Calculation of the global system of the field-aligned currents on the dayside of the magnetosphere

Using the well-known equation for the normal component of the current which exist near the tangential discontinuity in the plasma in the case of the frozen-in magnetic field, and supposing that the current closes in the ionosphere in the auroral oval in the region 1, one calculates and compares with the data of observations the dependence of the density of the field-aligned current at the level of the ionosphere on the local time.     

On the theory of the oblateness of the Sun

In this paper we first emphasize why it is important to know the successive zonal harmonics of the Sun's figure with high accuracy: mainly fundamental astrometry, helioseismology, planetary motions and relativistic effects. Then we briefly comment why the Sun appears oblate, going back to primitive definitions in order to underline some discrepancies in theories and to emphasize again the relevant hypotheses. We propose a new theoretical approach entirely based on an expansion in terms of Legendre's functions, including the differential rotation of the Sun at the surface. This permits linking the two first spherical harmonic coefficients (J ₂ and J ₄) with the geometric parameters that can be measured on the Sun (equatorial and polar radii). We emphasize the difficulties in inferring gravitational oblateness from visual measurements of the geometric oblateness, and more generally a dynamical flattening. Results are given for different observed rotational laws. It is shown that the surface oblateness is surely upper bounded by 11 milliarcsecond. As a consequence of the observed surface and sub-surface differential rotation laws, we deduce a measure of the two first gravitational harmonics, the quadrupole and the octopole moment of the Sun: J ₂=−(6.13±2.52)×10⁻⁷ if all observed data are taken into account, and respectively, J ₂=−(6.84±3.75)×10⁻⁷ if only sunspot data are considered, and J ₂=−(3.49±1.86)×10⁻⁷ in the case of helioseismic data alone. The value deduced from all available data for the octopole is: J ₄=(2.8±2.1)×10⁻¹². These values are compared to some others found in the literature. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005238718479     

Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation

We calculate the so-called convective term, which shows up in the expression for the angular velocity of the elastic Earth, within the Andoyer formalism. The term emerges due to the fact that the elasticity-caused perturbation depends not only on the instantaneous orientation of the Earth but also on its instantaneous angular velocity. We demonstrate that this term makes a considerable contribution into the overall angular velocity. At the same time the convective term turns out to be automatically included into the correction to the nutation series due to the elasticity, if the series is defined by the perturbation of the figure axis (and not of the rotational axis) in accordance with the current IAU resolution. Hence it is not necessary to take the effect of the convective term into consideration in the perturbation of the elastic Earth as far as the nutation is related to the motion of the figure axis.     

在后牛顿引力理论(PPN形式)中引力常数变化对地球自转产生的效应

介绍和论述了在后牛顿引力理论(PPN形式)中在优越参考系和非优越参考系中经过参数化后引力常数变化对地球自转产生的效应,其中特别重点介绍了年周期变化的效应。此外也将理论结果同观测结果相对比。     

Accounting for the viscosity of the fluid core in the problem of the physical libration of the moon

A two-component theoretical model of the physical libration of the Moon in longitude is constructed with account taken of the viscosity of the core. In the new version, a hydrodynamic problem of motion of a fluid filling a solid rotating shell is solved. It is found that surfaces of equal angular velocity are spherical, and a velocity field of the fluid core of the Moon is described by elementary functions. A distribution of the internal pressure in the core is found. An angular momentum exchange between the fluid core and solid mantle is described by a third-order differential equation with a right-hand side. The roots of a characteristic equation are studied and the stability of rotation is proved. A libration angle as a function of time is found using the derived solution of the differential equation. Limiting cases of infinitely large and infinitely small viscosity are considered and an effect of lag of a libration phase from a phase of action of an external moment of forces is ascertained. This makes it possible to estimate the viscosity and sizes of the lunar fluid core from data of observations.     

On the determination of the north direction of the sun's image

For a perfectly aligned Coudé heliograph the north direction of Sun's image in the image plane of the heliograph changes linearly with the hour angle of the Sun or in a common heliograph it is constant. But if the alignment is not perfect and there are instrumental errors the angle between the north direction of the Sun's image and a direction fixed in the image plane is a complicated function of the hour angle of the Sun. In this paper we derive this dependence.     

Properties of the solar nebula and the origin of the moon

The basic geochemical model of the structure of the Moon proposed by Anderson, in which the Moon is formed by differentiation of the calcium, aluminium, titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this Moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the Moon slightly inside the orbit of Mercury. Some condensed metallic iron is likely to enter the Moon in this position, and since the Moon is assembled at a very high temperature, it is likely to have been fully molten, so that the iron can remove the iridium from the silicate material and carry it down to form a small core. Interactions between the Moon and Mercury lead to the present rather eccentric Mercury orbit and to a much more eccentric orbit for the Moon, reaching past the orbit of the Earth, establishing conditions which are necessary for capture of the Moon by the Earth. In this orbit the Moon, no longer fully molten, will sweep up additional material containing iron oxide. This history accounts in principle for the two major ways in which the bulk composition of the Moon differs from that of the Allende inclusions.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

Modeling the effects of shear on the evolution of the holes in the condensational clouds of Venus

Near-infrared brightness temperature contrasts observed on the night side of Venus indicate variations in the size and distribution of particles in the lower and middle cloud decks. McGouldrick and Toon [McGouldrick, K., Toon, O.B., 2007. Icarus 191, 1-24] have shown that these changes can be explained by large-scale dynamics; in particular, that downdrafts may produce optical depth “holes” in the clouds. The lifetimes of these holes are observed to be moderately short, on the order of ten days. Here, we explore a simple model to better understand this lifetime. We have coupled a microphysical model of the Venus clouds with a simple, two-dimensional (zonal, vertical) kinematical transport model to study the effects of the zonal flow on the lifetime of the holes in the clouds. We find that although wind shear may be negligible within the cloud itself, the shear that is present near the top and the bottom of the statically unstable cloud region can lead to changes in the radiative-dynamical feedback which ultimately lead to the dissipation of the holes.     

On some problems concerning the calculation of the form of the magnetopause and the electric field on the magnetopause in the framework of the continuum medium model

In order to understand the reason of the existence of the electric field in the magnetosphere, and for the theoretical evaluation of its value, it is necessary to find the solution of the problem of determination of the magnetosphere boundary form in the frameworks of the continuum medium model which takes into account part of the magnetospheric plasma movement in supporting the magnetospheric boundary equilibrium. A number of problems for finding the distribution of the pressure, the density, the magnetic field and the electric field on the particular tangential discontinuity is considered in the case when the form of discontinuity is set (the direct problem) and a number of problems for finding the form of the discontinuity and the distribution of the above-mentioned physical quantities on the discontinuity is considered when the law of the change of the external pressure along the boundary is set (for example, with the help of the approximate Newton equation). The problem which is considered here, which deals with the calculation of the boundary form and with the calculation of the distribution of the corresponding physical quantities on the discontinuity of the 1st kind for the compressible fluid with the magnetic field with field lines which are perpendicular to the plane of the flow in question, concerns the last sort of problems. The comparison of the results of the calculation with the data in the equatorial cross-section of the magnetosphere demonstrates that the calculated form of the boundary, the value of the velocity of the return flow and the value of the electric field on the magnetopause, agree satisfactorily with the observational data.     

On the role of the motion of the photospheric footpoints of the magnetic field lines

By means of a simple relation between the velocity v of the fluid particle and the velocity v_f of the photospheric footpoint of the magnetic field line v_z and B_z being respectively the components of v and the magnetic field B normal to the photospheric surface, it is shown formally that through the phtospheric surface the transport of all the quantities attributed to the magnetic field, such as the magnetic flux, the magnetic energy and the helicity, is independent of v_z, and v_f is the only kinematical quantity on which the transport depends. In addition, in the neighborhood of the neutral line the velocity v_l of the moving curve of constant B_z is found to be equal approximately to the component of v or v_f in the direction of v_l. Since v_l can be measured or extimated, so can the components of v and v_f near the neutral line.     

On the validity of the chapman-enskog description of the solar wind

The validity of the Chapman-Enskog method in the calculation of the heat conductivity of the solar wind is studied. The predictions of the Chapman-Enskog theory are compared with known results of rarefied gas kinetic theory. The results suggest that the use of the Chapman-Enskog theory to describe the transport processes in the solar wind is not strictly justified.     

Hypothesis on the origin of the spiral structure of the galaxies

The spiral waves in a model galaxy consisting of differentially rotating and non-rotating subsystems are considered on the basis of participating phenomena. The subsystems involved represent the Populations I and II of normal spirals, respectively. The spiral waves in such a systems are unstable in the Landau sense. Due to this instability they grow up to attain finite amplitude. This growth is stopped by a non-linear effect (the quasilinear effect), the steady state with waves of finite amplitude being established. The hypothesis is proposed that these waves should be identified with the spiral structure of the galaxies.     

Results of observations of the dust distribution in the F-corona of the sun

The results of modeling of the distribution of dust in the circumsolar zone are presented. The dust distribution was retrieved from observations of the line-of-sight velocities in the F-corona to the distances of 7–11 solar radii during the total eclipses of the Sun in different years: on July 31, 1981; August 11, 1991; March 29, 2006; and August 1, 2008. Comparison of the results has shown that the dust composition varies from year to year and the dust is dynamically nonuniform. In addition to the dust related to the zodiacal cloud and concentrating to the ecliptic plane, the dust of retrograde motion and the ejections and accretion in the polar regions are observed. From the results of observations of eclipses on July 31, 1981, August 11, 1991, and August 1, 2008, the east–west asymmetry in a sign of the line-of-sight velocities was detected: they are negative to the east of the Sun and positive to the west. Such distribution of the velocities is indicative of the nearecliptic orbital dust motion, whose direction coincides with that of the motion of the planets. In the course of the eclipse of March 29, 2006, almost no dynamical connection with the zodiacal cloud was found. At the same time, the direction, where the observed velocities are largest in value and opposite in sign on opposite sides of the Sun, was determined, which provides evidence of the orbital motion deviating from the ecliptic plane. The results of observations in 2006 reveal a clear genetic connection of the observed orbital motion of dust with the parent comets of the Kreutz family found near the Sun close to the eclipse date. The velocities observed near the symmetry line in the plane of the sky grow by absolute value with increasing the elongation, which may take place, if the line of sight croßses an empty zone that is free of dust. The modeling of the data of observations near the symmetry plane allowed the parameters of the dust distribution near the sublimation zone to be obtained. In 2006, the “black” cometary dust with a low albedo (A = 0.05) was observed; it showed high values of the power-law exponents in the distance distribution of the dust concentration (V = 2.2 > 1) and in the size distribution of grains (γ = 5.2 > 4.0) and a strong radiation pressure (β = 0.70–0.74). We estimated the mean radius of grains as ≈0.8–0.9 µm and the radius of the dust-free zone as ≈9.1–9.2 solar radii. The latter corresponds to the distances, where the low-melt components of olivines and pyroxenes disintegrate. In 2008, the observed zodiacal dust concentrating to the ecliptic plane demonstrated the canonical parameters: A = 0.1–0.2, V ≈ 1, ß ≈ 0, γ = 4.0, the mean radii of grains were 0.9–1.2 µm, and the radius of the dust-free zone was 7.0–7.6 solar radii.     

On the origin of warps and the role of the intergalactic medium

There is still no consensus as to what causes galactic discs to become warped. Successful models should account for the frequent occurrence of warps in quite isolated galaxies, their amplitude as well as the observed azimuthal and vertical distributions of the H  i layer. Intergalactic accretion flows and intergalactic magnetic fields may bend the outer parts of spiral galaxies. In this paper we consider the viability of these non-gravitational torques to take the gas off the plane. We show that magnetically generated warps are clearly flawed because they would wrap up into a spiral in less than two or three galactic rotations. The inclusion of any magnetic diffusivity to dilute the wrapping effect causes the amplitude of the warp to damp. We also consider the observational consequences of the accretion of an intergalactic plane-parallel flow at infinity. We have computed the amplitude and warp asymmetry in the accretion model, for a disc embedded in a flattened dark matter halo, including self-consistently the contribution of the modes with azimuthal wavenumbers   m = 0  and   m = 1  . Since the m = 0 component, giving a U-shaped profile, is not negligible compared to the m = 1 component, this model predicts quite asymmetric warps, maximum gas displacements on the two sides in the ratio 3 : 2 for the preferred Galactic parameters, and the presence of a fraction ∼3.5 per cent of U-shaped warps, at least. The azimuthal dependence of the moment transfer by the ram pressure would produce a strong asymmetry in the thickness of the H  i layer and asymmetric density distributions in z , in conflict with observational data for the warp in our Galaxy and in external galaxies. The amount of accretion that is required to explain the Galactic warp would give gas scaleheights in the far outer disc that are too small. We conclude that accretion of a flow with no net angular momentum cannot be the main and only cause of warps.     

Kinematics of the outer pseudorings and the spiral structure of the Galaxy

The kinematics of the outer rings and pseudorings is determined by two processes: the resonance tuning and the gas outflow. The resonance kinematics is clearly observed in the pure rings while the kinematics of the outflow is manifested itself in the pseudorings. The direction of systematical motions in the pure rings depends on the position angle of a point with respect to the bar major axis and on the class of the outer ring. The direction of the radial and azimuthal components of the residual velocities of young stars in the Perseus, Carina, and Sagittarius regions can be explained by the presence of the outer pseudoring of class R ₁ R′₂ in the Galaxy. We present models which reproduce the values and directions of the residual velocities of OB-associations in the Perseus and Sagittarius regions and also model reproducing the directions of the residual velocities in the Perseus, Sagittarius, and Carina regions. The kinematics of the Sagittarius region accurately defines the solar position angle with respect to the bar elongation, θ _b = 45° ± 5°.     

The behaviour of the geomagnetic pulsations near the boundary of the plasmasphere

Based on the observational data obtained at eleven stations along a geomagnetic meridian (Φm = 45–63°), the characteristics of pc 3, 4 pulsations are investigated. It has been shown that pc 3, 4 pulsations possess two amplitude maxima: one in the high latitudes and the other in middle latitudes. Consequently, the amplitude minimum between the two maxima is observed in subauroral latitudes (Φm ≈ 60°). Examining the peculiarities of the polarization behaviour of pc 3, 4 pulsations along the meridian array, two different regions, where the pulsations are generated, are noticed. One is situated in the middle latitudes of about 55–60°, and the other in the auroral area of about 65–70° in geomagnetic latitude. The former region corresponds to a projection of an area inside the plasmapause and the latter of an area of the outer radiation belt in the magnetosphere. The dependence of the pc 3, 4 periods on the position of the plasmapause is clarified. It is also shown that both the position of the pc 3 amplitude maximum in the middle latitudes and the position of pc 4 minimum in the subauroral area shift according to the variation in the magnetic activity and the position of plasmapause.The dynamic spectra of the simultaneous wave-packets of Pc-pulsations are investigated along the meridional profile. The maximum time delay of the Pc-signals is found at a latitude of about 57°, corresponding to the region of low values of Alfvén velocity inside the plasmasphere. On the other hand, a sharp decrease in the time delay is observed at a latitude of about 60°, the region of the rapid increase of Alfvén velocity at the plasmaspheric boundary in the magnetosphere.     

Investigation of the kinematics and structure of the Galaxy in the vicinity of the North galactic pole

In the framework of the programme of studying the meridional section of the Galaxy (MEGA) the absolute proper motions of more than 11000 stars with respect to 3000 galaxies and their stellar magnitudes in the B, V Johnson system are determined in two sky regions near the North Galactic Pole (NGP) by means of Tautenburg Schmidt plates. The limiting and completing apparent stellar magnitudes are B = 20.4 and 18.3 mag, the overall and the investigated sky areas are 16.4 and 14.6 square degrees, respectively. Distances have been determined using the stellar magnitudes, colours, proper motions and reduced proper motions. Stellar kinematics, eccentricities of Galactic orbits, spatial distribution and changes of these characteristics with Z-distance from the Galactic plane are obtained up to 15 kpc. Four subsystems distinguished in the NGP direction, respectively with semithicknesses of 0.25, 0.38, 0.67, 1.48 kpc and density ellipsoid axial ratios of 0.09, 0.20, 0.28, 0.49 show mean velocities in the Galactic rotation direction relative to the LSR of 5.6 ± 0.6, − 11.0 ± 0.6, − 62.5 ± 1.2, − 181.6 ± 4.4 km/s, and ages of 0.1, 0.4, 0.9, 1 of the Galaxy age.     

Influence of the east-west component of the interplanetary magnetic field on the intensity of the auroral electrojet

Analysis of interplanetary data has been made to evaluate the influence of the Biny component of the IMF on the magnitude of the AL index, especially with reference to the contribution of B_y in the reconnection process between the IMF and geomagnetic fields in the dayside part of the magnetosphere. The results of the analysis showed that the effect of Biny on AL is predominantly of a different type from that expected by the current theory of reconnection, and the B_y effect of the latter type was found to be much less significant in magnitude than the theory predicts. The discrepancy may be resolved if the region where the reconnection takes place has an elongated shape.     

Perturbations by the oblateness of the Earth and by the planets in the motion of the Moon

Perturbations in the motion of the Moon are computed for the effect by the oblateness of the Earth and for the indirect effect of planets. Based on Delaunay's analytical solution of the main problem, the computations are performed by a method of Fourier series operation. The effect of the oblateness of the Earth is obtained to the second order, partly adopting an analytical evaluation. Both in longitude and latitude are found a few terms whose coefficient differs from the current lunar ephemeris based on Brown's theory by about 0.01. While, concerning the indirect effect of planets, several periodic terms in the current ephemeris seem to have errors reaching 0.05.As for the secular variations of and due to the figure of the Earth and the indirect effect of planets, the newly-computed values agree within 1/cy with Brown's results reduced to the same values of the parameters. Further, the accelerations in the mean longitude, and caused by the secular changes in the eccentricity of the Earth's orbite and in the obliquity of the ecliptic are obtained. The comparison with Brown shows an agreement within 0.3/cy² for the former cause and 0.02/cy² for the latter. An error is found in the argument of the principal term for the perturbations due to the ecliptic motion in the current ephemeris.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.     

Determination of the temperature of the solar corona from the spectrum of the electron-scattering continuum

When the K-corona is formed by the scattering of photospheric radiation from free electrons, the Fraunhofer lines are greatly broadened by the thermal motions of the hot electrons. This paper discusses the possibility of measuring the coronal electron temperature from the residual depressions in the K-coronal spectrum. If the ratio of the intensities at 4100 Å and 3900 Å can be measured to an accuracy of ±1%, the coronal temperature can be inferred to an accuracy of ±0.2 MK. The temperature of a coronal inhomogeneity may also be measured by this method, provided the position angle is known.Now at Fraunhofer Institute, Freiburg, Germany.