functions, and are obtainable from the same matrix of coefficients which furnished the most probable values of the elements.     

A qualitative discussion on the possibility of gravitational instabilities at the origin of explosions in magnetospheres

This paper discusses the possibility of using the Chandrasekhar and Fermi (1953) model of gravitational instabilities in superconductive infinite cylinders subjected to magnetic fields, to explain explosions arising from plasma cumulations in neutral regions at certain magnetospheres, and solar explosions in particular. The cylinder (or sausage) might result from neutral sheet collapse when critical conditions are attained. The cylinder is unstable, from the virial theorem. A transverse perturbation of amplitudea and wavelength (equivalent to the Alfvén wavelength) might break the cylinder up into gravitationally unstable pieces for whicha ²constant. The overall event might eventually be idealized as a string of explosive spots.     

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.     

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.     

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 .     

The motion of a satellite in an axi-symmetric gravitational field

The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C _jk ⁿ (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin²t - i inclination of the orbit - J _n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S _jk ⁿ (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M₊+m) (gravitational constant times the sum of the masses of Earth and satellite) - _n,k coefficients ofR component of disturbing acceleration (funtions off) - _n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X ₀ ^n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node     

On the stability of equilibria of Hamiltonian systems near the main resonances

The equilibrium point O of an autonomous Hamiltonian system of two degrees of freedom is considered for small-oscillation frequencies related as ₂=2₁+. If under the precise resonance (=0) the equilibrium is unstable, the inner diameter () of the domain of stability containing the point O is estimated. It is shown that for the normalized variables ()/b where b is the corresponding resonance coefficient. The estimates () for other main resonances are reported.     

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.     

Singposts of shock waves in the metagalactic medium

Explosions of quasars and young galaxies at large redshifts must cause propagation of blast waves in the metagalactic medium. The shock waves formed can, during the radiative cooling stage, produce dense cold spherical shells around the epicentres of explosions. But, even before that, at the stage of adiabatic expansion, each spherical shock-wave front, if it lies on one line-of-sight with a more distant quasar, can imprint into the quasar spectrum a specific absorption doublet with a distance between the components (in the rest frame) ₀ 3 Å. The L doublet components have a small but the same equivalent widthW ₀ 0.3 Å, the ratioW ₀/₀ weakly depending onW ₀ ifW ₀ is small. We demonstrate here that such absorption L doublets are really present among the L forest in the absorption spectra of distant quasars which are, according to Sargentet al. (1980), of mostly intervening (and not intrinsic) origin. Further accumulation of data on absorption doublets, which can serve as direct indicators of metagalactic shock-waves, may provide valuable information about the physical conditions in the metagalactic gas at large redshifts.     

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.     

Redshift cutoff and evolution of QSOs

In this paper I present a new evolution model of QSOs luminosity. The model is based on edges distribution of apparent magnitude-redshift of QSOs. After the quasars were formed, the luminosities were increasing until they attained their maximum value atz=2+a, where –0.1a0.6, then the luminosities were decreasing. If the QSOs originate from superconducting cosmic string of same initial massM _i 10¹² M , the formation epochs are different, most of the quasars start atz _cutoff5.6. The most luminous QSOs start at later epochz _cutoff5.15. The present sky survey echniques may give us the possibility to see the formation of QSOs at apparent magnitudem _V 22.5 by chance of 0.3%.     

A hypothetical estimated mass of the muon neutrino and the mass of the tau neutrino

Using the see-saw mechanism and estimation of the hypothetical mass of the electron neutrinom _e we find the hypothetical mass of muon neutrinom _µ and hypothetical mass of the tau neutrinom .     

Search for the matter clumps in scalesZ ~ 1

The diagramV - log(1 +z _e ) as function of (, ) is considered for the quasars. HereV is the apparent visual magnitude,z _e is the emission line redshift, and are the equatorial coordinates. Two opposite extreme spots NE and SE are observed on the sky, where the inclination of the straight line fitting the dependenceV - log(1 +z _e ) is maximum and minimum. The coordinates of the centres of these extreme spots are ( _NE, _NE) = (282°, +42°) and ( _SE, _SE) = (70°, -38°) with errors 5°. A hypothesis of the Superattractor (SA) is proposed to explain such an effect. Two independent tests of this hypothesis are realized. First, the dependence or the frequency a of the absorbers in QSO spectra on (, ) is investigated. A region of the larger a is found. The coordinates of its centre are (, ) = (82°, - 10°) with error 5°. Second, the cases ofz _a >z _e are plotted in the Mercatorial projection (, ). The most of the casesz -z _e > 0.02 are concentrated within the circle with radiusR = 34° and centre (, ) = (50°, - 15°). The both anomalous regions overlap the Southern extreme spot around SE. The SA direction is (, ) = (67°, -21°) with errors about 12°. The redshift of SA isz _SA = 1.7 ± 0.3 that corresponds to the distancer _SA = (3100 ± 300)h ^–1 Mpc for the Hubble constantH ₀ = 75h kms^–1 Mpc^–1. The SA mass isM _SA ~ 10¹⁸-10²⁰ M . The orientation of the normal to the quasiperiodical large-scale sheet structure on the sky occurs near SA.     

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.

     

Electron-cyclotron maser emission from the sun and stars: Variations with plasma temperature and density

Very bright and highly circularly polarized radio bursts from the Sun, the planets, flare stars, and close binary stars are attributed to the electron-cyclotron maser instability. The mode and frequency of the dominant radiation from the maser instability is shown to be dependent on the plasma temperature and the ratio _p / _e of the plasma frequency to the electron-cyclotron frequency. For the emission from the Sun _p / _e is probably greater than 0.3 and for 0.3 < _p / _e < 2 the emission can be either in the x-mode at the second harmonic or in the o- and/or z-modes at the fundamental. For higher _p / _e , the emission moves to higher harmonics of _e with the emission being predominately in the z-mode when _p / _e > 3.Proceedings of the Workshop on RadioContinua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

Photometry of the outer solar corona from lunar-based observations

Two-dimensional isophotes of the extreme solar corona (r _max 45 R ) have been derived from integrated vidicon pictures taken from the Moon's surface by the unmanned probes Surveyors 6 and 7. These data were calibrated through use of previously published values for the coronal brightness gradient along the ecliptic. The resulting structure of the outer corona is compared to ground-based observations of the innermost corona 1.125 r/R 2.0 made by the High Altitude Observatory K-coronameter. The possible existence of a streamer seen by Surveyor 7 is analyzed over the region 15 r 22.5 R .     

The influence of satellite flexibility on orbital motion

The orbital perturbations induced by the librational motion and flexural oscillations are studied for satellites having large flexible appendages. Using a Lagrangian procedure, the equations for coupled motion are derived for a satellite having an arbitrary number of appendages in the nominal orbital plane and two flexible members normal to it. The formulation enables one to study the influence of flexibility on both the orbital and attitude motions. The orbital coordinates are expanded as perturbation series in =(l/a ₀)²,l anda ₀ being a characteristic length of the satellite and unperturbed semi-major axis of the orbit, respectively. The first order perturbation equations are solved in terms of elastic deformations and librational angles using the WKBJ method in conjunction with the variation of parameter technique. Existence of secular perturbations is noted for certain librational flexural motions. Three specific examples, Alouette II, Radio Astronomy Explorer and Tethered Orbiting Interferometer, are considered subsequently and their possible secular drifts estimated.List of Symbols A _ij, B_ij coefficients in the eigenfunction expansion ofv _i andw _i respectively, Equation (10) - C _k, D_k constants, Equation (21) - EI _i flexural rigidity of theith appendage - E(u₀) ²(1+e ₀ cosu ₀)² h ₀ ³ - F(u₀) perturbation function, Equation (17b) - F ,F ,F functions of librational angles and flexural displacements, Equation (11i) - F ,F ,F F ,F ,F with change of independent variable fromt tou ₀ - I _xx, I_yy, I_zz principal moments of inertia of the undeformed satellite - [J ⁱ] inertia dyadic of the deformedith appendage - [J _d] inertia dyadic of the deformed satellite - M mass of the satellite - P _R, P_u functions of librational angles and flexural displacements, Equation (15d) and (15e), respectively - R _c magnitude ofR _c - R _c0, R₁ unperturbed value and first order perturbation ofR _c, respectively - R _c ,R ₀ position vectors of the c.m. of the deformed and undeformed satellite, respectively - T kinetic energy of the satellite - U potential energy of the satellite - U _e, U_g elastic and gravitational potential energy, respectively - X, Y, Z orbital co-ordinate axes, located at the c.m. of the deformed satellite - Y ₁(u₀), Y₂(u₀) functions ofu ₀, Equation (18b) and (18c), respectively - a semi-major axis - a ₀ unperturbed value ofa - e eccentricity - e ₀ unperturbed value ofe - h ₀ unperturbed angular momentum per unit mass of the satellite - i inclination of the orbital plane to the ecliptic - i, j, k unit vectors alongx (or ),y (or ) andz (or ) axes, respectively - l characteristic length of the satellite - l _i length of theith appendage - [l ⁱ] matrix of direction cosines ofx _i, v_i andw _i - l ,l ,l direction cosines ofR _c - m ₀, m_i mass of the main body andith appendage, respectively - p _i ² - q _m, Q_m generalized co-ordinate and force, respectively - r ₁ R ₁/R_c0 - r position vector of an element of the body referred toxyz axes - r _u position vector of an element after deformation, referred to axes - r _c x _c i+y _c j+z _c k, position vector of the c.m. of the deformed body referred toxyz axes - s x _i/l_i - t time - u true anomaly - u ₀, u₁ unperturbed value and the first order perturbation ofu, respectively - u elastic displacement vector - u _c u–r _c - velocity of an element relative to axes - v _i, w_i flexural deformations - x, y, z body co-ordinate axes with origin at the c.m. of the undeformed satellite - x _i distance of an element of theith appendage from the root - _j jth eigenfunction (normalized) of a cantilever - angle between the line of nodes and vernal equinox - , , components of nondimensionalized angular velocity of the satellite - , , pitch (spin), yaw and roll, respectively - _i nominal inclination of theith appendage in the orbital plane - - small parameter, (l/a ₀)² - _j jth eigenvalue of a cantilever - gravitational constant - _jk constant, Equation (11j) - , , body co-ordinate axes with origin at the c.m. of the deformed satellite - ( i + j + k), angular velocity of the satellite