Refinement of the geopotential scale factorR 0 on

Altimetric measurements of the GEOSAT satellite were used for the determination of geopotential scale factorR ₀. The geopotential valueW ₀ on the geoid surface was then computed (W ₀ =GM/R ₀).The GEOSAT Geophysical Data Records (GDR's) covering an initial period of the Exact Repeat Mission (ERM) were filtered and processed. The necessary corrections were made in order to allow a precise detection of the sea surface. Gravitational geopotential, rotation and permanent tides were taken into account and the equipotential surface which is the best approximation of the sea surface was found.The determination of the potential valueW ₀ on the mean geoid surface in this way is very promising. An associated value withW ₀ - the geopotential scale factorR ₀ - seems to be a very good Earth dimension defining quantity. Moreover, there are many possible applications ofW ₀ (R ₀) in modern geophysics.The incorporation of one of these parameters - we now recommendR ₀ - into the set of the Primary Geodetic Parameters (PGP) is discussed and suggested.     

Rate of change of vorticity covariance of MHD turbulence in a rotating system

In this paper we are concerned with incompressible MHD turbulence in a rotating system and have derived an equation for the rate of change of vorticity covariance of MHD turbulent flow. The result derived shows that the defining scalars (r,t), (r,t), and (r,t) for the rate of change of vorticity covariance solely depend on the defining scalars of the tensorsW _ij, P_ik,j, F_kj,i, T_ik,j, andR _kj,ialready defined in the text.     

Primary and derived parameters of common relevance of Astronomy,Geodesy, and Geodynamics

Problem of selecting primary parameters has been discussed. Primaries should be defined uniquely, as well as, physically. Since no unique definition for semimajor axis exists, it should be replaced by the geoidal geopotential valueW ₀ or by the geopotential scale factorR ₀ =GM/W ₀, geocentric gravitational constantGM be also primary parameter. Current best estimates of some parameters are given numerically.     

Hydromagnetic stability of some non-dissipative flows subject to non-axisymmetric disturbances

We study the linear stability of nondissipative flow of an electrically conducting fluid subject to non-axisymmetric disturbances in the following cases: (i) the radial flow of an incompressible fluid between two concentric porous circular cylinders in the presence of a radial magnetic field and (ii) axial flow of a compressible fluid between two concentric circular cylinders permeated by a helical magnetic field (0,B ₀(r),B _0z) in a cylindrical coordinate system. It is shown that in case (i), the flow is stable if the Alfvén velocity based on the undisturbed radial magnetic field exceeds the radial velocity due to suction or injection at the cylinder surfaces. In case (ii), it is found that under certain conditions the complex wave speed for an unstable mode lies within a circle of diameterW _max-W _min, whereW _max andW _min are the maximum and minimum values of the axial velocity in the flow region. In the presence of a purely axial magnetic field, however, the complex wave speed for an unstable mode always lies within the above circle.     

The significance of observed rotational magnetic hysteresis in lunar samples

Rotational Magnetic hysteresis (W _R ) curves for lunar soils 10084, 12070, 14259, and rock 14053, have been published. There is no adequate explanation to date for the observed largeW _R at high fields. Lunar rock magnetism researchers consider fine particle iron to be the primary source of stable magnetic remanence in lunar samples. Iron has cubic anisotropy with added shape anisotropy for extreme particle shapes. The observed high fieldW _R must have its source in uniaxial or unidirectional anisotropy. This implies the existence of minerals with uniaxial anisotropy or exchange coupled spin states. Therefore, the source of this observed high fieldW _R must be identified and understood before serious paleointensity studies are made. It is probable that the exchange coupled spin states and/or the source of uniaxial anisotropy responsible for the high fieldW _R might be influenced by the lunar surface diurnal temperature cycling. The possible sources of high fieldW _R in lunar samples are presented and considered.     

Interstellar extinction and diffuse absorption features

The equivalent width of the 2175 Å band,W ₂₁₇₅, well known as the big bump in the interstellar extinction curves, has been found to be closely correlated with the colour excessE _B-V as well as with the extinction differencesE _8–6 andE _9–7 defined to characterize quantitatively the steep slopes of the extinction curves in the far ultraviolet.The equivalent widths of the 5780 and 5797 Å diffuse lines show good correlation withE _B-V. The correlations ofW ₅₇₈₀ andW ₅₇₉₇ withE _8–6 resp.E _9–7 are, however, rather weak. Correlations betweenW ₂₁₇₅ andW ₅₇₈₀ and betweenW ₂₁₇₅ andW ₅₇₉₇ are indicated.The results have been qualitatively interpreted in favour of the dust model consisting of a mixture of small silicate grains and larger silicate grains coated by molecular mantles.Paper presented at the Symposium on Solid State Astrophysics, held at the University College, Cardiff, Wales, between 9–12 July 1974.     

Dimension of the Earth's General Ellipsoid

The problem of specifying the Earth's mean (general)ellipsoid is discussed. This problem has been greatly simplified in the era of satellite altimetry, especially thanks to the adopted geoidal geopotential value, W₀ = (62 636 856.0 ± 0.5) m² s^-2.Consequently, the semimajor axis a of the Earth's mean ellipsoid can be easily derived. However, an a priori condition must be posed first. Two such a priori conditions have been examined, namely an ellipsoid with the corresponding geopotential that fits best W₀ in the least squares sense and an ellipsoid that has the global geopotential average equal to W₀. It has been demonstrated that both a priori conditions yield ellipsoids of the same dimension, with a–values that are practically identical to the value corresponding to the Pizzetti theory of the level ellipsoid: a = (6 378 136.68 ± 0.06) m.     

On the problem of detection of the circumstellar clouds from 2800 MgII observations

A new method for the detection of the circumstellar clouds around the hot stars of O-B classes is developed. The method is based on the fact, connected with the large dispersion in the observed equivalent widths,W _*(2800 MgII) of non-stellar origin, for a selected group of stars withE(B-V)=0. The separation of observed magnitudes ofW(2800) in two components interstellarW _i, and circumstellarW _c is realised. It is shown that the circumstellar clouds really existed around 90% of hot stars analysed in the present paper (total number of stars 46, Table II). In 30% cases of hot stars circumstellar clouds are very powerful (the radii are less than 1pc, the masses less than 1 solar mass). The usual model for interstellar medium seems to be unacceptable for the system hot star+circumstellar cloud.     

Some Peculiarities of Intensity Oscillations in Ca <Emphasis Type="SmallCaps">ii</Emphasis> Lines under Coronal Holes

Observations of the central intensity of the Ca ii K and 849.8 nm lines are used to derive the ratios of the oscillation power in the frequency ranges of the “five-minute” (W ₅) and “three-minute” (W ₃) oscillations. It is shown that at high significance level ratios, (W ₅/W ₃) >1 at coronal hole bases, and W ₅/W ₃ ≈1 in quiet chromospheric areas far from holes.     

The equivalent width of the Hβ emission line and the evolution of the Hii regions

The synthetic equivalent width (W _H) of the line H in emission is obtained for Hii regions opaque to the Lyman photon flux, with embedded OB associations with different initial chemical compositions and initial mass functions. The variation ofW _H as a function of the evolution of the ionizing stars is analysed. The observations ofW _H for M33, M101, and M51 by Searle (1971) are discussed.     

A generalized method for deriving mass-loss rates: The first order moment of unsaturated P Cygni line profiles

For the case of optically thin lines, we show that the relation existing between the first order momentW ₁ (E()/E _c –1)(–₁₂)d of a P Cygni profile and the quantityMn(level), whereM is the mass-loss rate of the central star andn(level) the fractional abundance of the ion under study, is in fact independent of any Sobolev-type approximations used for the transfer of line radiation, contrary to what has been assumed in some previous works (Castoret al., 1981; Surdej, 1982). Consequently, all results established in the context of very rapidly expanding atmospheres and mainly referring to the non-dependence ofW ₁ vs various physical (underlying photospheric absorption line, limb darkening, etc.) and geometrical (velocity fieldv(r), etc.) effects remain unchanged for arbitrary (e.g non-Sobolev type) outward-accelerating velocity laws.Whenever applied with caution, Equation (50) thus provides a very powerful means of deriving mass-loss rates—with a total uncertainty less than 60 percent—from the measurementW ₁ of unsaturated P Cygni profiles observed in the spectrum of early—as well as late—type stars, quasars, etc.     

The interpretation of the Wilson-Bappu effect

The problem of the physical interpretation of the Wilson-Bappu effect is examined. A postulate is forwarded according to which this effect expresses the dependence of the complete kinetic energyE _t of turbulent motions in the medium generating magnesium emission in the doublet 2800 Mgii on the velocityW ₀ of turbulent motion. One of the consequences of the application of this postulate is the appearance of the relationships (8) and (11) which give the magnitude of the kinetic energyE _t of turbulent motions in the first case (Figure 2) and the magnitude of the mass of emitting mediumM ₀ in the second (Figure 3) depending on the turbulent velocityW ₀ (k). This postulate unit in a common conception all variety of the magnesium emission escaped from a single star as well as from binary systems on the one hand and the magnesium emission generated in chromospheres as well as in intercomponent clouds or streams on the other.     

Contribution to the higher levels of neutral helium atoms deviating from Boltzmann distribution

The deviations from Boltzmann distribution have been carried out for higher energy levels of neutral helium atoms. The computations have been done up to the quantum numbern=10, for variety of both electron temperature (T _e) and radiation temperature (T _s). Furthermore, computations for more values of the dilution factor (W) enable applications of results to atmospheres of intermediate heights and to lower parts of stellar atmosphere. Also for the special casesT _e=T _s=10080 K, 20160 K andW=0.3, 0.1, and 1.00, was treated, to afford at least a rough comparison between the new and old results.     

Determination of mass-loss rates from the first order momentW 1 of unsaturated P Cygni line profiles

The escape probability method introduced by Sobolev to treat the transfer of line photons is used in order to derive the expressions of thenth order momentW _n (E()/E _c –1)(–₁₂) ⁿ ·d of a P Cygni profile formed in rapidly expanding envelopes around a central point-like source under various physical and geometrical conditions.With the only assumption that there is mass-conservation of the species in the flow, we state for the case of optically thin lines that the relation between the first order momentW ₁ and the quantityM _n (level), first established by Castoret al. (1981) under more restrictive conditions, is in fact independent of the type of velocity fieldv(r) and a fortiori of the distribution adopted for the radial opacity ₁₂ ^r (X). These results also remain unchanged when including collisions (0) and/or an additional rotational velocity fieldv (r) in the expanding atmosphere. We investigate the presence of an underlying photospheric absorption line and conclude that for realistic cases, neglecting this boundary condition to the radiative transfer leads to an underestimate of the mass-loss rate by a factor of about 20%. By means of a three-level atom model, we demonstrate that all results derived for a single line transition equally apply for an unresolved doublet profile providedW ₁ andM _n (level) are calculated with the weighted wavelength _D and total oscillator strengthf _D of the doublet.Considering the occultation and inclination effects caused by the finite size of the central core, we refine the value of the multiplicative constant fixing the ratio ofW ₁ toM _n (level). We show that this relation allows a determination of the mass-loss rate with an uncertainly less than 30%, irrespective of the sizeL _max of the atmosphere and of the limb-darkening affecting the stellar core. Reviewing all possible sources of error, we finally conclude that this method of deriving a mass-loss rate from the analysis of an unsaturated P Cygni profile is very powerful. The total uncertainty affecting the determination ofM _n (level) from the measurement ofW ₁ should be smaller than 60%.     

Properties of the solar chromosphere Hα spicules as observed spectrally

Time succession of 25 H spicules has been studied. The spectra are obtained at a height of 6 arc sec during 21 min (38 pictures) with the 53 cm Lyot coronagraph. Total intensities W, widths and radial velocities V _r are determined (about 650 H line profiles). For 14 spicules the sign of V _r varies, for the rest the sign variation is absent or it is doubtful. Characterized period of V _r variation is 3–7 min with a mean amplitude of ± 4km s^–1. W and also vary with a similar period and mean amplitudes equal to 50% and 30% respectively. dependence of W (Figure 1) points to the existence of two spicules groups: group I (70%) characterized by relatively small W and (mean values are 0.08 Å and 1.3 Å respectively); group II comprising brighter (W 0.13 Å) spicules with wider profiles ( 1.6 Å). Group II may consist of the unresolved, superimposed group I spicules. We believe, that H spicules involve formations consisting of separate elements having the temperature of 6000 K and non-thermal velocities of 25 km s^–1.     

Intensity and polarization line profiles in a semi-infinite Rayleigh-scattering planetary atmosphere. II. Variations of equivalent width over the disk

The study of the variation of equivalent width in a Rayleighscattering planetary atmosphere along the intensity equator and along the mirror meridian on whichμ =μ ₀ shows that the equivalent widths decrease monotonically towards the poles, the limb and the terminator with the following characteristics: (i) the weakest lines exhibit the maximum change; (ii) theI ^e _r component shows more change than theI ^e _r component; (iii) the decrease towards the limb or the terminator is not as sharp as that towards the poles; (iv)I ^e _r component shows more decrease towards the limb whileI ^e _r component shows more decrease towards the terminator; and (v) the relationW (μ, φ;μ ₀,φ ₀)= W (μ ₀,φ ₀;μ, φ) holds for the total intensity. These results are qualitatively in agreement with the observations of absorption bands in the spectra of Venus, Jupiter and Saturn.     

An exact differential form to check analytical theories

As a result of a Von Zeipel's elimination of periodic arguments, the linear differential form W _i dv _i , where theW _i 's are the constant actions and thev _i 's the mean motions of the averaged angles, is exact, because, as we prove here, it is the differential of the principal function averaged over the new angles. We propose to use this exact form to check the analytical expressions developed from an elimination of periodic arguments, and we take as an example the main problem of artificial satellites.     

Fourier analysis of the light curves of eclipsing variables,XVI

The practical procedures for the solutions of the elements of any eclipsing system in the frequency-domain have been described in a previous paper of this series (Kopal and Demircan, 1978, Paper XIV). The fundamental quantities from which we depart in quest of our solution are twog-functions defining by the momentsA _2m (see Equations (2.13)–(2.16) in Paper XIV, or Equations (3.2)–(3.6) in Paper XV: Demircan, 1978b). If we establish the observational values for these functions, they constitute two independent relations between the unknown parametersa andc _o, and can be numerically solved for them with the aid of the general expressions for the respective moments. However, the determinacy of these parameters depends on not only the accuracy of observations but also the employedg-functions. For better understanding of the geometrical determinacy of the eclipse parametersa andc _o, different combinations of the momentsA _2m have been worked out asg-functions. For the index 2m, the values between 0 and 6 were applied. It has been noted that the behaviour of these functions vary but very little with applied different combinations of the moments. A choice of the most convenient moments to obtain a good determinacy for the eclipse elements were discussed. In this connection, (i) them-dependence of the moments, and the errors in their observational values have been considered, (ii) different practical procedures for the solution of eclipse elements were introduced, and (iii) different type of moments were tested.     

Effect of coriolis force on acceleration covariance in MHD turbulent flow of a dusty incompressible fluid

In the present problem, acceleration covariance in MHD turbulent flow of dusty fluid with Coriolis force have been obtained.The obtained result shows that the defining scalars (r,t), (r, t), (r, t) of the acceleration covariance in the presence of Coriolis force depends on the defining scalars of tensorsQ _ij, H_ij, _i,j,S _ik,jandT _ij,kalready defined in the text.     

Width of emission cores of the line K Ca ii in sunspots

Emission core widths of K Ca ii line in the umbra and penumbra of 9 sunspots and in their vicinity are measured. All sunspots are located near the solar disc center. Data on variation of widths W _K along the mean sunspot radius are obtained. Values W _K in the umbra and penumbra centers are equal or somewhat less than on stars of the same luminosity.