Intensity fluctuations in Fraunhofer lines

An expression is derived for the fluctuation (t) in emergent intensity (observed at some wavelength in a Fraunhofer line or the continuum) caused by a perturbation in temperature (z, t) in the Sun's atmosphere. If the contribution function for the observed intensity is single-peaked near z and if (z) and p(z) are not too rapidly varying, then (t) m (z , t)+N p(z , t) where m and N depend on the structure of the atmosphere. We compute M, N, and contribution functions for several values of and in the inner wings of the K line (13933 Caii).Presently on leave of absence from the Institute for Astronomy, Honolulu, Hawaii.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the line intensity ratios E(Hα)/E(D3) and E(Hβ)/E(D3) in prominences

The intensity ratios E(H)/E(D3) and E(H)/E(D3) in prominences depend on the total optical thickness in H of the layer. The emission of the He D3 line appears relatively enhanced in thin layers and in outer parts of the prominences.     

Hydromagnetic Ekman layer on free convection past an infinite porous flat plate

Free convection in a conducting liquid past an infinite porous vertical flat plate in a rotating frame of reference when the Hall current is present is considered. Exact solutions for the velocity and temperature fields have been derived. The effects ofM (Hartmann number),m (Hall parameter), andE (Ekman number) on the velocity field are discussed.Nomenclature C _p specific heat at constant pressure - g acceleration due to gravity - E Ekman number - G Grashof number - H ₀ applied magnetic field - j _x ,j _y ,j _z components of the current densityJ - k thermal conductivity - M Hartmann number - m Hall parameter - P Prandtl number - Q heat flux per unit area - T temperature of the fluid near the plate - T _w temperature of the plate - T temperature of the fluid in the free-stream - u, v, w components of the velocity fieldq - U uniform free-stream velocity - w ₀ suction velocity - x, y, z Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - _e cyclotron frequency - _e electron collision time - _u skin friction in the direction ofu - _v skin friction in the direction ofv - dimensionless temperature - density of the fluid - kinematic viscosity - _e magnetic permeability - electrical conductivity of the fluid - angular velocity     

Mass and orbit estimation of Planet X via a family of comets

The crucial assumption of this paper is, that the observed clustering of aphelion distances of intermediate-period comets in the 70–90 AU range is due to the influence of a tenth planet, called Planet X. We contribute to the search for Planet X a new and extended evaluation of a family of comets assumed to be Planet X's family of comets.By averaging the aphelion distances of comets that belong to a transplutonic family of comets, we get Planet X's semi-major axis a _x = (83.0 ± 5.3) AU. The comets' orbits also yield the upper limit of the planet's orbital eccentricity e _x - 0.019. If this planet played an important part in sending quasi-periodic comet showers to the inner solar system, we can calculate its orbital inclination i _x = 46 .1 ± 3 .6. By distributing all planets' masses into the heliocentric, torus-like zones, in which they were formed, we get the density distribution of the primordial solar nebula. Extrapolating this distribution we find the mass of the planet M _x = (5.1_–2.4 ^+3.6 M _Earth. A few plausible assumptions (e.g. Uranus and Neptune perturbations being caused by Planet X) lead to Planet X's actual location with declination and eccliptic longitude being = 57 ± 17 and = 54 ± 34 , respectively (1989.5 position). In addition, we give Planet X's apparent brightness dependent on its unknown albedo. All those properties and predictions are more or less in agreement with earlier work on Planet X.     

Free-convection effects on MHD flow past a porous plate with step function change in suction velocity

Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) ^1/2–1/2 - M magnetic field parameter - N _u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - ₁ suction velocity att0 - ₂ suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function     

Simultaneous measurements of Ca+ K,Ca+ H,Hα, Hβ, and He D3 emission in prominences

Simultaneously measured line intensities of Ca⁺ K and H, H, H and He D₃ are presented and compared with recent model calculations by Heasley and Milkey (1978). The model calculations are compatible with the observations. There is indication that the observed branching of the relation E(Ca⁺ K and H) E(H) depends on the widths of the Ca⁺-lines.     

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.     

Planetary accretions in jet streams

The problem of planetary accretion in a jet stream is studied using the model developed by Alfvén and Arrhenius. We find that there are basically three types of planetary accretion: namely, fast process _c < _i , slow process _c ~ _i and delayed process _c > _i where _c is the characteristic time of the occurrence of catastrophic accretion and _i the time-scale of mass injection to the planetary system (3×10⁸ yr). These different time scales of accretion are found to be closely related to the primordial thermal profiles and equatorial inclinations of the planets. Finally, Venus' retrograde rotational spin is shown to be a possible result of accretion process in a jet stream.     

Multiple expansion of the tidal potential

The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O Tide raising object - (, , ) Spherical coordinates of the T.R.O. - (J, _E ) Earth spin axis orientation. _E is the longitude of the ascending node of Earth's equator on thexy-plane - (a ,I ,e , , ,M ) Elliptics elements of the T.R.O     

Thermal and electrical conductivities of crystals in neutron stars and degenerate dwarfs

Thermal and electrical conductivities due to electron scattering on phonons are calculated for degenerate cores of white dwarfs and envelopes of neutron stars for wide ranges of density, temperature and ion charge. In the stellar zones, in which T _pi(Z^1/3e²/_F) (_piis the ion plasma frequency and _F the Fermi velocity of electrons), the main contribution into scattering comes from the Umklapp processes. In the zones with lowerT, the Umklapp processes are frozen out, that results in a sharp growth of electrical and thermal conductivities. This, for instance, should make nuclear burning more stable in such zones.     

On symmetrical planetary corotations

Exact corotations are equilibrium points in the phase space of the asteroidal elliptic restricted problem of three bodies averaged over the synodic period, at a mean-motions resonance. If the resonant critical angle is =(p+q) _jup –p–q, exact corotations are double resonant motions defined by the conditionsd/dt=0 andd(– _jup )/dt=0. The first condition is characteristic of the periods resonance(p + q) : p and the second one is a secular resonance equivalent to that usually known as thev ₅-resonance. This paper presents the symmetric solutions =0 (mod ), = _jup (mod ). Corotations have a coherence property which is unique in non-collisional Celestial Mechanics: An elementary calculation shows that, in the neighbourhood of these solutions, the motions cluster aroundp independent longitude values and are, in each cluster, as close together as and are close to the equilibrium values.     

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.

     

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.     

Spectroscopic Study of a Large Sample of Galaxies Discovered in the Second Byurakan Survey Fields

The Second Byurakan Survey (SBS) is a well known combined survey, which uses the presence of UV-excess radiation in the continuum, or the presence of emission-lines in the spectra for the identification of active and star-forming galaxies. This paper reports on a comparative study of 77 galaxies identified with UV-excess, and 34 galaxies identified via emission-line techniques in the fields of the SBS. The spectroscopic parameters used for the comparison are the [OII]3727/H and [OIII]5007/H emission-lines ratios, the equivalent widths of [OII]3727, [OIII]5007 and H emission-lines, and the C _[OII]-C _H index. Spectroscopic parameters as well as new redshifts were determined from the spectra obtained with the 6m telescope of the Special Astrophysical Observatory (Russia). The main results are: 1) Galaxies discovered via UV-excess technique are preferably more active. 2) Galaxies discovered via emission-line technique are preferably high-excitation low-luminosity star-forming galaxies. 3) UV-excess galaxies with faintest UV-excess radiation are likely candidates to be LINER or Sy2 type objects.     

Free convection and mass transfer effects on the hydro-magnetic oscillatory flow past an infinite vertical porous plate

Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberG _c , Schmidt numberS _c and frequency , on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (G _r ,E>0), or heated (G _r ,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M0) is also made whenever necessary.List of symbols B₀ applied magnetic field - |B| amplitude of the skin friction - C concentration inside the boundary layer - C concentration in the free stream - C _w concentration at the porous plate - C _p specific heat at constant pressure - D diffusion coefficient - E Eckert number - g _x acceleration due to gravity - G _c modified Grashof number - G _r Grashof number - M magnetic parameter - N _u Nusselt number - P Prandtl number - |Q| amplitude of the rate of heat transfer - S _c Schmidt number - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid in the free stream - T _r ,T _i fluctuating parts of the temperature profile - u, v velocity components in thex, y directions - u dimensionless velocity in thex direction - u ₀ mean steady velocity - u ₁ unsteady part of the velocity - u _r ,u _i fluctuating parts of the velocity profile - U dimensionless free stream volocity - U ₀ mean free stream velocity - v ₀ suction velocity - x, y co-rodinate system Greek Symbols phase angle of the skin-friction - coefficient of volume expansion - _* coefficient of expansion with concentration - phase angle of the rate of heat transfer - dimensionless co-ordinate normal to the plate - dimensionless temperature - ₀ mean steady temperature - ₁ unsteady part of temperature - k thermal conductivity - v kinematic viscocity - density of fluid in the boundary layer - density of fluid in the free stream - electrical conductivity of the fluid - skin friction - ₀ mean skin friction - frequency - dimensionless frequency     

Quantum theory of the dielectric constant of a magnetized plasma and astrophysical applications

A quantum mechanical treatment of an electron plasma in a constant and homogeneous magnetic field is considered, with the aim of (a) defining the range of validity of the magnetoionic theory (b) studying the deviations from this theory, in applications involving high densities, and intense magnetic field. While treating the magnetic field exactly, a perturbation approach in the photon field is used to derive general expressions for the dielectric tensor . The properties of are explored in the various limits. Numerical estimates on the range of applicability of the magnetoionic theory are given for the case of the one-dimensional electron gas, where only the lowest Landau level is occupied.     

On the A-transform of the exponential integrals

In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE _n which is denoted as _n (). The main result of this analysis enables us to establish a two-term recurrence formula for _n (0) and a three-term recurrence formula for _n (); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy.     

Equation of state of dense nuclear matter and an upper bound on neutron star masses

We have discussed, in general, the important physical parameters, likemaximum mass, radius, and the minimum rotation period of self-bound,causally consistent, and pulsationally stable neutron stars (Q-starmodels) by using a realistic stiff EOS (such that, the speed of sound,v P ^N, or nP=K(E-E _a ) ⁿ, where K 1 and n =1/(1-2N);where P and E represent respectively, the pressure and theenergy-density, and E _a is the value of E at the surface (r = a) of the configuration) within the two constraints imposed by: (i) The minimumrotation period, P _rot, for the pulsar known to date corresponds to1.558 ms, and (ii) The maximum number density anywhere inside thestructure for the models described as Q-stars cannot exceed 1nucleon/fm³. By using the empirical formula given by Koranda,Stergioulas and Friedman (1997) (KSF-formula), and imposing constraint(i), we have obtained an upper bound of M _max 7.76 M radius a 32.5 km, and the central energy-density around 2.17 ×10¹⁴ g cm^-3 (for n =1.01). Constraint (ii) provides the minimumrotation period, P _rot 0.489 ms for the maximum mass M _max 2.4 M, and the central energy-density around 2.20 ×10¹⁵ g cm^-3 (for n =1.01). The speed of sound at the centre ofthese models approaches 99% of the speed of light `c' (in thevacuum) and vanishes at the surface of the configuration together withpressure. If we relax the maximum Kepler frequency imposed by the fastestrotating pulsar known to date (constraint (i)), in view of certainobservational effects and theoretical evidences, and allow the present EOSto produce larger rotation rates than the 1.558 ms pulsar, the maximummass of the non-rotating model drops down to a value 7.2 M .The higher values of masses ( 7 M ) and radii (31-32 km) obtained in this study imply that these models may representthe massive compact objects like Cyg X-1, Cyg XR-1, LMC X-3, and otherswhich are known as black hole candidates (BHCs). This study also suggestthat the strongest contender for black hole at present might be recurrentnova V404 Cyg (mass estimate 8 -12 M ).     

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 .     

Analysis of extreme-ultraviolet spectroheliograms of solar prominences

The optical depth at the head of the Lyman continuum, _H, is determined at a number of positions in three hedgerow prominences using spectroheliograms (5 × 5 resolution) of C III 977, LC 896, and O IV 554 observed with the Harvard experiment on Skylab. At heights greater than 10 above the limb the maximum value of _H is 30 to 50, which occurs at the central part of the prominences. For one of the prominences the determination of _H is found to be consistent with data from spectroheliograms of Mg X 625. The degree of ionization of hydrogen is estimated from the intensity of LC 896 at _H 1. In the central part of a model prominence N _P/N _HI1.9 for a reasonable range of the electron densities, where N _P and N _HI are the proton density and the neutral hydrogen density, respectively.